Development of an Autonomous Test Driver and Strategies for Vehicle Dynamics Testing and Lateral Motion Control. Dissertation

Transcription

1 Development of an Autonomous Test Driver and Strategies for Vehicle Dynamics Testing and Lateral Motion Control Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of the Ohio State University By Anmol Sidhu, M.S. Mechanical Engineering Graduate Program The Ohio State University 21 Dissertation Committee: Professor Dennis Guenther, Advisor Dr. Gary Heydinger Professor Giorgio Rizzoni Assistant Professor Junmin Wang

2 Copyright By Anmol Singh Sidhu 21

3 ABSTRACT As safety continues to take an increasingly important place in the automobile industry, there has been significant research and development in the area of closed loop control of vehicle dynamics. It first started with antilock brake systems (ABS) that prevented loss of steering control due to wheels locking up with hard braking or low friction. Vehicle dynamics control further developed to include traction control: a system that optimally distributes tractive forces and prevents excessive wheel slip. The most recent developments have been in the area of electronic stability control (ESC). As vehicle technology has evolved over the years and ABS and ESC are now becoming standard on most vehicles, not only automobile manufacturers but even governments and regulation bodies have programs dedicated to ensure standards and understand limitations of these systems. As a result, efforts have been made to develop testing systems and test maneuvers to quantify dynamic properties. This research focuses on studying standard maneuvers and developing new strategies to evaluate and rate the performance of modern vehicles equipped with advanced vehicle dynamic control systems. Another significant development of the last decade is autonomous (or unmanned) vehicles. An important application of autonomous vehicles is automated test drivers, which are systems that replace human drivers in vehicle dynamic testing. This increases the reliability and repeatability of test maneuvers, which is imperative for dependable results in some specialized maneuvers. Most vehicle dynamic tests involve precise actuation of steering wheel or brake/throttle pedals. Steering controllers and braking ii

4 robots are designed to do just that. One such system designed by SEA, Ltd and used extensively by OSU researchers, has been demonstrated to perform various standard tests accurately for a wide range of vehicles and is also used by various organizations worldwide. In this research the areas of vehicle dynamics control and autonomous vehicles come together; the automated test driver is developed to execute path-following maneuvers to evaluate the performance of vehicle dynamics controllers, including those used in ESC, in evasive driving situations. During evasive maneuvers the tire forces are no longer a linear function of slip angles and the vehicle response is nonlinear and potentially unstable, a condition which the active stability systems are designed to mitigate. The definition of understeer gradient in the linear-range does not lend itself to analysis of nonlinear-range dynamics. Another focus of this research is to assess stability and controllability based on estimation of tire forces. A vehicle observer is designed for the purpose of detecting and measuring understeer and oversteer in dynamic maneuvers. The method can be used to benchmark a vehicle regardless of passive or active control. As an extension of the autonomous steering control problem, this project involves the study of application of active steering for vehicle stability control. Control algorithms are developed that use the information from tire force estimator and driver intent models to yield linearized and predictable vehicle lateral response by an active steering system. This research brings together the development of an automated test driver, active vehicle motion control systems and testing for dynamic stability by using tire force estimation. iii

5 To my parents. iv

6 ACKNOWLEDGEMENTS Professor Guenther, I cannot thank you enough for the opportunity to allow me to pursue a Ph.D. with you despite the fact that I went away after getting my Masters at Ohio State. I was mistaken to think there could be a better place to continue graduate studies. You believed in me and accepted me again. For that, I will always be grateful. Thank you for your guidance in matters of academics and life. Dr. Gary Heydinger, you provided a wonderful environment to work at SEA. You were always there to provide direction whenever I felt stuck. Thank you for much needed motivation and academic guidance without which I would not have been able to achieve this degree. Ron Bixel, you are the most fun manager. Your versatile knowledge on vehicles, driving, programming, building and testing was a great resource. You were always available to share long and frustrating hours of debugging and troubleshooting. You made work exciting and fun. Thanks for being a great friend. Special thanks to Hank, the technician at SEA who provided his expert support in the laboratory. My buddies, David Mikesell and Dilip Karpoor, thanks for your friendship and support whenever I needed you. v

7 To Holly Ruppel: you did everything possible to make the last few months of my PhD very comfortable. Thanks for being there. Mama, Daddy, Puneet Didi and Jaisal, you have sacrificed so much just so I could get an education. I have been extremely lucky to have you as my family. You have supported me in every possible way to pursue my dreams. I know you have been praying for me and waiting patiently for me to finish. It would not have been possible without your wishes. Thank you very much. vi

8 VITA September to present... Born Chandigarh, India B. Tech. Mechanical Engineering I.I.T. Roorkee, India M.S. Mechanical Engineering The Ohio State University Graduate Research Associate, Mechanical Engineering, The Ohio State University PUBLICATIONS 1. Sidhu, A., Mikesell, D.R., Guenther, D.A., Bixel, R., and Heydinger, G., Development and Implementation of a Path-Following Algorithm for an Autonomous Vehicle, SAE Paper , Mikesell, D.R., Sidhu, A., Guenther, D.A., Heydinger, G.J. and Bixel R., Automated Steering Comtroller for Vehicle Testing, SAE Paper , Sidhu, A.S., Guenther, D.A., Bixel, R.A., and Heydinger, G.J., Vehicle To Vehicle Interaction Maneuvers Choreographed With An Automated Test Driver, SAE Paper , Coovert, D., Heydinger, G.J., Bixel, R.A., Andreatta, D., Guenther, D.A., Sidhu, A.S. and Mikesell, D.R., Design and Operation of a Brake and Throttle Robot, SAE Paper , 29. FIELDS OF STUDY Major Field: Mechanical Engineering vii

9 TABLE OF CONTENTS ABSTRACT... II ACKNOWLEDGEMENTS... V VITA... VII TABLE OF CONTENTS... VIII LIST OF FIGURES... XIV LIST OF TABLES... XIX CHAPTER INTRODUCTION Introduction and Motivation Purpose and Scope Thesis Outline... 3 CHAPTER viii

10 VEHICLE DYNAMICS TESTING Introduction Vehicle Roll Stability Vehicle Yaw Stability Vehicle Dynamics Control Systems Path Following Maneuvers First Generation Automated Test Driver System Architecture Lateral Control: Path Following Algorithm Longitudinal Control: Speed Trajectory Following Test Results CHAPTER APPLICATIONS OF OBSERVERS AND ESTIMATORS States and Estimation Methods Sideslip Roll Angle and Road Bank Angle Tire Forces Kalman Filter Introduction to Kalman Filter Extended Kalman Filter Kalman Filter Validation Dynamic Testing Metrics ix

11 3.3 Vehicle Observer: Dynamic Instability Detection Introduction Sliding Mode Observer Dynamic State Detection Test Maneuvers Sine wave with increasing amplitude Slowly increasing steer Path Following Maneuvers Proposed Transient Nonlinear Understeer Factor Transient Understeer/Oversteer Metric Validation Transient Understeer/Oversteer Metric Variation ESC Testing Conclusion CHAPTER ACTIVE STEERING Introduction to Steer-by-Wire Linearized Lateral Response: State Feedback Lie Derivatives Tire parameter estimation Dugoff Tire Model Tire Force-Slip Curve Fitting: CarSim Simulation Results x

12 4.4 Upper Level Lateral Controller Sliding Mode Simulation Results: High Friction Simulation Results: Low Friction Discussion of Results CarSim Simulations: Sliding Mode Active Steering CarSim Active Steering: Low g CarSim Active Steering: High g CarSim Active Steering: Slowly Increasing Steer Discussion of Results Optimized Tire Force Distribution for Vehicle Stability Control Discussion of Results CHAPTER ATD PATH FOLLOWING Introduction and Role of the Automated Test Driver Single Track Vehicle Model State Space Vehicle Model in Terms of Following Errors State Feedback Path Following in a Virtual Potential Field Closed Loop Stability Calibration of the Potential Function Gain: Lyapunov Function Highly Dynamic Path Following: Yaw Acceleration Control xi

13 5.4 CarSim Simulations: Yaw Acceleration Control Introduction Single Lane Change: Low g Single Lane Change: High g CU Short Course: Severe Double Lane Change: Low g CU Short Course: Severe Double Lane Change: High g Results Discussion CHAPTER LONGITUDINAL CONTROL: BTR Introduction Background Design and Development Installation Controls Testing and Results Summary and Conclusions CHAPTER OTHER PRACTICAL APPLICATIONS Vehicle-To-Vehicle Interaction xii

14 7.1.1 ATD as a Relative Path Tracker System Outline Overtaking Maneuver Experimental Results Choreographed Collision Test Experimental Collision Results Conclusion CHAPTER CONCLUSION AND FUTURE WORK Research Conclusion Future Direction LIST OF REFERENCES BIBLIOGRAPHY xiii

15 LIST OF FIGURES Figure 1: J Turn Maneuver...7 Figure 2 NHTSA Fishhook Maneuver...8 Figure 3 NHTSA's Sine Maneuvers...8 Figure 4 Ford of Europe's Robot Roll Stability Test (RRST)... 1 Figure 5 ESC (Electronic Stability Control) Intervention Figure 6 ISO Lane Change and Consumer Union Short Course Figure 7 Hardware System Schematic Figure 8 ATD Block Diagram... 2 Figure 9 Goal Point Calculation Figure 1 Sample Static Process Characteristic (SPC) for Brake and Throttle Actuator (BTA) Figure 11 Constant Radius Circle Results: Toyota Camry Figure 12 Figure 8 Path Following Results: Toyota Camry Figure 13 Kalman Filter: Basic Pricipal Figure 14 Kalman Filter Validation: Steer Angle Profile Figure 15 Kalman Filter Validation Figure 16 Force Prediction Results: Sine With Dwell Maneuver Figure 17 Force Prediction Results: Sine With Dwell Maneuver Large Dwell Figure 18: Linear and Nonlinear System Outputs - Sliding Mode Observer Figure 19: Unexpected Signals - Sinusoidal Maneuver xiv

16 Figure 2 Energy Metrics vs. Understeer Gradient Figure 21 Unexpected Inertial Metrics vs. Understeer Gradient Figure 22 Varying Sine-with-dwell Response with Same Understeer Gradient... 6 Figure 23 Varying Instability Metrics Sine with dwell Figure 24 Varying Response Increasing Amplitude Sinusoid Figure 25 Instability Metrics Increasing Amplitude Sinusoid Figure 26 Lateral Response Slowly Increasing Steer Figure 27 Instability Metrics Slowly Increasing Steer Figure 28 Path Following Maneuvers for Stability Testing Figure 29 Single Lane Change: Instability Metrics Figure 3 Quarter Circle Turn: Instability Metrics... 7 Figure 31 Nonlinear Complement Force and Moment Arm Figure 32 A Signature Signal of Transient Understeer Test Figure 33 Transient Understeer/Oversteer vs. Target C.G. Loaction Figure 34 Transient Understeer/Oversteer vs. Moment of Inertia Figure 35 Transient Understeer/Oversteer Variation for Same Linear Understeer Gradient Figure 36 Transient Understeer/Oversteer vs. Vehicle Mass Figure 37 Comparison of "Sine with Dwell" with ESC On and Off Figure 38 Vehicle Observer in Active Steering Mode Figure 39 Tire Axis System and Forces Figure 4 Magic Formula Lateral Force Fit Society of Automotive Engineers, Inc xv

17 Figure 41 Magic Formula Aligning Moment Fit Society of Automotive Engineers, Inc Figure 42 Magic Formula Longitudinal Force Fit Society of Automotive Engineers, Inc Figure 43 Linear Fit in Linear Range Figure 44 Linear Fit in Nonlinear Range Figure 45 Dugoff Tire Model Curve Fitting Figure 46 Stabilization by Yaw Acceleration Control Block diagram Figure 47 Active Steering Control Linear Range Run Figure 48 Active Steering Control Nonlinear Range Run Figure 49 Active Steering Control Stabilization Figure 5 Active Steering Control Low Friction, Linear Range Figure 51 Active Steering Control Low Friction, Nonlinear Range Figure 52 Active Steering Control Low Friction, Stabilization Figure 53 CarSim Active Steering Control, Sine with Dwell, Low g Figure 54 CarSim Active Steering Control, Sine with Dwell, High g Figure 55 CarSim Active Steering Control, Slowly Increasing Steer Figure 56 Active Steering Control Low Friction, Stabilization Figure 57 Active Steering Control High Friction, Stabilization Figure 58 Single Track Linear Model (Bicycle Model) Figure 59 Path-following Error Coordinates Figure 6 State Feedback Simulation Results: Path Following Performance Figure 61 Path Following Block Diagram [65] xvi

18 Figure 62 Phase Margin with respect to Speed And Lookahead Distance Figure 63 Root Locus with respect to Lookahead Distance Figure 64 Root Locus with respect to Feedback gain Figure 65 Virtual Potential Field Figure 66 Effect of Control Force Application Point Figure 67 Effect of Lookahead on Closed Loop Eigen Values Figure 68 Nonlinear Relationship Between Lookahead Distance and Speed Figure 69 Path Following Geometry Figure 7 Path Following by Yaw Acceleration Control Block diagram Figure 71 Quarter Circle Path: low g Figure 72 Quarter Circle Path-following: Lateral Acceleration =.2 g's Figure 73 Quarter Circle Path: high g Figure 74 Quarter Circle Path-following: Lateral Acceleration =.5 g's Figure 75 CarSim Path-Following Block Diagram Figure 76 CarSim Simulation of Single Lane Change: Low g Figure 77 CarSim Simulation of Single Lane Change: High g Figure 78 CarSim Simulation of Double Lane Change: Low g Figure 79 CarSim Simulation of Double Lane Change: High g Figure 8 BTR Mounted in Vehicle Figure 81 The BTR With The Cover Removed Showing The Internal Mechanism Figure 82 Close-up View of BTR Mounted in Vehicle Figure 83 ATD Brake-Throttle Robot Tab Figure 84 Brake Position Control xvii

19 Figure 85 Vehicle Speed Control Figure 86 Constant Deceleration (-.32 g) from 5 kph Figure 87 Constant Deceleration (-.32 g) from 35 kph Figure 88 Following a Recorded Path with Speed and Steering Control Figure 89 Vehicle - to - Vehicle Interaction Maneuvers for Testing Automotive Sensors (Credit: General Dynamics) Figure 9 Relative Path Tracking Block Diagram Figure 91 A Typical Path Tracking Scenario Figure 92 Relative Path Tracking With Target Vehicle At Rest Figure 93 Relative Path Tracking With Target Vehicle Moving Figure 94 Collision Scenario Figure 95 Collision Test With Target Vehicle Speed = 2 mph Figure 96 Collision Test With Target Collision Speed = 3 mph Figure 97 Collision Test With Target Vehicle Headed Not Perpendicular xviii

20 LIST OF TABLES Table 1 of Vehicle Parameter Sets With Varying Understeer Gradient Table 2 Varying Vehicle Parameters for Constant Understeer Gradient Table 3 Varying Vehicle Parameters for Constant Understeer Gradient xix

21 CHAPTER 1 INTRODUCTION 1.1 Introduction and Motivation Autonomous vehicles are a major technological advancement in automobile technology. Numerous research programs have been undertaken by various governments, research organizations and institutes towards development of unmanned ground vehicles. These include Automated highway research where autonomy is applied to passenger cars to drive on paved roads and unmanned off road driving such as the DARPA grand challenge. Another very important application of autonomy in vehicles is automated test drivers which are systems that replace human drivers in vehicle dynamic testing. This increases the reliability and repeatability of test maneuvers which is imperative for dependable results. As safety takes an important place in vehicle design, testing for dynamic response has gained significant attention. Most vehicle dynamic tests involve precise actuation of steering wheel or brake/throttle pedals. Steering controllers and braking robots are designed to do just that. One such system designed by SEA, Ltd and used extensively by OSU researchers, has been demonstrated to perform various standard tests accurately for a range of vehicles and is also used by various organizations worldwide. This research is focused on development of the Automated Test Driver (ATD) (steering control and brake-throttle robot (BTR)) as well as extending the applicability of the ATD for dynamic path following maneuvers and variable speed tests. 1

22 1.2 Purpose and Scope Vehicle technology has evolved over the years and ABS and ESC are now becoming standard on most vehicles. Furthermore, not only automobile manufacturers but even governments and regulation bodies have programs dedicated to ensure standards and understand limitations of these systems. As a result, efforts have been made to develop test maneuvers to quantify dynamic properties. This research focuses on studying standard maneuvers and developing new strategies to evaluate and rate the performance of modern vehicles equipped with advanced vehicle dynamic control systems. The goal of this project is to develop testing methodologies to test vehicle dynamics using an automated test driver. A test signal will be designed to evaluate vehicle stability and effectiveness of vehicle dynamic controllers of modern vehicles. Where understeer gradient provides useful information about vehicle directional stability in the linear range, it does not provide a complete picture because it ignores the nonlinear range. During evasive maneuvers the tire forces are no longer a linear function of slip angles and the vehicle response is nonlinear and potentially unstable, a condition which the active stability systems are designed to mitigate. New parameters are proposed in this study defined to measure a vehicle s dynamic understeer-oversteer state. Another focus of this research is to assess stability and controllability based on estimation of tire forces. A vehicle observer is designed to detect and measure understeer and oversteer in dynamic maneuvers. This method can be used to benchmark a vehicle regardless of passive or active control: evaluation of performance will be based on the lateral forces developed at the tires and not only on traditional measurable states of the vehicle. Vehicle handling characteristics will be related to the knowledge of forces between the tires and 2

23 road that govern vehicle motion. Methodology will be developed to evaluate effectiveness of ESC by comparing the forces in a test run to the baseline. 1.3 Thesis Outline This document is organized to provide an insight into this research project in the following order. Chapter 1 introduces the project by explaining the need for vehicle dynamic testing and the aspects of dynamic testing that are the focus of this project. Then the motivation to conduct this research is brought in. This project proposes to use an automated test driver to replace human drivers in vehicle dynamics testing. The project consists of three broad aspects; Design of the automated test driver (ATD) Test strategies and application of the ATD Design of dynamic stability control Chapter 2 deals with the current state of dynamic testing. Existing test maneuvers are explained including how they are performed and interpreted. Key areas of application of the ATD are pointed out that form the basis for this research. Current design and test abilities of the ATD are explained in the remaining part of chapter 2. Key components of the automated test driver are described in this section. Control algorithms are explained and test results are briefly discussed. Chapter 3 lists various signals relevant to analysis and control of lateral vehicle dynamics and estimation and measurements methods for those signals. The importance of 3

