Vehicle Stability Control of Heading Angle and Lateral Deviation to Mitigate Secondary Collisions

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1 Vehicle Stability Control o Heading Angle and Lateral Deviation to Mitigate Secondary Collisions Byung-joo Kim, Huei Peng The University o Michigan G41 Lay Auto Lab, University o Michigan Ann Arbor, MI Phone: Fax: bjukim@umich.edu The objective o this study is to develop a post-impact vehicle stability control system that regulates both heading angle and lateral deviation rom the original driving path, so that the severity o possible subsequent (secondary) crashes can be reduced. To characterize the vehicle motion ater a crash event, an impact orce estimation method and a vehicle motion prediction scheme are proposed. I the predicted unmitigated inal heading angle is undesirable, and/or a large lateral deviation is expected, then proper dierential braking and possibly steering action will be taken to drive the vehicle motion to a desired inal state. Simulations and analysis results o the proposed state estimation and prediction algorithm will be evaluated, ollowed by the presentation on the proposed control algorithm. 1. INTRODUCTION Topics / Active Saety & Passive Saety, Integrated Chassis Control Motor vehicle accidents are one o the major societal problems the world is acing today. Approximately. million motor vehicle crashes were reported to the police during 29 in the United States and about 33, persons were killed [1]. Some statistical studies [2-4] show that over 3% o all crashes have two or more harmul events ollowing the initial collision. In about 7% o these multiple event crashes, the secondary harmul event is a collision with another vehicle. The remaining secondary events consist o collisions with ixed objects (23%), such as trees or utility poles, and rollovers (7%). It is also shown that risks o both injury and atality increased with the number o collision events [2]. Moreover, A National Highway Traic Saety Administration (NHTSA) crash analysis report or advanced restrained system [4], based on the data rom 1988 to 24, shows the vehicle spin angle distribution in the most harmul secondary event crashes by multiple impacts. As shown in Fig. 1, around 8% o the cases involved 9 turns to either clockwise or counter clockwise that caused results o high-risk secondary crashes. Since the sides o vehicles are more vulnerable than ronts and rears in terms o absorbing crash energy and shielding occupants, the risk o atal and serious injury to occupants is estimated to be high. This report also shows that 3% o atalities in the driver and ront-seat passenger 13 years old or older were ront to side impacts based on Fatality Analysis Reporting System (FARS) crash databases. To prevent and reduce vehicle crashes, various Fig. 1. Vehicle spin angle distribution o the most harmul secondary event crashes with multiple impacts. (CW: Clockwise, CCW: Counter clockwise) [4] vehicle saety systems have been developed. Among them, the vehicle yaw stability control system, called Electronic Stability Control (ESC), has demonstrated positive eects on reducing single vehicle crashes [, 6]. However, its eect on secondary crashes has not been ully analyzed. Since these control algorithms are not speciically designed to intervene ater a vehicle-tovehicle impact occurs, only limited control actions can be applied. Moreover, under typical high speed driving conditions, even a minor collision between vehicles can lead to devastating consequences i the driver ails to react properly. Hence, it is critical to actively maneuver the vehicle to avoid subsequent accidents or mitigate their severity. I the vehicle sensors and control actuators still unction normally, there is a chance to stabilize the vehicle to counteract the undesired vehicle motion ater an impact. Using steering or braking actions ater a minor collision has been studied in the literature. Chan et al. [7] developed a steering control system in a post-impact situation to stabilize the vehicle. Bosch introduced a