24 estimation of tire forces is discussed in dynamic analysis in the nonlinear range approaching limits of adhesion. Kalman filter implementation is discussed to estimate tire forces and parameter identification. Development of test strategy involving path following and open-loop maneuvers is discussed that is useful to compare dynamic behavior of a vehicle in the nonlinear range with or without active control to the baseline linear range behavior. A new metric to quantify transient nonlinear understeer/oversteer is proposed based on an observer to estimate nonlinear complement of lateral forces and yaw moment. Chapter 4 discusses design of active steering controller based on knowledge of lateral tire forces. Parameters identified from curve fitting of lateral tire forces and slip angles allow for inverting the tire model to determine the steering angle for desired tire force. Sliding mode control and state feedback concepts are used to linearize vehicle response beyond the linear range and stabilize the vehicle in extreme maneuvering situations. Chapter 5 covers the research methods dealing with the design of path-following steering controller. The problem is formulated in state feedback terms. Sensitivity to parameters and adaptability studies are proposed to enable the ATD to be useful for different kinds of vehicles. The Lyapunov method is used to establish conditions for stability and for bounding the path-following performance as a function of various vehicle parameters. Knowledge of lateral tire forces and friction parameters is used to determine the operating point on the tire-force/slip angle curve. The path-following problem is formulated as yaw acceleration control and methods used for active steering are used for steering to negotiate dynamic paths with high lateral acceleration and steering reversals. 4

25 Chapter 6 discusses the design elements of the brake and throttle robot, control methods used and test results. Chapter 7 briefly outlines the possible practical application of the ATD like multi vehicle testing and other driver assistance systems. Testing of systems such as adaptive cruise control, collision warning and lane departure warning requires vehicle-to-vehicle interaction. The ATD will be configured to perform such maneuvers accurately and repeatably. Chapter 8 summarizes the accomplishments, results and conclusions of this research. Future directions to advance this work are proposed. 5

26 CHAPTER 2 VEHICLE DYNAMICS TESTING 2.1 Introduction In response to statistics of severe vehicle crashes, a new focus on vehicle dynamic testing has emerged in the past few years. Auto manufacturers, government agencies and consumer groups, have programs dedicated to developing maneuvers to evaluate vehicle stability and safety merits. NHTSA covers the areas of crash avoidance, crash worthiness, and biomechanics. The category of crash avoidance involves testing for roll-over, spin outs, braking performance, etc. Numerous test procedures exist, which yield useful information about vehicle stability. Some involve steering inputs and will be referred to as Open loop. There are also tests that require brake-throttle actuation to study longitudinal dynamics. Another category of maneuvers is the one involving pathfollowing. An ATD can perform not only open-loop tests but can drive a vehicle on a desired path at desired speed. Such maneuvers are referred to as closed-loop (with respect to position and speed) and are the focus of this research Vehicle Roll Stability Hundreds of thousands of results show up on the Internet from the search phrase, Vehicle rollover. Rollover accidents are the most discussed in vehicle crash reports. Without getting into much detail, one statistic is worth mentioning; roughly one-third of traffic fatalities in the US involve single-vehicle rollovers. Rollover propensity of 6

27 vehicles is typically rated based on various open loop tests namely; J-Turn and NHTSA Fishhook (Roll rate feedback fishhook maneuver) [1]. Severity and frequency of vehicle Two-Wheel-Lift (TWL) is examined under these maneuvers. These, as well as various ISO maneuvers, Consumer Union s double lane change and a host of auto manufacturers specific maneuvers fall into the category of dynamic testing. The static type of rollover metrics based on measurements of static stability factor, tilt table angle and critical sliding velocity fall into the category of static testing. The latter in general do not incorporate the effects of transient tire behavior, effects of suspension motions and compliances, effects of stability controllers and so forth. Other rollover metrics have been investigated to form the basis of rollover warning and anti-rollover warning algorithms. Chen et. al. [2, 3] proposed a Time-To-Rollover (TTR) metric to predict an impending rollover. Susceptibility of SUVs to rollovers is difficult to be concluded from one or a handful of dynamic maneuvers. Although the dynamic test procedures have been generally determined to be too complex they add significant benefit beyond simpler approaches such as SSF. Figure 1 and Figure 2 show two representative open loop maneuvers used to evaluate vehicle rollover propensity. Figure 1: J Turn Maneuver 7

28 Figure 2 NHTSA Fishhook Maneuver Figure 3 NHTSA's Sine Maneuvers 8

29 2.1.2 Vehicle Yaw Stability Spinning out and plowing out are two modes of instability in the yaw plane of motion as well. A vehicle entering a curve at a speed too high for the curve can have the rear end slide out (called spinning out or oversteering ). If the vehicle enters a curve at the limit of traction, and the front of the car begins to slide out, this is known as plowing out or understeering. Sine with dwell maneuver is commonly used to excite spin out for testing of ESC. Two variants of the sine maneuvers are shown in Figure 3. Measures of the vehicle's yaw response after the steering input returns to zero are typically used to evaluate the vehicle's degree of yaw stability. Although all the above-mentioned tests provide useful information to predict vehicle response in extreme situations, they are certainly not perfect. Stability has been shown to be heavily dependent on longitudinal location of the center of gravity by Travis et. al. [4] whereas Static Stability Factor (SSF) accounts only for center of gravity height. Some of the tests prescribe a typical evasive steering maneuver to determine the worst case for rollover or spin out. Many researchers have noted that these maneuvers are not being representative of the worst case for many reasons. Most maneuvers involve steering only with dwells and reversals. The numbers of steering reversals, relative magnitude of different ramps and dwell times at each steering level are too many parameters to predict a worst case for every vehicle. Furthermore, they ignore the dynamics associated with the abrupt changes in velocity that comes before crashes [5]. Heydinger, in an unpublished testing report shows the use of a stability test procedure (The Robot Roll Stability Test (RRST) developed by Ford of Europe) that uses an additional steering ramp to the NHTSA fishhook. The results show that during the RRST 9

30 maneuver wheel lift occurred using steering inputs that were much less aggressive than during a J-turn maneuver. Figure 4 shows the steering wheel motion for the RRST Maneuver. The RRST maneuver involves varying the amplitude as well as the dwell time until the worst case is found for each vehicle. Figure 4 Ford of Europe's Robot Roll Stability Test (RRST) Roll angle may be an important indicator of impending rollover but it is not the only indicator and does not give sufficient advanced warning [6, 7]. In the real world though, the vehicle is subjected a combination of inputs especially in panic situations. This occurs even though the driver s intent is usually to follow a path. ESC algorithms compare vehicle state to driver s intended motion. This is why it is important to consider path following maneuvers along with braking/throttle inputs to evaluate vehicles. NHTSA 27 rollover research (Forkenbrock 22) disqualifies driver in the loop (pathfollowing/closed-loop) maneuvers because they fail in repeatability or discriminatory capability. Just like steering machines that are considered reliable for open-loop tests, the 1

31 ATD is a very good tool for repeatable path following and precise longitudinal control. Tests where every vehicle is accurately driven on the same path with the same intended longitudinal motion every time will improve the ability of regulation agencies and manufacturers to evaluate vehicles. Presence of sophisticated active control systems on modern vehicles brings another layer of complexity to the dynamic testing process. The tests should not only be focused on testing the limit performance of vehicles but also on the transparency of the controllers. It is argued that for an active stability control system, the actuation effort should be progressive and not intrusive because the latter can lead to a panic situation [8]. In other words, a test maneuver should not only report a pass/fail result but also report how jerky/smooth the control action was or how well within limits the body slip angle was and so forth. The main emphasis of the development of the ATD and this research is that pathfollowing maneuvers are considered to be more representative of real world driving. People drive vehicles with the intent of staying in lanes. Although emergency situations induce severe handwheel maneuvering, the intent still remains to follow a path. The Alliance of Automobile Manufacturers (December 24) provides the results of lane avoidance maneuvers - regarded as "a typical accident avoidance scenario and yaw stability assessment tool". However, the early test results do not appear to be very conclusive. The driver in the loop adds complexity to the already complex vehicle system that is the vehicle. In addition to that is the electronic stability control system that imposes forces on the vehicle independent of the driver. Determining the performance metrics of this driver-vehicle system is the key focus of this research. Researchers have 11

32 devised methods to do that but this research proposes a new method of evaluation. A strategy will be developed to determine the baseline performance characteristics of a vehicle and measure deviation from the baseline in a dynamic maneuver. It will be useful to compare different vehicles, design configurations or performance with or without ESC. Introduction to ESC algorithms or stability problems of vehicle dynamics often refer to understeer-oversteer with respect to deviation from desired path. The actual path can be determined from onboard sensor measurements but the desired path is based on a predetermined model of vehicle dynamics. This model outputs in real time, the desired dynamics based on driving conditions and user input. This model can be a simple linear bicycle model or highly non-linear model with many degrees of freedom. Many of the algorithms trigger ESC intervention based on threshold values of yaw rate and/or sideslip. This research is not about developing such ESC algorithms or testing the algorithms in isolation; instead, the focus is to develop methods to test the overall driver-vehicle system close to the performance limits of the test vehicle. First, a test method to establish the performance limit must be developed, and then it will be possible to determine how close the system gets to this limit in a maneuver. Such a method will provide a continuous scale on which a vehicle could be measured as opposed to pass/fail criteria. 12

33 2.2 Vehicle Dynamics Control Systems Recent trends in the automotive industry are such that there is an increased use of on-board computers controlling various functions, performance, efficiency and overall system robustness. There has been emphasis on stability and particular interest in active safety. Electronic Stability Control ( ESC ), which has been available for a few years, is a safety feature that could prevent catastrophic injuries and save lives. Some claim that ESC is as important as seatbelts in terms of protecting drivers and passengers. ESC is the evolution of Antilock Brake Systems (ABS) and Traction Control Systems (TCS). ABS brakes are systems that prevent wheel lock-up by automatically modulating the brake pressure during hard braking or an emergency stop. Traction Control Systems (TCS) are designed to address primarily side-to-side loss of friction between the vehicle s tires and the road surface while the vehicle is accelerating. Electronic Stability Control (ESC) systems are technological developments evolving from and incorporating these two technologies. ESC combines a third yaw control stability system, which compares the direction the driver is intending to steer the vehicle to the direction the car is actually traveling. It assists drivers in maintaining control of their vehicles during extreme steering maneuvers by keeping the vehicle headed in the driver's intended direction, even when the vehicle nears or exceeds the limits of road traction. This is accomplished by selected braking and by reducing excess engine power. If a vehicle begins to oversteer in a turn and the rear end starts losing its lateral force capacity and it starts to come around (which would cause the car to spin out), the speed difference between the left and right front wheels increases. If the vehicle understeers (loses front traction and goes wider in a turn), the speed difference between the left and right front wheels decreases. If the 13

34 stability control software in the ABS control module detects a difference in the normal rotational speeds between the left and right wheels when turning, it immediately reduces engine power and applies counter braking at individual wheels as needed until steering control and vehicle stability are regained. In addition to braking and traction systems, active front steering has been used to improve lateral stability. Figure 5 shows a schematic of ESC intervention during oversteer and understeer situations. Figure 5 ESC (Electronic Stability Control) Intervention Ackerman et. al. [9] have shown the advantages of active steering for vehicle dynamics control. Active steering, with regard to fundamental mechanical consideration, is more efficient than braking systems in attenuating yaw disturbances and preventing rollover. It is argued that Active Front Steering (AFS) systems are most efficient in the 14

35 linear range, while driveline based and brake based control systems are more effective when the tires saturate [1]. Coordinated control of traction forces instead of slip angles is shown in [11] as one way of handling the coupled behavior of longitudinal and lateral dynamics. Falcone et al [12] discussed predictive active steering control for autonomous vehicle systems. This is where autonomous vehicle research ties in with electronic stability control as explained in the next chapter. Recent Studies from Japan, Europe, the National Highway Traffic Safety Administration and the Insurance Institute For Highway Safety all reveal the effectiveness of electronic stability control systems (ESC). Toyota s research indicated that Electronic Stability Control would reduce single-vehicle crashes in Japan by a remarkable 35 percent and head-on crashes by 3 percent. In the European study, Mercedes-Benz, which has provided ESC as a standard feature on most vehicles since 1999, reported a 29 percent drop in single-vehicle accidents and crashes of all types fell 15 percent. In June 26, the IIHS updated the results of their 24 study by stating that up to 1, fatalities could be avoided in the USA annually if all vehicles were equipped with stability control. In September, 26, NHTSA issued a regulation to require new passenger cars be equipped with electronic stability control starting in 29, with all cars and light trucks to have it by 212. NHTSA estimates that the ESC has the potential to save more than 1, lives a year and prevent 25, injuries. The following is a brief summary of the NHTSA's regulatory requirements. Establish a new Federal Motor Vehicle Safety Standard (FMVSS) No. 126, Electronic Stability Control Systems. 15

36 Under the performance standard, vehicles must pass a dynamic test that would work effectively in limit oversteer and understeer situations. ESC systems must augment directional stability by applying the vehicle's brakes individually to induce correction of yaw torques; be computer controlled; be able to determine vehicle yaw rate and velocity; be able to monitor driving steering input; and be operational within the full speed range of the vehicle (except when there is a below-speed threshold under which loss of control is unlikely). The system must have a telltale mounted inside the occupant compartment in clear view of the driver to alert the driver when the ESC system is not functioning properly. A driver-selectable off-switch would be permitted to address times when a vehicle is stuck in sand or gravel or is being run on a test track. Needless to say, such systems must be thoroughly tested; this is where the automated driving system gains importance. Usually it is required that the driver must not have the impression that with ESC the car is more sluggish than without ESC. Unexpected vehicle motions may lead to panic reactions of normal drivers. The design of vehicles should therefore center on the normal driver. Professional test drivers, test engineers and endurance testers are not at all typical for the real population of normal drivers, and therefore it is expected that they may judge vehicle behavior according to criteria that are not relevant to the large number of average drivers. 16

37 2.3 Path Following Maneuvers This section is dedicated to test maneuvers involving path following. The main difference between such maneuvers and the ones performed by steering machines is that the latter are open loop in a sense that the test specifies a handwheel angle profile to be executed whereas path following maneuvers specify a path or course that a vehicle is made to negotiate. There are two standard double lane change courses that are being employed by various researchers and developers around the world (Figure 6). 1. ISO Lane Change test. This maneuver simulates a severe lane change with obstacle avoidance. 2. Consumer Union short course The main purpose of these tests is to validate vehicle s dynamic response with respect to handling. Modern vehicles are being equipped with electronic stability control systems and the tests are designed to evaluate them. There are a number of reports by various manufacturers and regulation bodies on how to test vehicle stability control systems and how to rate the performance. The few key questions that these procedures should be able to answer are: Whether or not an electronic stability control system exists How different is basic handling with and without ESC Determine levels of ESC activity For ISO and CU lane change courses, instability or failure to negotiate the path is considered failure of the test. For NHTSA s dynamic test for evaluating whether a 17

38 vehicle is equipped with ESC, spin out is defined by a predetermined yaw rate limit. Vehicles that do not spinout to this limit are deemed to have ESC. Figure 6 shows the two path following maneuvers commonly used. One problem with such courses is that the deviation tolerance for the actual path is large; a test driver can use many combinations of steering magnitudes rates and timing of inputs to negotiate these courses. The deviation tolerance afforded by an ATD is much smaller than that typically found for human test drivers, and the test repeatability with an ATD is much better than with a human driver. Figure 6 ISO Lane Change and Consumer Union Short Course 18

39 2.4 First Generation Automated Test Driver System Architecture This section introduces the first generation ATD developed by SEA, Ltd. and OSU researchers. The hardware components are shown in Figure 7. The ATD gets the vehicle states from a real-time kinematic differential GPS-INS system. This information is used by the path planner to compute the desired goal point. A path following algorithm discussed later in this chapter then determines the handwheel angle desired to keep the vehicle on the desired path. Another control loop runs in parallel to control the speed of the vehicle to the desired profile. Figure 7 Hardware System Schematic 19

40 Figure 8 shows a block diagram of the overall architecture. Specifications of the handwheel unit, brake-throttle actuator components, GPS-INS module and the real-time controller can be found in [13]. Figure 8 ATD Block Diagram Lateral Control: Path Following Algorithm Lateral control refers to steering control of a vehicle. Modeling and control of lateral dynamics is a complex subject. A vehicle's lateral response to steering inputs depends on a number of parameters such as vehicle inertia, tire properties, road surface, speed, etc. Researchers have developed various models to study lateral vehicle dynamics and control [14, 15, 16, 17]. One simplified model known as The Bicycle Model is commonly used. In this model the front and rear axles of the vehicle are represented by a single wheel in the front and rear respectively, like a bicycle. It is also referred to as 2

41 Single Track Model. For higher accuracy, four wheel models that include lateral load transfer effects are also used. Various other complex effects like suspension compliances, tire relaxation lengths and steering compliances have been included in high fidelity models. The bicycle model as simple as it is, captures the lateral dynamics in the linear range fairly well and is considered appropriate for many control applications. A path following algorithm along with the knowledge of lateral dynamics of the vehicle, forms the complete steering controller of the ATD. A number of path following algorithms have been discussed in the literature [18, 19]. Pure pursuit and vector pursuit are two of many geometric algorithms applied to the path following problem. Other complex control strategies such as sliding mode control and neural networks have been developed. Most researchers in the autonomous vehicles field consider sensitivity to parameter variation and adaptability of any algorithm to different vehicles to be sufficient challenges. The algorithm implemented by Mikesell [13] is briefly discussed here. The controller determines the goal point which is a certain fixed lookahead distance on the path ahead. Once the goal point is known, the angle between the goal point direction and vehicle heading, called heading error is computed. PD control applied to this heading error results in the steering command. = + (1) The proportional gain, in the above equation is adapted from Tseng et. al. [2]. This method offers a way to determine based on four key vehicle parameters. 21

42 = 2( + ) ( + ) (2) where the notation is : Distance of C.G. From the rear axle : Wheelbase : Vehicle forward speed : Steering ratio (handwheel angle to rooad wheel angle) : Understeer gradient Figure 9 Goal Point Calculation 22

43 2.4.3 Longitudinal Control: Speed Trajectory Following The second part of the ATD is the longitudinal control or speed control. Speed control is accomplished by throttle and brake pedal position control. The design of the actuator assembly is such that a single motor controls both pedals, allowing for a combined algorithm for brake and throttle control and a simpler and smaller mechanical arrangement than would be necessary with two separate actuators. The algorithm is essentially a combination of a PID control loop with speed feedback and a feedforward term. The feedforward is based on a static process characteristic (SPC) curve as described in [13]. SPC is simply a steady state response curve that establishes a relation between the accelerator pedal position and vehicle speed. The algorithm uses this predetermined information to effectively account for highly non-linear low speed dynamics of the vehicle. Figure 1 Sample Static Process Characteristic (SPC) for Brake and Throttle Actuator (BTA) 23

44 2.4.4 Test Results Current capabilities of the ATD in terms of path following accuracy and speed control have been reported in [13]. The ATD has been used to test over ten vehicles for this research. Figure 11 and Figure 12 show some test results that are relevant to assert the promise of the ATD for vehicle dynamic testing. A very important test that involves path following is the constant radius test (CRT) used to determine understeer gradient as outlined in SAE J266 [21]. Figure 11 shows representative results of this test, typical of those achieved from testing a variety of vehicles. It is important to note the difference between path following accuracy and repeatability of the ATD over human driver. Figure 12 shows the test results of a figure 8 path performed at high lateral acceleration level. Whereas the performance of ATD is very good there are areas that require further research that will considerably help the adaptability aspect of the ATD. 24

45 Figure 11 Constant Radius Circle Results: Toyota Camry 25

46 Figure 12 Figure 8 Path Following Results: Toyota Camry 26

47 CHAPTER 3 APPLICATIONS OF OBSERVERS AND ESTIMATORS This chapter outlines some of the important vehicle states and their estimation methods discussed in literature. The Kalman filter method is explained and applied to estimate tire forces. Importance of tire force estimation and how it can be used to supply useful information of vehicle operating conditions is discussed. The use of this knowledge is discussed in later chapters about active stability control and path-following algorithms. The effectiveness of closed loop vehicle dynamics control is dependent on accurate knowledge of vehicle states. Some of the states like yaw rate, lateral acceleration, wheel speeds, etc can be easily measured using inexpensive sensors. Other states like vehicle side-slip, longitudinal speed, etc have to be estimated using other means involving measured signals, vehicle dynamic models and other sophisticated tools. Some of the states are often obtained by direct integration of measured signals a process which is prone to errors and highly sensitive to disturbances. Other ways to obtain reliable state information include fusion of different sensors and redundancy in measurement systems combining various properties of individual sensors to obtain reliable state estimation. Recent developments in embedded processors has made possible the use of computationally intensive methods like Kalman filters to be used to combine various sensor data and mathematical models in real time for state estimation. 27

48 Global Positioning System (GPS) measurements and Inertial Sensors (INS) can be combined to estimate lateral velocity and vehicle heading with high accuracy. Errors introduced by the integration of INS sensor data can be overcome by absolute GPS data while INS provides fast updates of measurements [22]. Researchers have shown the use of a Kalman filter to estimate side-slip using just inertial measurement without any vehicle models [23]. With electric steering systems becoming increasingly common on vehicles, steering angle and torque measurements are easily available. More complex methods using additional knowledge of vehicle parameters such as pneumatic trail have been discussed in literature to estimate front slip angles, front lateral force and side-slip angle [24, 25]. Roll dynamics state estimation is another important aspect of robust closed loop dynamics control. Road bank angle and vehicle roll have important affects on lateral response and stability. Various researchers have used Kalman filter and GPS/INS fusion to estimate roll angle and road bank angle [6, 26]. There is extensive literature on longitudinal and lateral force estimation using extended Kalman filter. Knowledge of longitudinal forces and wheel slip is critical to the function of anti-lock brakes and traction control systems. In the same manner lateral forces estimates are useful for lateral stability control. Most electronic stability control systems (ESC) rely on vehicle models, side-slip and slip angle estimation for feedback control. Chrstos [27] proposed a method that employs Kalman filter to estimate tire forces and aerodynamic forces and correlate the balance of front and rear forces to the driving feel of understeer/oversteer in race cars. 28

49 3.1 States and Estimation Methods Knowledge of vehicle states is necessary for stability control systems to work. Yaw rate and lateral acceleration are easily measured by inexpensive sensors. Other parameters like sideslip angle, roll angle and tire forces, etc. are not readily measured and must be estimated by other methods. Various estimators have been discussed in the literature and are employed by current stability systems available on production cars that use different methods. Direct integration of inertial sensor signals accumulates error over time and is unpractical to implement. More sophisticated methods involve sensor fusion in which data is combined from inertial sensors, GPS, subsystems on board and vehicle dynamics models to better estimate immeasurable states. The following is a brief discussion of various signals of interest and the method and systems used in their estimation Sideslip Side slip can be estimated by a method combining inertial navigation system (INS) and Global Positioning Systems (GPS) signals. GPS provides absolute heading and velocity measurements at a relatively slow rate which complements the faster updates of inertial sensors. Absolute GPS heading and velocity measurements eliminate the errors from INS integration; conversely, INS sensors complement the GPS measurements by providing higher update rate estimates of the vehicle states. However, during periods of GPS signal loss, which frequently occur in urban driving environments, integration errors can still accumulate and lead to faulty estimates. There are methods developed for sideslip estimation without the use of GPS. Instead a combination of measurements from 29

50 3 axis rate gyros, 3 axis accelerometers and vehicle math models is used to estimate the sideslip. Presence of electric power steering systems in production vehicles offers another sideslip estimation method as discussed in [24, 25]. Absolute measurement of steering torque is available from which vehicle sideslip angle can be estimated. Steering torque is directly related to the lateral front tire forces, which in turn relate to the tire slip angles and therefore the vehicle states. Steering angle and yaw rate sensors are both inexpensive and common to vehicles already equipped with stability control systems. A disturbance observer based on the steering system model estimates the tire aligning moment; this estimate becomes the measurement part of a vehicle state observer for sideslip and yaw rate Roll Angle and Road Bank Angle Roll angle and road bank angle act as undesirable disturbances to accelerometer measurements and reliable estimation of lateral acceleration and lateral velocity (or sideslip angle) is compromised. Many researchers have emphasized the importance of roll angle and road bank angle estimation for robust performance of stability control systems. Based on these results, this paper presents a new method for identifying road bank and vehicle roll separately using a disturbance observer and a vehicle dynamic model. First, a dynamic model, which includes vehicle roll as a state and road bank as a disturbance, is introduced. The disturbance observer is then implemented using the measurements of the sideslip angle, yaw rate, roll rate, and vehicle tilt angle (the sum of road bank and vehicle roll angles). The yaw rate and roll rate of the vehicle can be easily measured using rate gyros. The sideslip angle and vehicle tilt angle can be accurately 3

51 determined using GPS and INS as demonstrated in previous work [26]. From the disturbance observer, road bank angle and vehicle roll can be separately estimated Tire Forces Besides vehicle motion states external tire forces are also important to determine the dynamic behavior of a vehicle. Tire forces provide useful information about the handling characteristics of a vehicle and are especially important to know when the vehicle operates in the nonlinear range. Design of active safety and stability control systems relies on analytical or empirical tire models obtained from extensive testing. Because the forces are dependent on uncontrollable external factors such as road/tire friction, tire pressure and wear and vehicle loads that are difficult to sense or anticipate the usefulness of tire models is limited [28]. Because knowledge of tire force characteristics and the vehicle state is vital to examining and controlling vehicle performance, a straightforward method of determining the forces and motion from sensor measurements is of paramount importance. Researchers have applied extended Kalman filter (EKF) technique to estimate the states and longitudinal and lateral tire forces [27, 28]. The ability to determine tire forces and state estimates has major implications on the analysis and control of all types of ground vehicles. The following section details the formulation of a Kalman filter in general terms and later system matrices pertaining to vehicle dynamics are provided. 31

52 3.2 Kalman Filter Introduction to Kalman Filter As mentioned before, state estimation plays an important role in control system design. Many studies have been done in the use of a Kalman filter to estimate states that are difficult or expensive to measure directly. The Kalman filter, a relatively recent (196) development in filtering [29], has been applied in diverse fields such as aerospace, marine navigation, nuclear power plant instrumentation, manufacturing, demographic modeling, etc. [3]. The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error. The filter is very powerful in several aspects: it supports estimations of past, present, and even future states, and it can do so even when the precise nature of the modeled system is unknown [31]. Consider a discrete linear system written in state-space forms as = + + (3) where x is the state vector, u is the input, and w the process noise. The corresponding block diagram is shown in Figure 13 (Top). The measurement system is given by = + (4) where z is the measurement vector, and v the measurement noise. 32

53 The optimal state estimate is given by Figure 13 Kalman Filter: Basic Pricipal = + ( ) (5) where (Predictor equation) = + (6) 33

54 According to Kalman the estimate is optimal provided the random processes, w and v are white and gaussian and the gain matrix is chosen to be = + (7) The recursive form of the apriori covariance is given by = + (8) and the recursive calculation of the a posteriori covariance is given by = ( ) (9) Extended Kalman Filter Extended Kalman filter is developed for non-linear systems [45]. A continuous non-linear system equation is given by () = ((), (), ) + () and discrete measurement system equation is given by = h( ), ( ) + Linearizing the system about the current operating point:, = ((), ) ; () = () The measurement system is also linearized: 34

55 = h () ; = Covariance propagation is given by () = ((), )() + () ((), ) + () The update equations for Kalman gain, state estimate and covariance matrix are given by = [ + ] = + [ h ] = [ ] Kalman Filter Validation In this section a Kalman filter is applied to a single track vehicle model to predict lateral tire forces. In order to control the dynamics of the vehicle precisely, the automated test driver requires knowledge of the vehicle states, especially in the non-linear range where the uncertainty of system dynamics and susceptibility to instability are greatest. In order to monitor vehicle dynamics, engineers use inertial sensors (INS) to measure a vehicle's inertial states such as linear accelerations and angular velocities. Vehicle sideslip can be measured by optical speed sensors that measure velocity in the longitudinal and lateral directions. Various researchers have implemented Kalman filters to predict vehicle side-slip angle and slip angles of the tires from the measured inertial states. All 35

56 vehicle dynamic controllers require estimation of certain quantities to enable control. Chrstos [27] applied a Kalman filter to predict tire forces and tire slip angles on a race car. A computed value called Balance, the difference between the front and rear tire slip angles, was defined and shown to correlate between driver comments about oversteer and undertseer. Dunn [32] designed a Kalman filter to predict Jackknife instability of commercial Class 8 trucks. In this research, a Kalman filter will be implemented to predict tire lateral forces which in turn will provide useful information about vehicle stability beyond the measurable states of vehicle motion. Equations of motion are written in terms of unknown lateral forces. ( + ) = + (1) = (11) The lateral forces are modeled as second order Gauss-Markov processes of the form = 1 + (12) Where is the force, is the first time derivative of the force and is random white noise. The augmented system matrix equation then becomes = 1 + (13) 36

57 1 1 = 1 1 (14) For validation of the Kalman filter, the two measurements used are yaw rate and lateral velocity. The input is a Sine-with-Dwell maneuver used by NHTSA for evaluating ESC performance. For simulation purpose the outputs from the model are corrupted with noise of known variance. For practical implementation this variance will be measured from real sensor data. Process covariance is estimated to be based on literature. For the validation runs actual tire forces are obtained from the knowledge of tire cornering stiffness and tire slip angles. Predicted tire forces and other states are shown in Figure 14and Figure 15. Even from noisy measurements the filter predicts the forces well. This implementation also predicts tire force derivatives which are difficult to estimate from direct differentiation from forces. The next section discusses the application of predicted forces to analyze vehicle stability for dynamic tests. 37

58 Figure 14 Kalman Filter Validation: Steer Angle Profile Figure 15 Kalman Filter Validation 38

59 3.2.4 Dynamic Testing Metrics A Kalman filter was run on simulated data from CarSim to demonstrate its use to determine quality of vehicle performance in an evasive manuever. A Sine with Dwell maneuver was used on a typical passenger car. Two quantities that were observed are defined as 1. Specific Force Balance: Difference between total front and total rear lateral force per unit handhweel angle. = h 2. Specific Force Balance Rate: Difference between rate of change of front and rear lateral force per unit handhweel angle. = h It turns out that either of these quantities can be a good measure of vehicle's understeeroversteer state. Figure 16 and Figure 17 show the results of a Sine with Dwell maneuver with small and large dwell respectively. By looking at lateral velocity (or side slip) and yaw rate alone it would appear there is no instability. Balance plots (ϕ and ψ) on the other hand give more information. Ignoring the region in the vicinity of handhweel angle equal to zero, where ϕ becomes infinite, any region where ϕ becomes smaller than a certain amount corresponds to the vehicle not being able to develop yaw rate although side slip is significant indicating understeer effect. On the ψ plot it corresponds to the 39

60 region where ψ is negative. A large positive peak in ψ also indicates an important behavior; the yaw rate overshooting just before the vehicle sets into large understeer. Although this overshoot is not unexpected in a highly dynamic maneuver like this, it certainly can be used to determine the extent of instability. After studying a larger number of maneuvers and vehicles, it will be possible to quantitatively determine thresholds of these balance quantities to establish oversteering or understeering behavior. This is the ultimate goal of the analytical component of this research. Similarly, from the plots of large dwell maneuver in Figure 17, it is clear that the vehicle loses and regains the yaw rate during the dwell, which again corresponds well with positive and rising value of. These quantities also have the potential to be used in real time stability control systems. Instead of comparing measured states to a complex map of a vehicle model, observed quantities like the balance and/or rate of balance can be used to trigger ESC intervention. Implementation of such a strategy relevant to steering control is briefly outlined in the next section. 4

61 Figure 16 Force Prediction Results: Sine With Dwell Maneuver 41

62 Figure 17 Force Prediction Results: Sine With Dwell Maneuver Large Dwell 42

63 3.3 Vehicle Observer: Dynamic Instability Detection Introduction Understeer gradient is the most commonly used measure of vehicle s lateral response. It is a parameter that characterizes a vehicle s directional stability, responsiveness and overall handling under steady-state conditions. It provides useful information of vehicle response in most conditions of highway driving on dry surfaces. Most drivers are used to driving in such conditions when the response is linear, tire forces are well within limits of adhesion and quasi-static. However, vehicles are often subjected to nonlinear range tire forces and highly dynamic maneuvers. Considering nonlinear handling range, the slip angle difference between front and rear should smoothly increase with lateral acceleration. The lateral force of the front axle saturates at a lower level of lateral acceleration than the rear. This is necessary for stability in limit handling. Significant stability margin must be maintained by a passive vehicle throughout the entire range of lateral acceleration in order to remain stable in most conditions [42]. The stability margin can be affected by number of factors Surface friction Tire condition Vehicle payload Longitudinal forces During evasive maneuvers the lateral response becomes less predictable to most drivers because the vehicle deviates significantly from the linear range performance. At large 43

64 vehicle slip angle, the yaw moment becomes less sensitive to the steering angle. Because the driving experience of most drivers is limited to driving well within the linear range, when the adhesion limit is reached the driver is caught by surprise and steers wrong [43, 44]. The test maneuvers used for vehicle dynamics testing are usually open-loop. Various handwheel angle profiles are used for lateral response testing such as Terminated Ramp Steer (J-Turn) Pulse Steer Single Cycle Sine Wave Sine Sweep Sine with Dwell Open-loop maneuvers are generally considered more repeatable than closed-loop and hence better for objective assessment: closed-loop path-following maneuvers have been considered difficult to perform with adequate repeatability and accuracy to yield discriminatory results [Paine]. On the other hand, driver's intent during normal driving is that of path-following as well as evasive obstacle avoidance maneuvers. Some path following maneuvers are also preferred by some manufacturers and consumer groups [45] for transient response testing such as Single Lane Change Double Lane Change Consumer Union Short Course 44

65 The automated test driver (ATD) developed by SEA, Ltd. is capable of driving road vehicles on a programmable desired path in addition to executing other standard and custom test procedures [26, 46]. This paper proposes the stability evaluation method to be used with path-following maneuvers. The ATD s accuracy and repeatability, even in closed-loop maneuvers, makes it appropriate for this testing. Modern vehicles are equipped with various closed loop control systems to intervene during evasive maneuvers to keep the vehicle in control. Most literature on this subject discusses vehicle dynamics stability controllers in terms of matching the vehicle s response to a reference [5, 53 and 54]. The reference is the driver intent to which the vehicle motion must correspond. This paper discusses a method to compare the driver s intent with the vehicle response. A few metrics are developed to quantify the deviation from the desired response. The desired response is computed from the linear range model. The differences in the observed lateral force and moment from the linear counterpart are referred to as unexpected signals by Edwards et al [44]. The relative directions of these unexpected signals determine the mode of dynamic state of understeer or oversteer. This paper builds on this concept of unexpected force and moment. Various metrics derived from unexpected signals are defined and compared for different vehicle configurations. A sliding mode observer as designed in [44] is used to estimate the unexpected signals from the measured yaw rate and lateral acceleration. The vehicle parameters such as mass, yaw moment of inertia, C.G location and cornering stiffnesses are known. These parameters provide the baseline model, to which the actual response of a test maneuver is compared. 45

66 3.3.2 Sliding Mode Observer A sliding mode observer is detailed that estimates the unexpected lateral force and yaw moment. The term "unexpected" is used in [2] refers to the difference between actual lateral force (and yaw moment) and the linear equivalent that would have acted if the vehicle behaved linearly. In this paper the term used is "nonlinear complement". In other words it is the lateral force or moment when added to actual lateral force or moment would result in the linear equivalent as predicted by the bicycle model. The formulation below discusses how these unexpected or nonlinear equivalent signals are estimated. The terms unexpected and nonlinear complement are used interchangeably. Newton s second law for yaw motion = + (15) = (16) Where = = + (17) Substituting into + = (18) 46

67 = 2( ) 2( + ) (19) Newton s second law for lateral motion = + (2) = + + (21) Substituting for slip angles frm (17) ( + ) = (22) = 2( + ) + 2( ) (23) The outputs are chosen to be and, where = (24) Rearranging (23) and substituting from (2) = 1 + (25) Substituting (25) into (19) = (26) 47

68 = (27) Differentiation (24) and substituting from (19) and (2) = (28) + Estimator: Sliding mode method is used to estimate the unknown signals, and To track the measured states and from equations (26) and (27) = (29) 48

69 = (3) = (31) = Sliding Motion: = = = = = + (32) = + + (33) The unknown signals can be obtained using equations (32) and (33). 49

70 Variables and Parameters: : Vehicle Mass : Vehicle Yaw Moment of Inertia : Distance of Center of Gravity from Front Axle : Distance of Center of Gravity from Rear Axle : Front Cornering Stiffness (Combined for both Tires) : Rear Cornering Stiffness (Combined for both Tires) : Front Road Wheel Angle : Yaw Rate : Lateral Acceleration : Lateral Velocity : Longitudinal Velocity 5

71 3.3.3 Dynamic State Detection The dynamics mode of understeer and oversteer can be detected by observing the unexpected force and moment as follows; Understeer: When the unexpected force and the unexpected moment are in the opposite direction, the vehicle is in the state of understeer with respect to ideal (linear) behavior. Oversteer: The unexpected force and the unexpected moment in the same direction implies an oversteer state with respect to ideal vehicle. Figure 18 shows one cycle of sinusoidal handwheel angle input severe enough to force the vehicle into nonlinear region. The regions of the unbalanced signal plot showing understeer and oversteer are marked in Figure 19 based on the sign of the observed signals. To have a quantitative sense of the dynamic state (understeer/oversteer), various physical quantities computed from unbalanced force moment are defined as follows. 1. Unexpected Lateral Velocity: Integral of unexpected lateral acceleration = 1 (34) 2. Unexpected Yaw Rate: Integral of unexpected moment = 1 (35) 3. Unexpected Translational Energy: Integral of product of unexpected force and velocity = (36) 51

72 4. Unexpected Rotational Energy: Integral of product of unexpected moment and yaw rate = (37) 5. Total Unexpected Energy: The sum of translational and rotational unexpected energy = + (38) 6. Understeer Energy: Unexpected Energy during the understeer region of the maneuver = (39) 7. Oversteer Energy: Unexpected Energy during the oversteer region of the maneuver = (4) 52

73 1 Handwheel Angle 5 deg -5 deg/sec Time (sec) Yawrate Linear Nonlinear - Simulated Nonlinear - Sliding Mode Observer m/sec Time (sec) 1 5 Lateral Acceleration Linear Nonlinear - Simulated Nonlinear - Sliding Mode Observer Time (sec) Figure 18: Linear and Nonlinear System Outputs - Sliding Mode Observer 53

74 4 3 US OS Unexpected Signals US OS Force (N) Moment (N-m) Time (sec) Figure 19: Unexpected Signals - Sinusoidal Maneuver In order to study the use of these metrics to understand dynamic handling, the maneuver in Figure 18 is used to simulate a vehicle's response. Parameters are varied to have a range of steady state understeer gradient. The parameters varied are C.G. location Front cornering stiffness Rear cornering stiffness Various metrics calculated for the aforementioned maneuver are plotted with respect to the understeer gradient. The handwheel angle amplitude is selected for each configuration 54

75 so that the output lateral acceleration amplitude is the same for each one. That provides a reasonable method for benchmarking the response objectively for lateral dynamics. Table 1 shows the parameters varied and resulting understeer gradient. Vehicle Front Cornering Stiffness (N/rad) Rear Cornering Stiffness (N/rad) Distance of C.G. to Front Axle (m) Distance of C.G. to Rear Axle (m) Understeer Gradient (deg/g) Table 1 of Vehicle Parameter Sets With Varying Understeer Gradient 55

76 It is clear from Figure 2 that the trend of the metrics does not follow the steady state understeer gradient. A general rule is that larger positive understeer gradient results in slower but stable response. As it approaches neutral steer the response becomes faster at the cost of stability. Whereas understeer gradient provides useful information, it does not provide transient handling characteristics. The metrics defined above, however, provide a quantitative understanding of the balance of responsiveness and stability. The application of these metrics will be extended to evaluation of active control systems. It is expected that in an evasive maneuver a metric will be high for a baseline vehicle without stability control. The metric must be low with the stability control system active. The difference in these values can be useful to quantify the activity in terms of stabilization and responsiveness or balance between understeer and oversteer tendencies. 56

77 E un Unexpected Energy e un = E un /E in Unexpected Energy Ratio (J) Understeer Gradient (deg/g) Understeer Gradient (deg/g) 14 E u Understeer Energy 5 E o Oversteer Energy (J) 8 (J) Understeer Gradient (deg/g) Understeer Gradient (deg/g).6 e u Understeer Energy Ratio.9 e o Oversteer Energy Ratio Figure 2 Energy Metrics vs. Understeer Gradient 57

78 v un Unexpected Peak Lateral Velocity 6 r un Unexpected Peak Yawrate m/s deg/s Understeer Gradient (deg/g) Understeer Gradient (deg/g) 8 ψ un Unexpected Heading Error 3.5 Y un Unexpected Lateral Error (deg) 2 m Understeer Gradient (deg/g) Understeer Gradient (deg/g) Figure 21 Unexpected Inertial Metrics vs. Understeer Gradient The preceding analysis shows that there is a correlation between understeer gradient and understeer/oversteer energy with the dynamic mode. Using this energy definition of dynamic understeer and oversteer, various path-following and open-loop maneuvers are simulated in an effort to develop a simple test method. Two realistic paths considered are a quarter circle turn and a single lane change. The open-loop steering profiles considered are a slowly increasing steer, a sinewith-dwell and increasing amplitude sinusoid. An array of parameters is varied to get a 58

79 range of steady-state understeer gradients. Some of the instances are adjusted in order to produce the same understeer gradient to demonstrate that the developed test method captures the difference in response that the steady-state understeer gradient does not. The same maneuvers help quantify the effectiveness of stability control systems by comparing the energy levels with the assistance on and off. Performing the tests on path-following maneuvers provides a realistic scenario representative of real world driving and the path following metrics can be non-dimensionalized (normalized) with path dimensions. The parameters used are listed in Table 2. Vehicle Front Cornering Stiffness (N/rad) Rear Cornering Stiffness (N/rad) Distance of C.G. to Front Axle (m) Distance of C.G. to Rear Axle (m) Mass (kgs) Table 2 Varying Vehicle Parameters for Constant Understeer Gradient All the cases have an understeer gradient of 4. deg/g. To understand the relative understeer and oversteer tendencies, the response of all three cases to a sine-with-dwell maneuver is shown in Figure 22. Because of the tire non-linearity all the configurations respond differently. Clearly, vehicle 2 (shown in red) is the least stable (or the lease controllable) evident from the most delayed return of yaw rate back to zero. Figure 23 shows the magnitude of the unexpected force and energy to be the largest for vehicle 2. 59

80 This shows that these metrics can in fact be used to quantify the degree of deviation from the linear range performance in an extreme maneuver. 1 Handwheel Angle 5 deg deg/sec Time (sec) Yawrate m/sec Time (sec) Lateral Acceleration Time (sec) Figure 22 Varying Sine-with-dwell Response with Same Understeer Gradient 6

81 In Figure 22 the steering returns to zero at time 2.5 sec. Figure 23 shows the value of normalized unexpected energy increasing at the same instant. This is indicative of the onset of instability. The value is different for each vehicle configuration. This value can be used to compare relative performance of vehicles and to trigger stability control intervention..5 1 x 14 Unexpected Force Unexpected Moment N -1 N-m Time (sec) 12 x 14 Unexpected Energy Time (sec) Unexpected Energy - Normalized 1 8 Joules Time (sec) Time (sec) Figure 23 Varying Instability Metrics Sine with dwell 61

82 3.4 Test Maneuvers There are many stability-critical driving maneuvers (lane change, circular drive, J- Turn, fishhook, steering wheel step, etc.) used for limit performance testing. There is no single maneuver that reveals all handling characteristics. Objective assessment criteria for objective and subjective properties are difficult to obtain. The yaw-plane handling characteristics are described in terms of the states of motion including yaw rate, yaw angle, lateral acceleration, and lateral velocity. For stable performance, the side slip angle must remain bounded; there should be no divergent responses. Responsiveness is a quality that describes the sensitivity to the driver s inputs. There should be a predictable correlation between the driver s steering input and the output motion states. When the correlation is lost, target values for vehicle states provide the measure of degradation of stability and/or controllability. The sliding mode method explained before provides the magnitude of unexpected force and moment from which other metrics are derived to obtain an overall assessment for each of the maneuvers. The following three handwheel angle profiles are proposed to quantify the divergent behavior at the limits. Sine with dwell Sine wave with increasing amplitude Slowly increasing steer Response to sine with dwell maneuver was discussed in the previous section. The following are the results of two more steering profiles proposed. Sine wave with increasing amplitude to induce oversteer and slowly increasing steer for understeer. 62

83 3.4.1 Sine wave with increasing amplitude 2 Handwheel Angle 1 deg -1 deg/sec Time (sec) Yawrate Time (sec) Lateral Acceleration m/sec Time (sec) Figure 24 Varying Response Increasing Amplitude Sinusoid 63

84 12 x 14 Unexpected Force 3 x 14 Unexpected Moment N N-m Joules Time (sec) x 16 Unexpected Energy Time (sec) Time (sec) Unexpected Energy - Normalized Time (sec) Figure 25 Instability Metrics Increasing Amplitude Sinusoid In Figure 25 the normalized unexpected energy has a sharp increase at the point where the vehicle becomes unstable, also evident from the yaw rate response in Figure 24. The value of normalized energy metric approaching the instability is the same as obtained from the sine-with-dwell maneuver. The value is again different for each vehicle configuration. It is the highest for the least stable configuration (vehicle 2). 64

85 3.4.2 Slowly increasing steer 2 Handwheel Angle 15 deg 1 5 deg/sec Time (sec) Yawrate m/sec Time (sec) Lateral Acceleration Time (sec) Figure 26 Lateral Response Slowly Increasing Steer 65

86 8 x 14 Unexpected Force 1 x 14 Unexpected Moment N 2 N-m Time (sec) Time (sec) 4 x 16 3 Unexpected Energy 5 4 Unexpected Energy - Normalized Joules Time (sec) Time (sec) Figure 27 Instability Metrics Slowly Increasing Steer 66

87 3.5 Path Following Maneuvers It is difficult to determine the desired handling characteristic of a vehicle during a cornering maneuver since it is a comprehensive measure of the vehicle-driver combination. Path following maneuvers more closely represent real world driving scenarios. The previous section demonstrates the use of the previously defined metrics to detect instability and quantify the variability of different vehicles in deviation from linear response despite the same linear-range understeer gradient. In order to further show the efficacy of this method another set of simulations is performed. Two path following maneuvers are added in this set of simulation. The paths are shown in Figure 28. A single lane change expected to induce oversteer and A quarter circle turn for understeer These paths are used to compare the metrics from unexpected signals observed from the response desired to negotiate the paths. The understeer gradient is kept the same, with the same total mass and yaw moment of inertia. The parameters are listed in Table 3. The only variation is in the front and rear cornering balance and center of gravity location. As a result the yaw rate and lateral acceleration response to all the maneuvers is the same but the deviation from their counterpart linear response is different as measured by the metrics. An additional metric, relating to path-following is defined as: Displacement of front axle derived from unexpected lateral position and unexpected orientation error, = + Where 67

88 = and = Vehicle Front Cornering Stiffness (N/rad) Rear Cornering Stiffness (N/rad) Distance of C.G. to Front Axle (m) Distance of C.G. to Rear Axle (m) Table 3 Varying Vehicle Parameters for Constant Understeer Gradient Figure 28 Path Following Maneuvers for Stability Testing 68

89 5 Yawrate 1 Lateral Acceleration deg/sec m/sec Time (sec) 1 x 14 Unexpected Force Time (sec) 1 x 14 Unexpected Moment N -1 N-m Time (sec) 3 x 14 Unexpected Energy Time (sec) 3 Unexpected Energy - Normalized Joules Time (sec) Unexpected Position Time (sec) Figure 29 Single Lane Change: Instability Metrics 69

90 4 Yawrate 1 Lateral Acceleration deg/sec 2 m/sec Time (sec) 4 x 14 Unexpected Force Time (sec) 5 Unexpected Moment 2 N N-m Time (sec) 15 x 14 Unexpected Energy Time (sec) 4 Unexpected Energy - Normalized Joules Time (sec) 5 Unexpected Position Time (sec) Figure 3 Quarter Circle Turn: Instability Metrics The unexpected position metric follows the same trend in Figure 29 and Figure 3. Vehicle 2 has the maximum deviation and vehicle 3 the minimum. The energy metric for path following maneuvers is also at the same levels as open loop maneuvers explained earlier. 7

91 3.6 Proposed Transient Nonlinear Understeer Factor The previous section described the application of a sliding mode observer to identify a vehicle s state of understeer or oversteer. A few metrics were derived to quantify the dynamic mode. Various open and closed loop maneuvers were used to simulate vehicle response with respect to various metrics. In this section a simple metric is proposed that can be measured easily from vehicle response to a simple handwheel angle maneuver. The metric provides an objective quantification of a vehicle s tendency to transient nonlinear understeer and oversteer. The simple handwheel maneuver is a half sine wave signal. Figure 31 shows the Unexpected nonlinear complement of lateral force, the point of application and the direction in an overtsteer and understeer situation. Figure 31 Nonlinear Complement Force and Moment Arm The three principal outputs of the observer as explained in the previous section are plotted as shown in Figure

92 Handwheel Angle deg Time (sec) Nonlinear Complement of Lateral Force and Yaw Moment F nc (N) M nc (N-m) Time (sec) 2 x 14 Rate of Nonlinear Complement of Lateral Force N/s Time (sec) Figure 32 A Signature Signal of Transient Understeer Test Two regions of transient understeer and oversteer are marked based on the relative sign of the nonlinear complement of lateral force and yaw moment. The peak lateral force ( ), time rate of lateral force () and the yaw moment in both regions ( ) are recorded. 72

93 Depending on the region in consideration, understeer or oversteer, various quantities are denoted with the appropriate subscript. Nonlinear complement Moment is replaced with or Nonlinear complement Moment is replaced with or Nonlinear complement rate of Force is replaced with or The proposed transient understeer gradient is defined as = (41) The specific rate is a measure of the rate of the lateral force deficiency i.e. the nonlinear complement or the difference of the actual vehicle response from the target linear vehicle, per unit peak roadwheel angle rate per unit mass. The amplitude of the handwheel angle is chosen to result in peak lateral acceleration of.6 g s. As the vehicle has two degrees of freedom, lateral acceleration and yaw rate, the moment deficit has an important significance. It measures the moment arm at which a virtual lateral force must act to make up for the ideal linear equivalent yaw moment. The ratio of the peak moment and lateral force is a measure of the moment arm = (42) 73

94 Active yaw control systems provide additional yaw moment by differential braking effectively reducing the moment arm of the nonlinear complement lateral force. Rear wheel steering systems in combination with yaw moment control by differential braking or driving torque biasing alter the lateral force and the moment. This intervention can be effectively measured using the proposed metric as shown in the section. Before comparing passive and active vehicle response a few trends are discussed to validate the ideas presented. First is a set of simulations performed to measure of a vehicle where the target linear response configuration is varied by moving the center of gravity towards the rear axle Transient Understeer/Oversteer Metric Validation The transient understeer metric must pass a basic test. For a given vehicle, comparison of transient response to a target (ideal) response must result in the: Understeer Metric to increase as target response moves toward neutral Oversteer Metric to decrease as target response moves toward neutral Figure 32 shows the variation of in two regions. As the target response moves toward neutrality (configuration 1 through 4 marked on x-axis) the transient dynamic understeer increases and the oversteer decreases. It is intuitive and consistent with the fact that a vehicle is going to be less oversteer with respect to a neutral vehicle than an understeer vehicle. 74

95 F nc N Yaw Moment of Inertia 2 kg-m^2 3 Kg-m^2 4 Kg-m^2 M us M os 6 3 N-m 4 2 N-m x 14 2 x 14 N/s 1 N/s Ktr us Ktr os 6 3 g/deg. m 4 2 g/deg. m Figure 33 Transient Understeer/Oversteer vs. Target C.G. Loaction The trend is consistent for different yaw moment of inertia. Yaw moment of inertia is an important parameter that affects the transient response and is not captured by the linear range understeer gradient. The proposed metric here captures the effect of yaw moment of inertia as shown by the second set of simulations shown in the Figure

96 3.6.2 Transient Understeer/Oversteer Metric Variation Variation with Yaw Moment of Inertia F nc N Yaw moment of inertia varying from 2 Kg-m^2 to 4 Kgm^2 from configuration 1 through 4 marked on x-axis. M us M os 4 4 N-m 2 N-m x 14 2 x 14 N/s 1 N/s Ktr us Ktr os 4 4 g/deg. m g/deg. m Figure 34 Transient Understeer/Oversteer vs. Moment of Inertia 76

97 Variation with Different Vehicle Configuration and Same Understeer Gradient Vehicles with same understeer gradient (4. deg/g) but different center-of-gravity location and cornering stiffness combinations were compared to show the applicability of this method to objectively compare their transient response, which is not possible from a linear steady state analysis. 3 Vehicles with the same linear-range understeer gradient have different transient dynamics in nonlinear range Vehicle 2 has the minimum transient understeer Vehicle 3 has the minimum transient oversteer F n c N Target Vehicle Dynamics Understeer Neutral Steer M us M os 6 3 N-m 4 2 N-m x 14 N/s 1 5 N/s Ktr us Ktr os 6 2 g/deg. m 4 2 g/deg. m Figure 35 Transient Understeer/Oversteer Variation for Same Linear Understeer Gradient 77

98 Variation with Vehicle Mass F os N Vehicle Mass varying from 1 Kgs to 2 Kgs from configuration 1 through 5 marked on x-axis. M us M os 5 4 N-m N-m x 14 2 x 14 N/s 1 N/s Ktr us Ktr os 1 1 g/deg. m g/deg. m Figure 36 Transient Understeer/Oversteer vs. Vehicle Mass The last parameter whose effect is studied is vehicle mass. The heavier the vehicle, larger the lateral force complement. The moment on the other hand is smaller therefore the moment arm is shorter. The product results in a smaller. It is not intuitively apparent that the lighter vehicle has increased understeer as well as oversteer in nonlinear range. It does however provide a good measure of potential of actively 78

99 reducing the deviation from target response. If the moment arm is small then a differential torque method is not suitable as the dominant deviation is in the lateral force which has an inherent limitation based on road friction conditions. Depending on which source of nonlinear complement is dominant, control strategies can be chosen or tuning parameters can be selected. Rear wheel steering for controlling the sideslip and torque biasing for yaw rate. The transient method also provides a tool to compare ESC effectiveness with respect to both degrees of freedom combined. Comparing only the yaw rate to evaluate ESC can be misleading because improper tuning or large gains on yaw control can result in zero yaw rate error and excessive side-slip at the same time. The combined metric provides a practical weighted method to evaluate the instability and intervention effectiveness. While energy provides a realtime signal for control, the Ktr provides an aggregate numerical assessment. 79

100 3.7 ESC Testing Prior to the development of electronic or active control systems, vehicle handling characteristics were a function of purely mechanical systems, and vehicle designers were limited to the selection of passive components such as tires and suspension configurations to define a vehicle s handling character. Compromises were made between handling responsiveness (turning capability) and handling stability through mechanical component choices. In recent times designers have been able to include electronically controllable or active components which enable new levels of handling performance but still involve certain compromises. Testing of vehicles and their stability control systems is subjective. The criteria can be wide ranged. Common aspects for which the vehicles are tested from a stability and control assessment standpoint are maximum sustainable lateral acceleration and controllability at and past the handling limits. Vehicles with stability control systems generally are easier to drive and are more controllable at the limits. In the previous chapters this thesis has described various systems and design methods to achieve enhanced limit performance. Like any control system, calibration and tuning of stability control systems is crucial. The activity level of ESC is usually adjusted to match the type of vehicle. ESC is considered to have the following characteristics. It should: Complement the vehicle and driver characteristics. Be unobtrusive during normal driving but engage in an emergency handling situation. 8

101 Involve graceful or non-abrupt change in the vehicle motion and driver input relationship as the limit of adhesion is approached. The effectiveness of a stability control system can only be realistically determined for a specific vehicle by making comparisons of vehicle behavior with the system inhibited and operational. Figure 37 compares measured yaw rate and lateral acceleration of an actual vehicle with and without ESC. Along with the measured quantities are plotted observed unexpected signals and unexpected energy metrics. At about 2.5 secs when the yaw rate of the active vehicle returns to zero, the normalized energy of the active vehicle is about 5 and that of the uncontrolled passive vehicle is 2. The percentage reduction in this metric, in this case 75%, provides a measure of ESC effectiveness in mitigating oversteer. The same analysis can be performed to measure understeer mitigation using previously listed open loop and closed loop maneuvers. 81

102 4 Handhweel Angle 5 x 14 Unexpected Force 2 deg N Time (sec) -1 ESC Off ESC On Time (sec) 2 x 14 Unexpected Moment 1 ESC Off ESC On 4 2 Yawrate ESC Off ESC On N-m -1 deg/sec Time (sec) 1 5 Lateral Acceleration ESC Off ESC On Time (sec) 4 3 Unexpected Energy - Normalized ESC Off ESC On m/sec Time (sec) Time (sec) 3.8 Conclusion Figure 37 Comparison of "Sine with Dwell" with ESC On and Off The neutral steer vehicle characteristic is often considered as desirable during cornering maneuvers and hence the objective of handling enhancement is generally to reduce the understeer behavior of a vehicle without allowing it to become oversteer. This concept can be used to compare a vehicle with and without stability control. The observer 82

103 described in this chapter can be run with two sets of parameters depending on the analysis sought. Case 1. With neutral steer parameters Case 2. With linear range parameters observed from a low lateral acceleration test, e.g. a constant radius test or slowly increasing steer. The observed unexpected force and moment along with measured yaw rate and lateral acceleration from actual open-loop or closed-loop test maneuvers provide the measurement of deviation from desired neutral steer behavior (Understeer/Oversteer) in case 1. Case 2 provides the deviation from linear range performance of a vehicle while approaching the limits. Both of the methods are useful to compare different vehicle designs relative to one another and also to an ideal design objective, for instance, neutral steer. Resulting unexpected energy and position metrics can also be compared with and without stability control to determine the deviation of a passive vehicle from desirable limit behavior and measure the stability enhancement objectively. The percentage reduction in these metrics with the active control on in different maneuvers inducing understeer and oversteer provide a very good evaluation of effectiveness of the stability controller in the mitigation of these instabilities. 83

104 CHAPTER 4 ACTIVE STEERING 4.1 Introduction to Steer-by-Wire In recent years electric steering has replaced mechanical and hydraulic control mechanisms. A steering system that has electronically controlled active components is called Steer-by-wire. It is a significant leap from conventional steering systems in that it promises to significantly improve vehicle handling and safety. Vehicle handling characteristics are determined by various physical properties as discussed in [47, 48, 49]. Cornering stiffness of the tires amongst others is a critical one. Steering input from the driver results in tire slip which generates lateral forces. The relationship between the lateral force and slip is linear for small slip angles and nonlinear near the limit. The understeer gradient is a parameter that determines a vehicle s directional stability and response. Most vehicles are designed to be understeering by way of centerof-gravity location and selection of tire cornering stiffness, suspension characteristics, etc. Safety margin and responsiveness are important considerations while choosing these parameters. Conventionally, vehicles have passive handling characteristics defined at the design stage. Active control systems like steer-by-wire provide the potential of arbitrarily changing handling characteristics depending on driving scenario. The wide safety margin and responsiveness conflict can be dealt with by actively modifying the response by feedback of vehicle states [5]. Active steering uses yaw rate and lateral acceleration 84

105 feedback for control. Estimation techniques have been developed for side slip and sideslip rate using GPS-INS sensors, steering torque measurements, etc as discussed in section The steering angle does not directly correspond to the driver command as in a conventional vehicle; instead it is determined from measured or estimated vehicle states in order to match the vehicle response to driver command and maintain control in extreme maneuvers. Yaw rate is not enough to ensure stability. A vehicle can have perfect yaw rate tracking and yet be skidding sideways. Physically altered handling can be achieved by combined feedback of yaw rate and sideslip. This chapter outlines the function of an active steering system. The function comprises Learning of passive vehicle characteristics in linear and nonlinear range. Applying state feedback to linearize vehicle response beyond the linear range. Stabilizing the vehicle in extreme maneuvering situations. Assuming precise steering control and vehicle states availability, we can modify the vehicle handling characteristics. Knowledge of tire forces is used to determine the operating point and to stay below the limits to maintain controllability and avoid yawplane instability. The results are shown by: Slowly increasing steer for linearity Sine with dwell steering for stability control (oversteer mitigation) on high friction surface 85

106 A ramp steer for controllability and responsiveness (understeer mitigation) on a low friction surface. Figure 38 Vehicle Observer in Active Steering Mode 86

107 4.2 Linearized Lateral Response: State Feedback In recent years, electronically controlled 'active' components have been developed to enable new levels of performance with respect to vehicle handling and control. The advent of these new technologies potentially allows designers to avoid the traditional compromises between handling responsiveness and stability. Active Front Steering (AFS), Active Rear Steering (ARS), Direct Yaw Control (DYC) and Active Suspensions are some of the systems used on modern vehicles. Handling characteristics are studied from steady state as well as transient operation standpoint. Stable handling means that the vehicle yaw plane or roll plane motion does not exhibit any divergent response. Directional stability is an important concern for safety. The vehicles side slip angle and roll angle are the two primary indicators of stability and their magnitudes should remain bounded and held below certain thresholds. Sensitivity to driver inputs is another important characteristic of vehicle lateral dynamics, called responsiveness. There should be a predictable correlation between the driver's steering input and output motion states of yaw rate and lateral acceleration. Vehicle handling response depends on the balance of forces between the front and rear axle lateral forces. Most of the driving on dry and high friction roads surfaces is such that lateral forces and vehicle dynamic states remain in the linear range. In other words, most drivers, most of the time, experience a predictable linear response from the vehicle. However, in extreme situations such as an evasive maneuver or changes in road friction, the vehicle response departs from the linear range to nonlinear range due to saturation of tire forces. 87

108 A vehicle operating at the limits of adhesion due to an evasive steering maneuver or low friction or other disturbances like loss of tire pressure, can develop excessive sideslip and the vehicle tends to deviate from the intended path. Most ESC systems use differential braking to actively control vehicle yaw in order to control the vehicle trajectory and limit side-slip. More recently researchers have focused on combining the available technologies of longitudinal slip-control with differential braking and active front steering to achieve unified control of vehicle dynamics. The major difference between steer-by-wire systems and active stability control is that while the latter intervenes only when divergent unstable behavior is detected the former controls the vehicle dynamics continuously independent of what the vehicle states happen to be. Even in the linear range of stable operation, the steering angle and braking or traction commands are electronically controlled based on interpretation of driver intent and are not directly coupled to driver actuator commands. Beyond the linear range, a vehicle s response is unfamiliar to, and can be unpredictable by typical drivers. This chapter describes the methods of controlling the vehicle in the nonlinear range to maintain both responsiveness and stability. The control input is the front steering angle and the goal is to follow the desired trajectory or target as close as possible while fulfilling various constraints reflecting vehicle physical limits and design requirements. Vehicles with passive steering systems exhibit linear handling characteristics at low to medium lateral acceleration range. In the limit performance region however, the response becomes non-linear and unpredictable, often unstable. This behavior can be 88

109 mitigated by active steering control. The steering controller is designed using state feedback in order to linearize the output response. Measurement of yaw rate and side-slip are used as feedback along with the knowledge of tire forces (from the Kalman filter) to generate the steer angle required Lie Derivatives This section presents the fundamentals of linearization by state feedback. Lie derivatives are briefly discussed for a general nonlinear system and conditions for inputoutput linearization are listed. Then, the lie derivatives are applied to the vehicle model written in terms of nonlinear tire forces as described by Gerdes et. al. [25]. Consider a system defined by (43) = () = () = h() (43) First derivative of the output is = h [() = ()] (44) where h = h () (45) is the Lie Derivative of h along and 89

110 h = h () (46) is the Lie Derivative of h along If h =, from (44) = h Differentiating the output again = h [() = ()] (47) = 2 h() + h h() If h h() = = h() Similarly, if h() satisfies = (48) = 1, 2, 3,, 1 then does not appear in,,,.., and the output differential equation can be written as 9

111 = h() + 1 h() (49) The system is input-output linearizable if = 1 1 h() + (5) = The above explained formulation can be used to linearize the output yaw rate by choosing the desired yaw acceleration as the auxiliary input = Using tire forces from equation (4), vehicle dynamics can be written as 1 = ( + 1 ( (51) 4 The input I can be written in terms of Lie Derivatives = 1 h ( h + ) (52) Where 91

112 h = (53) And h = 4 (54) It is the desired yaw acceleration generated by a known linear vehicle model. It is a simple linear system formulation in state space form given by + = (55) The signal is modified by the difference between actual and desired yaw rate and actual side-slip. The road wheel angle can be determined from the input as = (56) Equation (55) is one method to generate the desired yaw acceleration signal. The following section outlines another method based on sliding mode control. The key is to use the actual slip angle of the controlled vehicle and penalize large side slip. 92

113 4.3 Tire parameter estimation Dugoff Tire Model Cornering behavior of pneumatic tires is a highly complex process. Various mathematical models and theories have been attempted to explain the mechanics of the tires over the years. Most tire friction models assume the coefficient of friction to be a ratio of the friction force to the normal force. The coefficient of friction depends on the vehicle velocity and road surface conditions amongst other factors. All models relate the lateral and longitudinal forces generated to the tire slip angle and wheel slip [51, 52, 55]. Figure 39 shows the axis system of a tire and the forces and moments acting on it. Figure 39 Tire Axis System and Forces 93

114 Figure 4, Figure 41 and Figure 42 show the variation of tire lateral force, longitudinal force and aligning moment with respect to slip angle and wheel slip. The relationships are mostly nonlinear with a small linear region at low slip angle and low slip. At high slip angles the lateral force starts to increase nonlinearly with slip angle and eventually saturates to a value dependent on the normal load and coefficient of friction (road adhesion) between the tire and the road surface. Figure 4 Magic Formula Lateral Force Fit Society of Automotive Engineers, Inc Figure 41 Magic Formula Aligning Moment Fit Society of Automotive Engineers, Inc 94

115 Figure 42 Magic Formula Longitudinal Force Fit Society of Automotive Engineers, Inc Often, experimental tire force data is used to create empirical models to accurately represent a real tire in simulations. For the purpose of control design an analytical model is more suitable. One model is the Dugoff model [56]. The following equations describe the model. It is one of the analytical models that express the lateral force as a function of slip angle and wheel slip. It is an attractive choice to estimate the coefficient of friction and cornering stiffness for real time control because it is simple and computationally efficient to implement. The next section explains a method to fit the nonlinear force-slip data to estimate cornering and friction using the Dugoff model. = 1 (57) = 1 (58) 95

116 = ( ) + ( tan ) 1 (1 ) 4( ) + ( tan ) (59) = tan ( ) + ( tan ) 1 (1 ) 2( ) + ( tan ) (6) Ignoring the longitudinal effects = tan () (61) () = (2 ) < 1 (62) () = 1 1 (63) = 2 tan (64) : Longitudinal Force : Lateral Force : Normal force on the : Slip Angle : Longitudinal Stiffness : Coefficient of Friction tire : Slip Angle : Longitudinal slip ratio In the linear range the lateral force is simply = tan (65) and in the nonlinear range the expression is 96

117 = () + 4 (66) Tire Force-Slip Curve Fitting: CarSim Simulation Results Cornering stiffness and the coefficient of friction are the two important parameters to determine the lateral force characteristics. Their knowledge in real-time is very useful for vehicle control. A scheme used to fit slip force data to estimate these parameters is described here. Various methods to estimate tire forces have been researched. Some methods use the steering system parameters to estimate front lateral force and others use vehicle motion to estimate these forces. The latter is the method used in this work. With the combination of GPS and INS sensors, vehicle side slip and yaw rate can be measured accurately. This thesis relies on the knowledge of these signals available for the estimation of forces and control. Knowing these quantities along with handwheel angle and steering ratio, the effective combined front and rear slip angles can be computed as follows Figure shows a scatter plot of force slip data. Line 1 is the linear fit to the data and Curve 1 is the nonlinear fit to equation (4). Comparing the linear mean squared error (LMSE) and the nonlinear mean squared error (NLMSE) indicates whether the data has enough nonlinearity to be used to estimate coefficient of friction or not. If the difference in the error is lower than a threshold, the data is assumed to be linear and the slope gives the cornering stiffness and when above the threshold the estimation of and is possible by fitting the data to the equation of the form 97

118 Once 'a' and 'b' are determined, and can be computed as And Figure 45 shows the result of this algorithm in a simulated run. Figure 45 shows the lateral force vs. slip angle curve for a non-linear range maneuver simulated in CarSim. The curve-fitting algorithm is divided into two different ranges; linear and nonlinear. In the linear range only the cornering stiffness can be measured from the slope of the curve. Estimation of coefficient of friction is possible only when the operation enters the nonlinear range. The algorithm detects the range of operation by comparing the errors of the linear fit. In the linear range the error is insignificant but grows in the nonlinear range as shown in Figure 43 and Figure 44. The linear range data set shows that the fit and data overlay closely and the RMS Error = 15.5 whereas in the nonlinear range data, the linear fit is not very good indicated by RMS Error = 245 and evident from the figure. A threshold for this error can be decided to indicate the availability of the nonlinear range data so that the cornering stiffness and coefficient of friction can be estimated by fitting to equation (66). Following are the details of the run simulated in CarSim. Maneuver: Constant Radius Understeer Gradient Test (radius = 3 m). Mass = 137 kg. Front Cornering Stiffness = 8.47e+3 N/deg Center of Gravity Location, a = 1.11 m, b = 2.77 m; The parameters identified are used to simulate vehicle response and compared to CarSim. The comparison is shown in Figure 45. Another important use of this method is 98

119 to detect changes in road surface conditions which is critical for active stability systems. The coefficient of friction is an important input to the control algorithm. Figure 43 Linear Fit in Linear Range Figure 44 Linear Fit in Nonlinear Range Figure 45 Dugoff Tire Model Curve Fitting 99

120 4.4 Upper Level Lateral Controller Sliding Mode An active steering control is designed in this chapter based on sliding mode control. It relies on knowledge of estimated tire forces, road friction and handling parameters to mitigate nonlinearities up to the tire saturation limits. At low friction, the tires saturate at low lateral acceleration. Most electronic stability control systems are designed to intervene during an evasive maneuver and intervene when the vehicle enters instability. Other than the design of a stable control system to keep the vehicle stable, another challenge is to decide the desired response. Active steering is a drive by wire system where the system does not just activate in an evasive maneuver or only at high lateral acceleration but is constantly monitoring the desired response and actively controlling the vehicle motion. The key issue here is to design an upper level controller that generates the desired response. In a conventional steering vehicle with active yaw stability control, the actual and desired yaw rate responses are compared and direct yaw control using differential braking is employed to match the two. Even when tires saturate in lateral force, it is possible to generate longitudinal forces to control the yaw rate. The problem is that a vehicle can be following the desired yaw rate accurately and have an excessive side-slip which is highly undesirable: vehicle motion becomes highly unpredictable. The desired yaw rate response is generated in terms of yaw acceleration. It is fundamentally easy to control knowing the actual forces and desired yaw moment. The desired yaw acceleration signal can be computed from a predetermined linear model of 1

121 the vehicle but for reasons mentioned previously the linear response, even if possible using direct yaw control may not be an adequate control strategy. The upper level control designed here generates the desired yaw acceleration signal from actual lateral acceleration and side-slip. This upper level controller penalizes high side-slip and takes into account changing tire cornering properties based on effective cornering stiffness and coefficient of friction estimated from actual tire forces as explained in the Kalman filter chapter before. Figure 46 Stabilization by Yaw Acceleration Control Block diagram Figure 46 shows the block diagram of the control system. Starting with vehicle dynamics equations in state space form, + = (67) 11

122 = + (68) Yaw acceleration can be written as = ( + ) + + ( ) ( + ) + ( + ) (69) + In simplified form = + + (7) = (71) and sliding condition as + = (72) + = (73) = + + ( + ) + + ( + ) (74) + Where, and are = ( + ) + = ( ) ( + ) (75) 12

123 = + ( + ) The cornering stiffnesses and are replaced by the estimated values, which include the inherent uncertainty and nonlinearity of these parameters. Actual yaw rate, lateral acceleration and steering command can be measured easily. The estimated values of effective cornering stiffness are used in real time to generate the desired yaw acceleration. Following figures show the desired linear response, nonlinear-uncontrolled vehicle and controlled vehicle. 13

124 4.4.2 Simulation Results: High Friction Figure 47 Active Steering Control Linear Range Run 14

125 Figure 48 Active Steering Control Nonlinear Range Run 15

126 Figure 49 Active Steering Control Stabilization The controlled vehicle s lateral response follows the target much better than the uncontrolled vehicle, which goes unstable. The handwheel angle is different from the commanded angle in order to keep the yaw rate responsive to the commanded handwheel angle. 16

127 4.4.3 Simulation Results: Low Friction Figure 5 Active Steering Control Low Friction, Linear Range 17

128 Figure 51 Active Steering Control Low Friction, Nonlinear Range 18

129 Figure 52 Active Steering Control Low Friction, Stabilization The active vehicle s lateral response follows the target much better than the uncontrolled vehicle. The handwheel angle is different from the commanded angle in order to keep the yaw rate responsive to the commanded handwheel angle. 19

130 4.4.4 Discussion of Results The performance of the active steering controller on a high friction surface simulation can be seen in the above plots. Figure 47 shows a run where the steering wheel command corresponds to a low lateral acceleration linear-range run. The linear vehicle and nonlinear vehicle lateral response is the essentially the same. Figure 48 shows the response to a steering wheel input forcing the vehicle into nonlinear range evident from the deviating response of the uncontrolled vehicle. The controlled vehicle on the other hand linearizes the output and the yaw rate is closely matched to that of a linear vehicle response. Figure 49 shows a stabilization run where the handwheel angle amplitude is high enough to cause the uncontrolled vehicle to go unstable. The vehicle yaw rate is no longer responsive and does not return to zero when the handwheel angle does. This instability is mitigated by the active steering controller and yaw rate is still closely matched to the linear vehicle. The steering angle desired to stabilize the vehicle deviates significantly from the commanded angle. Figure 5, Figure 51 and Figure 52 show the three runs namely, linear-range, nonlinear-range and stabilization on a low friction surface. The controller performs very well to keep the yaw rate stable. Much smaller steering amplitude is enough to force the vehicle into the unstable region when the coefficient of friction is low. As the sliding mode control uses the estimated effective cornering stiffness, the controller can accomplish the stabilization without any change in tuning parameters. This robustness is the key feature of this control method. 11

131 4.5 CarSim Simulations: Sliding Mode Active Steering CarSim Active Steering: Low g 1 5 Yawrate Uncontrolled Controlled Target.4.2 Lateral Acceleration Uncontrolled Controlled deg/s -5 g's Time (sec) Time (sec) deg Handwheel Angle Commanded Controlled (N) 4 2 Lateral Force Front-UC Rear-UC Front-C Rear-C Time (sec) Slip Angle (deg) Figure 53 CarSim Active Steering Control, Sine with Dwell, Low g 111

132 4.5.2 CarSim Active Steering: High g 4 2 Yawrate Uncontrolled Controlled Target 1.5 Lateral Acceleration Uncontrolled Controlled deg/s g's Time (sec) Time (sec) deg Handwheel Angle Commanded Controlled (N).5 1 x 14 Lateral Force Front-UC Rear-UC Front-C Rear-C Time (sec) Slip Angle (deg) Figure 54 CarSim Active Steering Control, Sine with Dwell, High g The active vehicle s lateral response follows the target much better than the uncontrolled vehicle. The handwheel angle is different from the commanded angle in order to keep the yaw rate responsive to the commanded handwheel angle. Yaw rate and lateral acceleration returns to zero at the same time as HWA. The uncontrolled vehicle is delayed by about.7 sec. 112

133 4.5.3 CarSim Active Steering: Slowly Increasing Steer 4 Yawrate 1 Lateral Acceleration 3.8 deg/s 2 1 Uncontrolled Controlled Target Time (sec) g's Uncontrolled Controlled Time (sec) 12 Handwheel Angle 8 Lateral Force 1 6 deg Commanded Controlled Time (sec) (N) 4 2 Front-UC Rear-UC Front-C Rear-C Slip Angle (deg) Figure 55 CarSim Active Steering Control, Slowly Increasing Steer 113

134 4.5.4 Discussion of Results The active control method was implemented in a co-simulation where CarSim simulates the vehicle and the controller is programmed in MATLAB. Figure 53 and Figure 54 show the response to a sine with dwell maneuver with low and high lateral acceleration respectively. In the low-g run the tire forces are in the linear range and the yaw rate and lateral acceleration matches that of the simulated linear vehicle output. The high-g run shows the stabilization that the active steering accomplishes and keeps the vehicle yaw rate responsive to steering angle in contrast to the uncontrolled vehicle. Figure 55 shows a slowly increasing steering response of an uncontrolled and controlled vehicle. The yaw rate output of the uncontrolled vehicle begins to deviate from the target linear response much sooner than the controlled vehicle. The active steering controller linearizes the yaw rate output up to a certain extent before the front tire forces saturate at which point it saturates the steering angle. This is the limit up to which the vehicle response can be matched to the linear target established by the available friction. 114

135 4.6 Optimized Tire Force Distribution for Vehicle Stability Control Various electronic stability control systems are available on modern vehicles aimed at improving handling and stability in a variety of driving scenarios. Direct yaw control (DYC) is a commonly used methodology that uses differential braking to generate additional yaw moment if and when necessary. DYC is often used in a combination with active front steering. Four wheel steering systems are available on some advanced vehicles. Various studies have compared the benefits of each of these control schemes with respect to stability, handling and controllability. An optimized force distribution method is discussed in [54] that enables the vehicle to achieve the target response by distributing the longitudinal and lateral forces independently to all four wheels depending on the vertical load and cornering capability at each wheel. The target response is interpreted from driver inputs of steering wheel angle and brake/throttle actuator position. Longitudinal response is simply a commanded longitudinal acceleration command. The cost function for the optimization problem can be chosen in many different ways. From the concept of the friction circle, the ratio of the resultant horizontal force and the vertical force is the coefficient of friction. The sum of friction usage of all four tires is used as the cost function. The individual longitudinal and lateral forces must be such that they minimize the utilization of friction while satisfying the total force and moment objectives commanded by the driver and determined by the linear vehicle model response. 115

136 This research improves the method by two additional concepts: 1. The upper level sliding mode controller generates the desired target lateral response based on estimated available friction and cornering stiffness. When differential longitudinal forces are used to generate yaw moment it is possible to track the yaw rate perfectly and yet have excessive side-slip at the same time. The upper level controller discussed in the previous chapter shapes the desired response in order to prevent this occurrence. Thus, same upper level controller is used. 2. The optimization routine may result in minimization conditions where one of the tires utilizes very little friction and another is close to saturation. The proposed method finds the minimum and then equally distributes friction utilization. The cost function used in [54] is = = + (76) The total lateral and longitudinal force can be written as = (77) = (78) Total yaw moment generated by individual longitudinal and lateral forces is 116

137 = 2 ( + ) + + ( + ) (79) The vertical load at each wheel is = 2( + ) h 2( + ) h = = 2( + ) h 2( + ) + h 2( + ) + h 2( + ) h (8) = 2( + ) + h 2( + ) + h To reduce the number of variables, and can be substituted into the cost function as = = (81) = Differentiating the cost function to minimize yields, = = (82) 117

138 = = + (83) = (84) = 118

139 = (85) = = = (86) The above system of linear equations can be expressed as = (87) The coefficients in the above equation are expressed in terms of the forces and moments and center-of-gravity location parameters. Equation (76) cost function does not include saturation for the coefficients of friction. The solution results in some of the tires saturating. The method used for simulation in this work equally distributes the friction utilization between left and right tires once a minimum is obtained. 119

140 Figure 56 Active Steering Control Low Friction, Stabilization 12

141 Figure 57 Active Steering Control High Friction, Stabilization 121

142 4.6.1 Discussion of Results Figure 56 and Figure 57 show the results of the optimized force distribution algorithm. The plots show simulated responses from a single track linear vehicle model (linear), single track vehicle model with non-linear tires (nonlinear-uncontrolled) and the non-linear vehicle model with optimized force control method (nonlinear-optimized). The commanded steering wheel angle is a sine wave. The amplitude is chosen high enough so that the uncontrolled vehicle goes unstable after the first cycle. The optimization algorithm distributes the lateral forces such that the friction utilization is approximately the same for all the four wheels. Steering angle for all four wheels are different as shown in the top plot of both figures. The high friction run in Figure 57 shows the friction utilization regulated at higher level than the low friction run. The algorithm performs as expected by matching the yaw rate output of the nonlinear vehicle with that of the simulated linear vehicle output while keeping the friction utilization uniform at all wheels. This was a simple optimization simulation with no longitudinal acceleration commanded. More advanced analysis is required to study the performance of such optimization methods in various evasive maneuvers involving combined braking/acceleration and steering. 122

143 CHAPTER 5 ATD PATH FOLLOWING 5.1 Introduction and Role of the Automated Test Driver The steering task of an autonomous vehicle is not much different from an active steering system. Both systems control lateral dynamics based on a reference signal. The reference in an autonomous vehicle is generated based on desired path and by the human driver in a regular vehicle with active steering. The algorithm used for active steering in Chapter 4 will be shown to apply to autonomous steering control. The current algorithm of the automated test driver (ATD) has demonstrated that the ATD maintains the vehicle on the desired path within.2 m for most vehicles tested on various paths. The algorithm employs inputs of vehicle measurements such as wheelbase, center-of-gravity location and the understeer gradient. Although the algorithm works, some tuning must be done to achieve this level of performance. Sensitivity of the current algorithm to variation in parameters will be studied and methods to minimize this sensitivity will be explored in order to create a robust control method that will ensure stability with a minimum of tuning. The path following algorithm that Mikesell [13] used on the ATD is based on a paper by Tseng [8]. The controller is designed as a function of vehicle parameters including wheelbase and understeer gradient. The algorithm works reasonably well but 123

144 there is a need to tune it by experiment. It is not uncommon for even rigorously designed control systems to have a need for tuning due to any un-modeled dynamics of the plant. What is being proposed here is a controller design which would adapt to the dynamic situation during a run. A parameter equivalent of the understeer gradient would be computed in real time to aid the controller in maintaining stability and performance balance. The goal is to guarantee stability during a path-following sequence while approaching or returning from a test maneuver site. It is safe to assume that this part of the overall test sequence would be mostly in the linear-range therefore a linear control design will suffice. Sensitivity analysis would be done on the designed controller with respect to vehicle parameter uncertainty. This will establish bounds on controller parameters for stability and performance. A strategy employing a Kalman filter will be developed to learn the dynamics. Furthermore, the understeer gradient defined in SAE J266 [21] includes yaw plane dynamics alone. Understeer gradient including roll dynamics would be a better representative of lateral dynamics of the vehicle. Therefore, controller design based on this roll corrected understeer gradient will be explored. To incorporate various elements of vehicle dynamic testing mentioned in the previous chapter, an automated test driver is the most appropriate choice. This project emphasizes the fact that drivers follow paths in the real world and therefore pathfollowing maneuvers such as single and double lane changes, panic lane changes, slalom, moose test, off-road recovery, etc. should be used to evaluate vehicle stability. For a test to capture the subtleties of the dynamics of a vehicle, especially when it is equipped with active systems, repeatability is critical [36]. The second generation automated test driver (ATD) being developed for this research will be able to perform these tests with much 124

145 better consistency than human drivers. Path Following Controller design and analysis is discussed in the following sections Single Track Vehicle Model Figure 58 Single Track Linear Model (Bicycle Model) In this section the well known bicycle model will be derived in terms of lateral displacement and yaw angle. Later it will be formulated in terms of error with respect to path. This formulation provides the lateral offset and orientation error from the desired path, which are critical to solving the path-following control problem. To begin with, the standard bicycle model is shown in Figure 58. Applying Newton's second law to the vehicle body frame y axis (pointing to the driver's left) gives: 125

146 = + (88) Now, = ( + ) therefore ( + ) = + (89) Moment balance about z axis yields: = (9) Tire forces are modeled to be proportional to the slip angle for small slip angles. The slip angle is defined as the angle between the orientation of the tire and the orientation of the velocity vector of the wheel. Slip angles can be written as follows: = + = (91) The lateral forces can now be written as: = 2 ( ) = 2 ( ) (92) The factor of 2 accounts for the fact that there are two wheels on each axle. Substituting from equations (91) and (92) into (89) and (9) and rearranging yields the state space model 126

147 = (93) State Space Vehicle Model in Terms of Following Errors The following section re-defines the above representation in terms of path following errors because the objective is to solve the problem of steering control for path following. Figure 59 Path-following Error Coordinates Defining two variables shown in Figure 59 as follows, the distance of the center of gravity of the vehicle from the center of the lane, the orientation error with respect to the lane. Defining the desired rate of change of orientation as 127

148 = (94) The desired lateral acceleration can be written as and can be written as = (95) = ( + ) = + ( ) (96) = (97) = + ( ) (98) Substituting from equations (2.1) through (2.5) into (1.1) and (1.2) yields = (99)

149 = In state space form the above equations can be written as A = (1) Now the model is formulated in terms of path following errors and an adequate control law can be implemented using the above system matrices. 129

150 5.1.3 State Feedback If the feedback of the complete state vector is implemented then the closed loop system is = ( ) + (11) where = (12) = (13) 2 = (14) 2 The feedback state vector is = [ ] (15) 13

151 The feedback gain vector being = [ ] (16) Steer angle therefore is = (17) Closed-loop poles are the eigenvectors of the matrix and they can be placed at any desired location. Simulations were performed to determine response to a step change in desired yaw rate. Parameters of the vehicle model used are listed in the Appendix. The gain matrix is determined for the arbitrarily selected closed loop poles: = [ ] Figure 6 shows the results of a simulation with the above designed state feedback. A radius of 1 m is desired at a longitudinal speed of 2 m/s. This results in a desired yaw rate of deg/s. The handwheel angle necessary for the desired yaw rate is determined by the controller to be 32 deg. The closed poles result in adequately damped system. There is a steady state error of.25 m in lateral position. 131

152 Figure 6 State Feedback Simulation Results: Path Following Performance The above example is taken from [59] to demonstrate the use of error coordinates of center-of-gravity as full state feedback for path-following. A more useful implementation of path following error feedback is discussed here. Lateral position of the path is measured at a location ahead of the vehicle instead of center-of-gravity. Assuming small yaw angle error, lateral offset can be approximated as, 132

153 + (18) Bearing error from desired path is Feedback law for bearing error therefore is = = + (19) The gain matrix is = = + (11) = 1 1 (111) Figure 61 Path Following Block Diagram [65] Figure 61 shows the block diagram of the path following problem with lookahead lateral offset feedback. The desired path affects the states (lateral offset) and (yaw angle 133

154 error) through transfer function G. The sensor is represented by the matrix 1 and the controller is a constant gain, k. Now that the closed loop transfer function of the control system is known, performance and sensitivity to parameters can be studied effectively. Phase margin and gain margin are important characteristics of a control system. Gain margin for this controller is infinity. Figure 62 shows the variation of phase margin with respect to the lookahead distance and longitudinal speed. Figure 62 Phase Margin with respect to Speed And Lookahead Distance 134

155 As intuition suggests, the phase margin Increases with increasing lookahead distance. Decreases with increasing speed. Somewhat less intuitive and not so obvious trends in the phase margin are that it is Less sensitive to speed at large lookahead distance. More sensitive to lookahead distance at higher speed. Figure 63 Root Locus with respect to Lookahead Distance At all speeds, a large enough lookahead can be chosen for the phase margin to be higher than 6 deg which is ideal for most systems. Figure 63 and Figure 64 show the root locus with respect to lookahead distance and feedback gain. Increasing lookahead distance makes the system more damped. Though large feedback gain gives a smaller steady state error, it makes the response increasingly oscillatory. 135

156 Figure 64 Root Locus with respect to Feedback gain Analysis presented so far yields the trends of closed loop system properties with varying lookahead distance and longitudinal speed. The model helps quantify the closed loop dynamics so that the lookahead distance and feedback gain can be chosen for varying vehicle speeds. Furthermore the path-following error state space representation is more suitable to evaluate path following performance than the standard bicycle model in terms of yaw rate and lateral velocity. Next section introduces an energy based method applied to the path-following problem to quantitatively derive the stability conditions and chose lookahead distance and feedback gain vector for varying speed. 136

157 5.2 Path Following in a Virtual Potential Field Modern and future automotive assistance systems like lane-keeping systems and collision avoidance systems control the vehicle motion in response to the environmental conditions. Vehicle dynamics is linked to the path ahead and obstacles on the path. Researchers have shown the interpretation of assistance systems as potential fields added to existing vehicle dynamics and driver inputs [62]. Virtual potential field framework was introduced in the context of robotic control and autonomous path following. The potential function is an intuitive way to represent the level of hazard experienced by the vehicle [63, 64]. The analogy is that of a charged particle traveling in an electric field. Vehicle dynamics present limitations or bounds to the trajectory the vehicle can track at a particular speed. This section details an analysis of a path-following problem in the context of virtual potential field. It is presented in order to calibrate the feedback gain to guarantee stability of the closed loop path-following controller. The conditions of stability obtained from [62] are combined with the phase margin analysis of the previous section in order to obtain a non-linear relationship between speed and lookahead distance to guarantee stability. An exaggerated representation of a lanekeeping potential is shown in Figure 65 where the potential function minimum is at the road center with height increasing towards the lane edges. The path following error intrudes the potential field and generates a virtual force on the vehicle. The path coordinates are associated with an artificial energy potential. The gradient of this energy provides the necessary virtual force that 137

158 returns the vehicle to the lowest energy region (the lane center). The virtual force is interpreted by the controller and physically realized by steer-by-wire and brake-by-wire actuator systems. The automated test driver has essentially a controlled steering system without any direct driver input. This chapter deals with applying the potential field concept to an autonomous vehicle with no driver inputs. The general idea is applied to development of a path-following controller. The formulation here is general system dynamics with combined driver and controller inputs. In the ATD application, however, the driver input is absent and the controller component is the only input. Figure 65 Virtual Potential Field 138

159 First the vehicle dynamics equations are written in the form most suitable for analyzing qualitatively the potential field strength. In other words, energy dissipation by lateral forces is related to the energy potential of the virtual field in order to calibrate the strength of the field necessary to keep the vehicle within the lane boundary. The Potential Energy function is assumed to be of the form = (112) The restoring force is generated by the lateral error at a projected lookahead distance. ( ) = ( ) = ( + sin ) (113) The controlled terms constituted by the forces and moments are combined into a virtual force to be applied at a distance from the center of gravity. = 2( + ) = 2( + ) (114) Writing vehicle dynamics equations in the virtual force framework from [62-64], = ( ) + cos + ( ) cos = ( ) cos + ( ) (115) 139

160 Using the transformation from global to body-fixed coordinates = cos + sin gives = sin cos cos (116) Substituting from equation (116) into (115) and applying small angle approximations sin and cos 1 the linear closed-loop system matrix is obtained as 1 2 ( + ) ( + ) 2 ( + ) = 1 2 ( + ) ( ) 2 ( + ) (117) 14

161 5.2.1 Closed Loop Stability From the linearized closed loop system matrix 1 2 ( + ) ( + ) 2 ( + ) = 1 2 ( + ) ( ) 2 ( + ) (118) The characteristic equation is = (119) where = + + ( + ) = ( + ) ( + ) = 2( + + ( + ) + + (12) = Linear system analysis provides useful insight into how the configuration parameters affect the stability and response of the controlled system. The distance of control force application is an important parameter for stability. It can be derived from the characteristic equation that the system is stable for: 141

162 > + (121) Figure 66 and Figure 67 show the locus of closed loop poles as the the point of application of control force moves from behind the center of gravity to front of the center of gravity and the lookahead distance increases. For a front steering vehicle the point of application of control force is the front axle, =. Figure 66 Effect of Control Force Application Point There is a limitation on where the application point can be. If the application point is such that the system is stable, increasing the lookahead distance provides for adequate damping. 142

163 Figure 67 Effect of Lookahead on Closed Loop Eigen Values 143

164 5.2.2 Calibration of the Potential Function Gain: Lyapunov Function The discussion so far was about the effects of the configuration parameters namely, the lookahead distance and the control force application point. The analysis assumed that the potential function gain in the energy equation is known. This section covers the calibration of the potential gain in order to satisfy the requirements of path following error. The Lyapunov method is used to determine a relationship between the potential and lookahead distance to guarantee system stability and path following performance. As only a negligible fraction of longitudinal energy is converted into lateral dynamics, the longitudinal motion is ignored and only energy in the lateral states is used for the Lyapunov function. Rewriting the dynamic equations only in two lateral states = () (122) = (123) ( ) = = ( + sin ) (124) = ( + ( + )) (125) = ( ) (126) Comparing the restoring force from the potential to the terms excluding the ones depending on velocities 144

165 = ( ) + + (127) = (128) Assuming the potential function to be of the quadratic form, the restoring force must be negative which is possible if = + 2 (129) = + + (13) Writing the potential as = 1 2 (131) Where = 2 (132) 2 And = = 2 (133) = ( ) 145

166 = 4 = ( ) (134) > + (135) This is the condition for stability obtained before. The control force application point for most vehicles is located at the front axle. = which satisfies condition (135). Substituting the lookahead condition from (129) into the feedback gain matrix (111) = + 2 = [1 ] The control force gain is = (136) It has been shown that the above feedback law guarantees stability of the closed loop system. Phase margin plot using above feedback law for varying speed helps choose the lookahead distance. The plot is shown in Figure

167 35 Looakhead vs. Speed 3 25 Looakhead (m) Speed (mph) Figure 68 Nonlinear Relationship Between Lookahead Distance and Speed The analysis presented in this section combined with the previous section allows one to determine the lookahead distance and gain based on vehicle parameters to guarantee stability of the closed-loop path-following controller. Lyapunov method allows for gain selection based on conditions on lookahead distance and cornering stiffnesses. Phase margin analysis determines the gain as a function of speed and lookahead distance. Combining the two identifies a nonlinear curve for lookahead distance as a function of speed as shown in Figure

168 5.3 Highly Dynamic Path Following: Yaw Acceleration Control The path-following problem defined in the previous chapters pertained to steady state control. Lanekeeping controller design assumes straight or small curvature roadway. Applications of the ATD such as the Constant Radius Test (CRT) even though it is a high lateral acceleration test, is a quasi-steady state application. One of the goals of this research was to develop a path-following controller that is capable of keeping the vehicle on the path even for dynamic maneuvers like single/double lane changes, quarter circle turn or any other maneuver that has a high rate of change in path curvature. Such paths are appropriate for testing the vehicles for stability/controllability issues. Researchers have shown the use of the virtual field concept in designing a lane keeping system with slowly varying disturbances, with limitations being the validity of the method only in the linear range of vehicle dynamics and slowly changing path curvature. This chapter explains the path following method for transient or dynamic paths. The method uses the path geometry and current vehicle states to generate the desired yaw acceleration signal to negotiate the curve. A Kalman filter estimates tire forces from the measured vehicle states which provides the incremental force necessary to meet the desired yaw acceleration. 148

169 Consider the path following scenario, Figure 69 Path Following Geometry The path information is saved as a 3 dimensional array of Cartesian coordinates and heading (x,y,φ). The desired yaw angle change, φ can be computed as the difference between the path heading at the goal point and current vehicle heading, = (137) R1 and R2 can be found out by the Sine rule, sin cos( ) cos = = 1 2 (138) The radius of curvature for the lookahead path segment can be assumed to be an average of R1 and R2. 149

170 = (139) Knowing the average radius and assuming that the vehicle travels the lookahed distance at a constant speed (not a necessary assumption: longitudinal acceleration can be easily included in this equation), the time taken to travel the arc length is given by Δ = (14) The yaw acceleration desired can now be computed from the first law of motion in angular terms, = ( ) (141) Substituting for and simplifying we get = (142) The yaw equation of motion for the vehicle is = (143) = 1 ( + ) The desired increment in the front lateral force can be written as Δ = Δ (144) 15

171 = ( ) The desired roadwheel angle can then be written as = (145) Everything on the right hand side of the above equation is known. This forms the control action for the desired trajectory control based on yaw acceleration. The cornering stiffness can be estimated from a learning run in which the vehicle is driven to a high lateral acceleration limit. The Kalman filter then estimates the front and rear forces as explained in chapter 3. This can be performed in real time if computational resources allow, so the actual effective cornering stiffness can be used in real time. A nonlinear tire model is included in the computation of the desired road wheel angle. Test results for a few dynamic maneuvers using this method are shown and discussed in the following section. A quarter-circle desired path is used as the dynamic path. Complete circle paths have been discussed before to demonstrate the application of the ATD. The difference here is that there is not enough time for the vehicle to enter a steady state and the path following performance is evaluated during the transient vehicle response. 151

172 (yaw rate, lateral velocity) Vehicle States (position, speed, yaw rate, lateral velocity) Figure 7 Path Following by Yaw Acceleration Control Block diagram Position -5 North (m) Desired Path Actual Path East (m) Figure 71 Quarter Circle Path: low g 152

173 Handwheel Angle (deg) Lateral Acceleration (g's) Handwheel Angle Time (sec) Lateral Acceleration Time (sec) Yaw Acceleration (deg/sec 2 ) Speed (m/s) Speed Time (sec) Yaw Acceleration Desired Actual Time (sec) Figure 72 Quarter Circle Path-following: Lateral Acceleration =.2 g's 153

174 Position Desired Path Actual Path North (m) East (m) Handwheel Angle (deg) Lateral Acceleration (g's) Figure 73 Quarter Circle Path: high g Handwheel Angle Time (sec) Lateral Acceleration Time (sec) Speed (m/s) Yaw Acceleration (deg/sec 2 ) 1 5 Speed Time (sec) Yaw Acceleration 5 Desired Actual Time (sec) Figure 74 Quarter Circle Path-following: Lateral Acceleration =.5 g's 154

175 It is clear and intuitive that path following is better with decreasing lookahead distance. The Lookahead distance for the above plotted runs is 7 m, roughly half of the 15 m radius of the path. The lookahead distance is of the order of path radius. A major benefit of this method is that it allows the lookahead to be large without significant loss of path following performance. This is due to the fact that the algorithm tries to follow the lookahead path trajectory by computing the desired yaw acceleration instead of just pointing at the goal point as in the pure pursuit method. Although looking closer corrects for errors aggressively, the control input can be oscillatory. Path following performance in all these runs is satisfactory considering the fact that the paths are highly dynamic and transient portions are also negotiated with errors of less than 3 cm. This method is demonstrated for the purpose of testing vehicles in maneuvers with specified longitudinal speed. The controller outputs the steering command necessary to negotiate a path. This method of yaw acceleration control can be applied as an active steering controller for yaw stability. In that case the steering command is generated in order to match the desired response while keeping the vehicle stable. The goal then is to keep the vehicle states within bounds to maintain controllability and not to maintain any desired path. The method easily lends itself to be useful to combine the path following and stability objectives. In other words, the active steering can be in the loop with the path following controller. The active steering command is generated based on a combined desired lateral acceleration and yaw acceleration. The Kalman filter outputs guide the high level controller to weigh the desired yaw and lateral response based on current forces and vehicle capability in order to maintain the path and stability. 155

176 5.4 CarSim Simulations: Yaw Acceleration Control Introduction CarSim software was used along with MATLAB to simulate the method developed for severe path-following maneuvers. The focus of this set of simulations is to show the performance of the control method in the transient portion of a maneuver. The paths simulated require high frequency steering reversals and high lateral acceleration with tire forces well into the nonlinear region that is typical of evasive maneuvers like obstacle avoidance, road-edge-recovery, etc. Yaw acceleration control method uses the knowledge of tire forces and tire force/slip angle curve characteristics defined by cornering and coefficient of friction estimated using the method explained in section Figure 75 shows the block diagram of the implementation. Two paths (single and double lane change) were simulated at two different acceleration levels (.3 g s and.7 g s). Figure 75 CarSim Path-Following Block Diagram 156

177 5.4.2 Single Lane Change: Low g 4 ATD Path-Following Controller Compared to CarSim Closed-Loop Control Lateral Distance (m) Desired Path CarSim ATD Longitudinal Distance (m).4 Lateral Acceleration 1 Yawrate.2 5 g's deg/s Time (sec) Handwheel Angle Time (sec) Lateral Force 4 2 front rear deg (N) Time (sec) Slip Angle (deg) Figure 76 CarSim Simulation of Single Lane Change: Low g 157

178 5.4.3 Single Lane Change: High g 4.5 ATD Path-Following Controller Compared to CarSim Closed-Loop Control Lateral Distance (m) Desired Path CarSim (p=1s) CarSim (p=.75s) CarSim (p=.5s) ATD Longitudinal Distance (m) 1 Lateral Acceleration 4 Yawrate.5 2 g's -.5 deg/s deg Time (sec) Handwheel Angle Time (sec) (N) Time (sec) 1 x 14 Lateral Force front rear Slip Angle (deg) Figure 77 CarSim Simulation of Single Lane Change: High g 158

179 5.4.4 CU Short Course: Severe Double Lane Change: Low g 4 ATD Path-Following Controller Compared to CarSim Closed-Loop Control Lateral Distance (m) Desired Path ATD Longitudinal Distance (m).4 Lateral Acceleration 1 Yawrate.2 5 g's deg/s Time (sec) Handwheel Angle Time (sec) Lateral Force 4 2 front rear deg (N) Time (sec) Slip Angle (deg) Figure 78 CarSim Simulation of Double Lane Change: Low g 159

180 5.4.5 CU Short Course: Severe Double Lane Change: High g ATD Path-Following Controller Compared to CarSim Closed-Loop Control Desired Path CarSim (p=1s) CarSim (p=.75s) CarSim (p=.5s) ATD Lateral Distance (m) Longitudinal Distance (m) 1 Lateral Acceleration 4 Yawrate.5 2 g's deg/s Time (sec) Handwheel Angle Time (sec) 1 x 14 Lateral Force.5 front rear deg -2 (N) Time (sec) Slip Angle (deg) Figure 79 CarSim Simulation of Double Lane Change: High g 16

181 5.4.6 Results Discussion The path-following performance of the control method proposed for ATD is compared to that of CarSim in-built closed-loop control. Plots for low acceleration maneuvers are shown in Figure 76 and Figure 78. The ATD control method performs just as well as CarSim. The handwheel angle amplitude is about 3 degrees and the tire forces are in the linear range. High acceleration maneuvers on the other hand show a difference in path-following performance as shown in Figure 77 and Figure 79. The path-following errors are large because of the severity of the maneuver as tire forces are in the nonlinear region in single lane change and almost saturated in the double lane change. The ATD performs significantly better than CarSim in terms of path-following error and oscillations. The simulations were run with three different values of the CarSim preview parameter. The values used were.5 sec,.75 sec and 1 sec. Smaller the preview, better the first turn performance but the overshoot and oscillations are much worse as expected. The proposed ATD control equation is dependent only on the tire force characteristics and lookahead distance. The lookahead distance values can be chosen as a function of speed and frequency based on the linear system analysis presented in section or methods presented in [13]. If a stable lookahead value is chosen the overall performance is robust with much better accuracy than CarSim. 161

182 CHAPTER 6 LONGITUDINAL CONTROL: BTR 6.1 Introduction This chapter describes the design and implementation of the SEA, Ltd. Brake and Throttle Robot (BTR). Presented are the criteria used in the initial design and the development and testing of the BTR, as well as some test results achieved with the device. The BTR is designed for use in automobiles and light trucks. It is based on a servomotor driven ballscrew, which in turn operates either the brake or accelerator. It is easily portable from one vehicle to another and compact enough to fit even smaller vehicles. The BTR is light enough so as to have minimal effect on the measurement of vehicle parameters. The BTR is designed for use as a stand-alone unit or as part of a larger control system such as the Automated Test Driver (ATD) yet allows for the use of a test driver for safety, as well as test selection, initiation, and monitoring. Installation in a vehicle will be described, as well as electronic components that support the BTR. Operational modes and controls will be examined, followed by testing and results. This chapter will close with an evaluation of the BTR and a brief view of possible future avenues of development and testing. 162

183 6.2 Background There is a need for a brake and throttle actuator in automotive and light truck testing. Properly designed, such a device can provide more consistent and repeatable actuation and test results than a human driver, and can be used in tests that are beyond the capabilities of a human driver or where safety concerns preclude the use of such a driver. A number of existing studies detail the development of automotive brake controllers, but none of them feature the portability and ease of adaptation necessary for the flexible testing of a variety of vehicles. Many studies implement brake control via alternate actuators that bypass the mechanical pedal linkages by directly controlling the brake fluid pressure. Others employ the vehicle s brake system and linkage, but still require significant and permanent vehicle alteration. The BTR featured herein is the second version to be built and tested. An earlier version was part of an automated test driver project and performed well. The second version was designed to have the same functionality, portability, and light weight of its predecessor as a stand-alone unit or as part of an automated test driver or similar device, and therefore borrowed much of the design from the first version. 163

184 6.3 Design and Development The design of the first version of the BTR began with a survey of many vehicles. Locations and angles of pedals, accelerator pedal force requirements, and potential mounting methods were looked at for passenger cars, SUV s, and pickup trucks. The first version of the BTR used a servomotor to drive a precision ballscrew. Depending on its direction of rotation, it operated either the brake pedal or accelerator pedal through mechanical linkages attached to the pedals. Though this first version performed well, there was a desire for increased performance, and some upgrading was required to better optimize the BTR. The second version has increased force capacity, faster application of force, increased durability, and the ability to directly measure the component of force applied normal to the brake pedal. These goals were achieved by retaining the same basic servomotor and ballscrew design of the earlier version, while modifying existing features and adding additional features as required to upgrade the unit. Guiding these design goals were criteria enabling accurate adherence to a vehicle speed profile as well as the specifications from various SAE test standards. One instance of the latter type is the SAE Service Brake Structural Integrity Test Procedure, which stipulates that brake pedal force be ramped from zero to 2 lb at a rate of 25 lb/s. Another example is the standard brake burnishing procedure associated with many SAE tests which requires two hundred 4- mph stops at 12 ft/s 2 deceleration (a tiresome exercise that few human drivers can accurately maintain). Specifically, the design goals for the current version BTR were as follows: 164

185 1. Capacity for 2 lb (89 N) of force perpendicular to the brake pedal. 2. Capacity for brake application time of.25 seconds at full rated load. 3. Not more than 2 lb (9 kg) of weight in the main base component. 4. Electrical limitations of 35 amps at 72 volts. 5. The unit should be able to be installed in a vehicle in about 3 minutes. 6. The unit should be fail-safe in case of electrical shutdown. If the power fails the throttle goes to idle and the brakes are applied. 7. The driver can override the system at any time. 8. The driver can sit in the vehicle in the normal position. 9. Position feedback control on the throttle, and force or position feedback control on the brake. 1. Algorithms for vehicle speed control. The force, speed, and size specifications (1-4 above) are a function of the motor size and hardware configuration. BTR s with different actuation capacities could be designed and built using different motors and minor hardware modifications. The BTR is shown mounted in two different vehicles in Figure 8 and Figure 81. The basic layout of the BTR mechanism is shown in Figure 82. A servomotor drives a ½ inch (12.7 mm) ballscrew. The ball nut moves laterally in the vehicle. Attached to the ballnut is a plate that acts as a face cam. At the cam s neutral position, neither the throttle nor the brake is applied. When the ball nut and face cam move to the right, the throttle is 165

186 applied through the action of a lever and rod arrangement. When the ball nut moves to the left from the neutral position the brake is applied, again through a lever and rod arrangement. Stops on both of the levers prevent either the brake lever or the throttle lever from going past their neutral positions. The face cam is not connected to either of the levers; it merely applies force in one direction. To retract the brake or throttle requires the action of the springs on these pedals. There is also a linear constant-force spring that pulls the face cam to the left with a force of about 1 lbs (45 N). In the event of a power failure or intentional shutdown of the motor, this spring is enough to backdrive the ballscrew and motor, and to lightly apply the brake. There is no brake on the motor. There is little friction in the lever attached to the throttle, so the spring in the throttle is enough to return the throttle to idle once the face cam is pulled out of the way by the linear spring. Releasing a thumb or foot switch can also shut down the system. Figure 8 BTR Mounted in Vehicle 166

187 Figure 81 The BTR With The Cover Removed Showing The Internal Mechanism Figure 82 Close-up View of BTR Mounted in Vehicle The body of the BTR sits on the floorboard of the vehicle just in front of the base of the driver s seat. This is normally behind the driver s feet, and it has a metal cover to keep the driver s clothing and feet out of the mechanism (See Figure 82). The actuating rod for the throttle goes from the right side of the actuator to a fitting mounted to the right side of the throttle pedal. On the brake side the actuator rod goes to 167

188 the left side of the brake pedal. This arrangement allows the driver to still get his foot comfortably on both the brake and throttle pedals. The driver keeps his right foot between the actuator rods, and applies the brake or throttle as he normally would. Typically, he would keep his right heel in a central location and pivot his foot as necessary. This drivability feature is important in that test vehicles are often driven from a garage to a test location without the Brake and Throttle Robot being active. In this manual drive mode where the BTR is present in the vehicle but not active, there is a mechanical block that can be inserted such that the linear spring and the block serve to keep the face cam at the neutral position. Since the face cam is not attached to either of the levers, it does not prevent the driver from applying either the brake or the throttle at any time. This design arrangement makes it impossible to apply the brake and throttle at the same time. The designers felt that there would rarely be a vehicle test in which one would need to do this, and that using a single motor to actuate both the brake and throttle made for a simple and compact arrangement. On the throttle side there is position feedback control via the rotary encoder attached to the servomotor. Before a test the system learns what encoder reading corresponds to the neutral cam position, and what encoder reading corresponds to the full throttle position. Brake control is accomplished through position control using position, deceleration, or force feedback. During development the force feedback was accomplished in two ways. The simplest option was with a load cell in the brake actuating rod reading the total force 168

189 directly being applied to the brake pedal through the actuating rod. This is good enough for basic vehicle maneuvers. A second method of measuring brake force is to measure only the component of the rod force that is perpendicular to the brake pedal face. This can be done using a suitable arrangement of pivots and a button type load cell, or it can be done with a commercially available sensing unit. In either case, the vehicle deceleration will not necessarily be proportional to the force perpendicular to the brake pedal, as there are many other sources of non-linearity in the braking system. 6.4 Installation The BTR is simple and quick to install. One places the device in the driver s footwell of the vehicle, restrains the BTR as needed and attaches the actuator rods to the pedals. Several features can be used in combination to restrain the BTR. First the mass of the unit is sufficient to prevent the reaction torque from lifting the BTR off the floor. Second, the rear edge of the BTR is positioned against some feature at the rear of the footwell, such as a ridge in the floorboard or the rails to which the driver seat is attached (See Figure 82). This counteracts the rearward pedal reaction force. Third, a ratchet strap is threaded through tie-down rings on the BTR s rear corners to the driver seat base, further securing the BTR. Fourth, a turnbuckle type strut may be used between the dash and the BTR to hold the front end down. Finally, Velcro pads may be attached to the bottom of the BTR base to adhere to the vehicle carpet to resist shifting of the BTR. Movement of the body of the actuator should be minimized, since this affects position accuracy when using position feedback. 169

190 Once the main body of the BTR is in place the actuator rods are attached. There are two actuator rods coming from the BTR, one for the brake pedal and one for the accelerator pedal. The rods each have spherical bearings attached to one end. The pedal ends of the rods are attached to small plates clamped to their respective pedals, thus advancing the pedal as the actuator rod is advanced by the BTR. The rods are designed such that their lengths can be adjusted to fit the specific test vehicle. 6.5 Controls The motor controller and motor power supply for the BTR are the same as those used in the Automated Steering Controller (ASC), also made by SEA, Ltd. In these systems, a bank of six 12V batteries powers the motors and the control is provided by a National Instruments Compact RIO, along with a servo amplifier. The software, both control and user interface, is written in National Instruments Labview and, along with the ASC software is an integral part of the Automated Test Driver (ATD) software. With all parts of the software enabled, the ASC and BTR can work together to function as an ATD capable of, among other things, accurately following a path at a fixed speed or a speed profile. The algorithm includes traditional PID components, augmented with feed-forward to minimize following error for large changes (step or near-step) in the desired brake or throttle positions. There are four modes available for the BTR: Open Loop, Speed Control, Speed Control and BTR, and Manual. The Open Loop mode is commonly used with a pedal position profile where the pedal position is a function of time. In this case, a 17

191 simple text file with two columns, time and pedal position, will govern the BTR. The Speed Control mode uses feedback from a speed sensor (either through CAN or analog input) to control the speed. Again, a simple text file may be used with time and speed columns, or vehicle position and speed columns. The Speed Control and BTR mode is for a maneuver with a closed-loop initial phase and with an open-loop final phase. The Manual mode is for when no control is needed only data acquisition. This mode is important when recording a path (position and speed profiles) for use in the path following routines. The deadbands, or the amount of pedal travel before the start of pedal effect, for the brake and the throttle pedals must be determined for each vehicle. These deadbands are entered in the Brake-Throttle Robot window of the ATD software. Typically, no tuning is necessary the control algorithm is robust and standard tuning parameters will suffice for a wide range of vehicles. The performance is significantly improved by adding an acceleration term to the control equation as shown below. = + + (146) : The error in desired speed : Proportional gain : Integral gain : Desired acceleration gain 171

192 Once the BTR has been installed, a process that takes about 3 minutes, the operator can begin running tests immediately. The user interface allows for the selection of files containing the desired profiles, or the user may use the ATD to record a brake/throttle profile. Figure 83 ATD Brake-Throttle Robot Tab Figure 83 shows the Brake-Throttle Robot tab of the ATD software. In this tab, the user can specify vehicle specific BTR ranges, BTR rate limits, and BTR control parameter gains, as well as select the specific BTR mode and input conditions. The software provides plotting capabilities, so test results can be viewed immediately after the maneuver has been completed. 172

193 6.6 Testing and Results The following test results will demonstrate that the BTR is capable of: Pedal position control Vehicle speed control Vehicle deceleration control Integration with the ASC and a GPS system for the Automated Test Driver (ATD) to provide full vehicle speed and path following control. Fixed Pedal Position Deceleration BTR Position (%) Desired BTR Position "Low " Actual BTR Position "Low " Desired BTR Position "Medium" Actual BTR Position "Medium" Longitudinal Acceleration (g) Low Decel Medium Decel Time (sec) Figure 84 Brake Position Control 173

194 Pedal position control is an important part of this system because the speed control algorithm uses pedal position in its feed-forward components. To demonstrate the pedal position accuracy, the subject vehicle was slowed from two speeds (5 kph and 27 kph) using a fixed brake pedal position. Figure 84 shows that the pedal position control was excellent and that this resulted in a constant or slightly increasing deceleration after the initial dynamic pedal application phase. The pedal position in Figure 84 is expressed as BTR Position as a percent of full-scale brake pedal position. In this paper, negative BTR positions indicate braking, and positive BTR positions indicate percent full-scale throttle position. For both levels of brake application ( Low and Medium ), the lines for Actual BTR Position lie on top of the lines for Desired BTR Position. Although pedal position control is important in itself, it is the main control component of the typical control methods speed, acceleration, or force control. Some tests, such as the constant speed technique for determining understeer gradient require a set vehicle speed, so accurate speed control is beneficial. In many cases, a human driver can adequately maintain the desired speed, but if there are perturbations, such as bumps or steering maneuvers, speed control becomes more difficult. In other cases, a varying speed profile is necessary. 174

195 4 Speed Control 35 Speed (kph) Desired Speed Run 1 Run 2 Run BTR Position (%) Time (sec) Figure 85 Vehicle Speed Control Figure 85 shows the ability of the BTR to control the speed with a changing speed profile. The speed control was always within 1.5 kph and typically within about.5 kph with a change from 2 kph to 35 kph. The speed and BTR position are shown to be very repeatable for the three runs shown on Figure 85. A planned change in the control strategy is expected to reduce the frequency of the oscillations about the steady-state speed while maintaining the fast response to the desired speed change. 175

196 Some tests, including the preliminary Forward Crash Warning System Confirmation Test evaluation method being studied by the NHTSA, require a constant deceleration. One deceleration level proposed by NHTSA in its preliminary method of November 27 is.32 g. with a tolerance of.3 g. It is relatively easy to block the brake pedal to a fixed position, or use a non-controlled actuator to get an approximately constant deceleration. However, this deceleration may not fall within the tolerance specified, especially when brake temperature is a consideration; heating of the brakes may require adjusting the pedal position. Evaluating one vehicle provided a quick estimate of this effect, that heating the brakes can result in a change in deceleration at a fixed pedal position of about 1%. Using the BTR to control the pedal position based on deceleration feedback can eliminate this error. Figure 86 shows controlled decelerations from 5 kph, while Figure 87 shows controlled decelerations from 35 kph. In all cases, the decelerations stabilize at the intended magnitude within about.4 seconds and are held accurately until the vehicle speed approaches zero. The repeatability of deceleration profiles from both initial speeds is very good. The ultimate goal of the BTR was its successful integration into the Automated Test Driver (ATD), a system that includes the Automated Steering Controller (ASC) for steering actuation and a high-end GPS-inertial navigation system (Oxford Technical Solutions model RT32) for position sensing. The ATD is capable of path following at a wide range of speeds, including varying speed profiles. Figure 88 shows test results with the BTR integrated as a component of the Automated Test Driver (ATD) in a figure-8 maneuver. The maneuver path was recorded, and it was repeated three times in succession by the ATD. For this maneuver, 176

197 the desired speed was set to be constant at 32.2 kph (2. mph) and the ASC controlled the steering to keep the vehicle on the desired path. The path was very accurate, with the absolute deviation from the recorded path typically less than.3m and repeatability (distance between actual paths) typically better than.3 m. Results from the three loop cycles are shown on Figure 88. The vehicle speed, BTR position, lateral acceleration, and handwheel angle results are all very repeatable. This maneuver was moderately severe, as the lateral acceleration ranged between +/-.5 g. Nonetheless, the speed was controlled to within +/- 1.5 kph. 177

198 Acceleration (g) Deceleration Control - From 5 kph Desired Acceleration Run 1 Run 2 Run 3 Acceleration (g) Deceleration Control - From 35 kph Desired Acceleration Run 1 Run 2 Run Speed (kph) Speed (kph) BTR Position (%) BTR Position (%) Time (sec) Time (sec) Figure 86 Constant Deceleration (-.32 g) from 5 kph Figure 87 Constant Deceleration (-.32 g) from 35 kph 178

199 3 2 East (m) 1 Goal Path Path for 3 Cycles Start of Cycles North (m) 36 6 Speed (kph) BTR Position (%) Lateral Acceleration (g) Time From Beginning of Cycle (sec) Handwheel Angle (deg) Time From Beginning of Cycle (sec) Cycle 1 Cycle 2 Cycle 3 Figure 88 Following a Recorded Path with Speed and Steering Control 179

200 6.7 Summary and Conclusions This chapter has presented the design, development, and implementation of a Brake and Throttle Robot (BTR). This unit has been developed into one that provides quick application of sufficient force to operate the brake and the throttle of any passenger car, SUV, or light truck currently available. Brake and throttle pedal position are used for control, and feedback from these positions and/or vehicle states (such as brake pedal force, vehicle speed and vehicle deceleration) are be used to control the pedals. The BTR is portable, easy to install, able to be overridden by a driver if desired, and offers fail-safe protection in the event of power failure. The BTR has been demonstrated to be capable of pedal position control, and vehicle speed and deceleration control. Also, results from testing with the BTR integrated into an Automated Test Driver (ATD), with an Automated Steering Controller and a GPS system, are presented. Future testing of all of the BTR modes of operation will be conducted and additional development of the BTR and ATD will be continued. 18

201 CHAPTER 7 OTHER PRACTICAL APPLICATIONS Besides active stability control systems there are numerous other features currently being offered on automobiles that help prevent crashes by delivering to the driver warnings and alarms of dangerous situations. Application of the ATD in testing such systems will be explored. ATD functionality to interact with another vehicle must be added in order to accomplish this. The ATD will be enhanced using radio communication with a system on-board another vehicle. It will then be used to drive a vehicle to precisely follow that other vehicle, perform passing maneuvers, or even crash into another moving vehicle. If the ATD can be used, crash tests would no longer be restricted to the cable-pulled laboratory environment, but could be done more easily on a variety of road surfaces, into barriers, and over a range of impact angles. Compatibility studies on vehicle crashes involving vehicles of significantly different sizes would be easy to perform using the ATD. The ATD, because of its ability to drive a vehicle accurately on or off path offers usefulness in evaluation of lane departure warning systems. NHTSA, in a report on testing these systems expresses difficulty in making these tests repeatable [67]. Figure 89 shows some traffic situations governed by vehicle-to-vehicle coordination. Such maneuvers will be studied as a potential application of the automated test driver. 181

202 Figure 89 Vehicle - to - Vehicle Interaction Maneuvers for Testing Automotive Sensors (Credit: General Dynamics) When testing the effectiveness for automotive sensors such as collision avoidance systems, adaptive cruise control, etc., the vehicle equipped with the sensors must interact with other moving vehicles. For repeatable results, the accuracy of the relative motion between the vehicles is important. High accuracy can be achieved more readily by using the ATD rather than a human test driver. 182

203 7.1 Vehicle-To-Vehicle Interaction Modern passenger cars are being equipped with advanced driver assistance systems such as lane departure warning, collision avoidance systems, adaptive cruise control, etc. Testing for operation and effectiveness of these warning systems involves interaction between vehicles. While dealing with multiple moving vehicles, obtaining discriminatory results is difficult due to the difficulty in minimizing variations in vehicle separation and other parameters. This research describes test strategies involving an automated test driver interacting with another moving vehicle. The autonomous vehicle controls its state (including position and speed) with respect to the target vehicle. Choreographed maneuvers such as chasing and overtaking can be performed with high accuracy and repeatability that even professional drivers have difficulty achieving. The system is also demonstrated to be usable in crash testing: that cannot be reliably performed by human drivers. Open loop steering machines used for vehicle dynamic testing are necessary but not sufficient for these tests. An automated test driver (ATD) developed by SEA, Ltd [46] is capable of driving road vehicles accurately on a pre-programmed path. The ATD uses a differential GPS-INS solution to determine vehicle states as well as steering, brake and throttle actuators to control speed, position and heading as desired. A goal point - seeking algorithm runs in real time and adapts to the vehicle speed. This algorithm, explained in [61] is a combination of two types of preview methods. Depending on the speed it prepares a preview of the path ahead. A goal point on the path at a certain lookahead distance is determined. The lateral offset of the system computed by finding the bearing to the goal point is used to compute the steering angle. The control law is easily adapted to different vehicles by measuring a few parameters such as mass, centre of gravity and 183

204 understeer gradient of the vehicle. The method is outlined by Tseng et al [8]. The control equation is given by equation (1). Equations for speed control in the brake and throttle actuator are governed by a combination of feedforward and feedback control (equation (146)). The feedforward is based on the powertrain s response characteristic, which is identified from a simple semiautomatic tuning procedure. A PID controller forms the feedback element. Separate gains for acceleration and braking are used. Design of ATD and performance results on a variety of vehicles can be found in [13] ATD as a Relative Path Tracker In this work, the path-following functionality of the ATD is extended for position and speed control relative to another moving vehicle (target). The same path-following algorithm is used with an additional preview of the target vehicle. The next section describes the system in detail with application to an overtaking maneuver System Outline The ATD is capable of following not only an absolute path but also paths relative to another moving vehicle. The target vehicle has an on-board RTK (real time kinematic) differential GPS receiver. The GPS output of position, speed and heading is transmitted on radio frequency to the ATD, which reads this transmission and also its own state from the on-board GPS-INS (GPS Inertial Navigation System) package. This information is used to prepare the necessary preview information. Desired relative path is predefined in the ATD memory. The modified path-following algorithm applies a translation and 184

205 rotation transformation to the recorded desired path array to account for the current state of the target vehicle. Figure 9 shows the system block diagram and information flow in the algorithm. Goal point seeking is a function of two components: desired path and lookahead distance. The lookahead distance is determined from the current speed of the ATD. The desired path is determined by a transformation that adjusts for any variation in the target vehicle heading that might have occurred as it is driven by a human. It also adds a translational component based on the prediction of distance travelled by the target vehicle in the time the ATD takes to cover the lookahead distance. This can be considered a magnification of the desired path in the instantaneous longitudinal direction that takes care of the variation in the speed of the target vehicle maintaining the same relative position as prescribed. Figure 9 Relative Path Tracking Block Diagram 185

206 7.1.3 Overtaking Maneuver The relative path-following ability of the ATD has been demonstrated by an overtaking maneuver. The position relative to another vehicle is the parameter of interest (or control parameter ). Figure 91 shows a typical relative path tracking scenario. Figure 91 A Typical Path Tracking Scenario The relative path desired is defined in the moving target vehicle co-ordinates (X, Y). A predictive transformation based on the longitudinal speed of target vehicle is applied to the relative path desired. Another rotation transformation accounts for any variation in the heading of the target vehicle that may occur. Equations (147) and (148) and 4 show the co-ordinates of the path seen by the ATD (X, Y). Once the actual path 186

207 desired by the ATD is determined, the lateral error from the desired path at a lookahead distance is computed. The control law is the same as explained in the introduction. Equations for coordinates relative to ATD are: = cos( ) + sin( ) + ( ) cos ( ) sin (147) = cos( ) + sin( ) + ( ) cos + ( ) sin (148) Experimental Results The relative path in a passing maneuver is a single lane change path with respect to the target vehicle. The relative path desired is shown in Figure 92 and Figure 93. The normal lane change would involve the controlled vehicle moving into the target vehicle s lane after passing. For safety reasons, the demonstration involved a lane change away from the target vehicle. The control processes and accuracy metrics are the same for both. Figure 3 shows the results of a test where the target vehicle is at rest. Figure 93 shows the results where the target vehicle was moving at an uncontrolled speed. In both cases, the ATD successfully maintains the desired relative position despite the variation in target vehicle speed and position. That path-following accuracy was within 1 cm. 187

208 Figure 92 Relative Path Tracking With Target Vehicle At Rest Figure 93 Relative Path Tracking With Target Vehicle Moving 188

209 7.2 Choreographed Collision Test In this section a collision test strategy is discussed. The automated test driver has the ability to control lateral and longitudinal motion as required by the test objective. The objective in this case is the ability to crash into another moving vehicle at a specified speed. The collision scenario discussed in this section is not that of a vehicle aiming directly at another moving vehicle and hitting it. The objective, instead, is to target the moving vehicle, predict the point of collision and collide without appreciable deviation from the initial course. Figure 94 shows the scenario of such a collision test. Figure 94 Collision Scenario 189