2 Secondary Collision Mitigation (SCM) saety eature linked with an airbag control unit as a part o their CAPS (Combined Active and Passive Saety) system [8]. Yang et al. [9, 1] proposed an optimization scheme using dierential brake to minimize the maximum course deviation induced by an impact. And, Zhou et al. [11, 12] developed a control measure to mitigate vehicle post-impact skid and yaw motions rom an external initial impact. Although these systems are able to stabilize yaw motion and minimize lateral deviation rom the original course, the threat o a vulnerable heading angle to subsequent collisions with another moving vehicle or stationary object still exists. For example, i the vehicle is broadsided by another vehicle, the occupant may suer more severe injury than the case with ront or rear-end collisions. The objective o this study is to design a vehicle motion stabilization system by predicting the heading angle induced by an external impact. The system can then control vehicle spin motion to reach a sae heading angle (, 18, 36, etc.) through proper activation o dierential braking and possibly steering. It is envisioned that this system may help to reduce the probability o occurrence and severity o secondary crashes. The remainder o this paper is organized as ollows. To predict a vehicle state ater an impact, the strength o impact is predicted by a proposed algorithm presented in Section 2. The vehicle motion characteristics are investigated using simulation in Section 3. And possible control actions based on the optimization scheme are shown, and its eectiveness or vehicle motion is demonstrated in Section 4. Finally, conclusions and uture work are drawn in Section. 2. IMPACT FORCE AND VEHICLE RESPONSE PROJECTION FROM CRASH EVENT In this section, schemes or predicting the strength o the impact orces and vehicle response ater the impact are proposed. The proper vehicle control action will then be determined based on the predicted vehicle motion. The algorithm is designed based on a ew assumptions. First, the entire event is assumed to occur on a straight road, and only two vehicles (a bullet vehicle and a target vehicle) are involved in the collision. The sensors and steering/braking actuators in the target vehicle are assumed to be intact ater the collision and unction normally despite the collision. Ater an impact, vehicle velocities and yaw rate may jump. From the algorithm shown in [11], a crash event can be detected in 3 time steps ater the crash, using yaw rate and lateral acceleration signals and properly selected threshold values. The estimation o the strength o the impulse and the impact location is perormed with vehicle dynamic transitional maneuvers. The overall process or predicting impact orce and vehicle response ater impact is shown in Fig 2. To start the control action as early as possible, the crash orce prediction is perormed beore reaching the hal-way point o the crash duration. Two impulse estimation steps are projected to the hal-way duration point. Fig. 2. Function diagram or impact orce and vehicle motion prediction Approximating the impact orce by a triangular pulse with a known crash duration [13], this orce proile can be predicted beore the crash ends. Once the orce proile is estimated, the vehicle response ater impact is predicted using the 4DOF vehicle model derived in [11]. 2.1 Impact Force Prediction Model Once the impulse proile is estimated, the magnitude and the location o the impulse can be computed by using a crash dynamics model and the measured vehicle states. The model includes the equations o motion in the longitudinal, lateral, yaw and roll degrees o reedom, approximated to the discrete time in a trapezoidal orm [11]. The strengths o the impulse and its location in the x-y plane are then inerred rom equation (1)-(3). Δt Px M Vx vx M V yωz v yz (1) 2 Δt Py M Vy vym V xωz vxzmrhωx x 2 Δt Vy aωz vy az Δt Vy bωz vy bz (2) C Cr 2 Vx vx 2 Vx vx Px y A Py x A IzzΩz z I xzωx x Δt Vy aωz vy az Δt Vy bωz vy bz (3) ac bcr 2 Vx vx 2 Vx vx The right-hand sides o the three equations above are assumed to be known rom vehicle sensor measurements, vehicle parameters, and collision time duration. There are our unknown quantities on the let hand side o the equations: strengths o the impulse in the x and y direction ( P x and P y ), and the location ( x A and y A ). To solve the 4 unknown variables based on the three equations, the ollowing strategy is used: I one o the impact location parameters ( x A, y A ) is less than the geometric maximum value, then the other one should be ixed at its maximum. So, the equations are calculated twice, assuming that the impact location is either on the side o the vehicle or on the rear bumper. Only the answer that is geometrically plausible is taken as the solution. Linear extrapolation is then used to project impulses ( P x, P y ) at the hal-way point o the

3 crash time duration. Assuming that the impulse proile is an isosceles triangle, the projected impulse will be hal o the area o the triangle. The impact orce ( F x, F y ) is then predicted by evaluating the maximum height o the impulse proile. 2.2 Vehicle Motion Prediction Model The calculated impact orce is used to predict the vehicle motion. The 4DOF vehicle dynamics model in [11] is used which accounts or vehicle motion and tire orces induced by external orces, M ( v x vyz) Fx (4) M ( v v ) m h F F F () y x z R x y y yr I zzz I xzx xafy yafx afy bfyr (6) I xxsx I xzz mrh( v y vxz ) F ( z h) ( m ghk ) D (7) y A R s s x where M is the vehicle mass, vx is the vehicle orward speed, vy is the vehicle lateral speed, z andx are the yaw rate and roll rate, Fx and Fy are impact orces, F y and Fyr are the lateral tire orce at the ront and rear axles, respectively. In the post-impact scenarios analyzed in this paper, the vehicle side slip angle varies in a very wide range. The typical range o side slip angle considered in ESC applications is around -3 to 3 degrees [14]. In this study, it is necessary to track a much wider range o side slip angle, up to 36 degrees. Fig. 3 shows the Magic Formula tire model [1] or combined longitudinal and lateral orces as unctions o the tire side slip angle and the longitudinal slip ratio ( ). Note that tire orces are displayed along a ull circle range o angles. The interesting regions are near the multiples o 18 degree angles including the zero degree. Around the regions, especially when is small, the directions (or sign) o lateral orces are signiicantly changed within the very narrow range o sideslip angles. It can be easily estimated that the combinations o dierent orce directional changes in each tire generate a certain amount o yaw moment on the car. This will be discussed with the simulation analysis in the ollowing subsection. F y-tire [kn] F x-tire [kn] Side slip angle [deg] = =-1 =-1 = Side slip angle [deg] Fig. 3. Lateral and longitudinal orces o a tire model as unctions o the side slip angle ( : Longitudinal slip ratio) 2.3 Analysis o Vehicle Spinning Motion In this subsection, vehicle motion is evaluated to igure out the trajectory o a spun vehicle ater an external impact. Simulation are perormed using the commercial sotware CarSim with the build-in template parameters corresponding to the Baseline big SUV (M=24kg, a=1.1m, b=1.74m) [16]. It is assumed that the vehicle is traveling with an initial longitudinal speed o 29m/s and zero initial lateral speed, yaw rate, and roll rate. The collision impact lasts or.1 seconds with the sine square orce proiles, and the impact location is.1m to the let o the center o the rear bumper. The road is assumed to be lat and straight, and its adhesion is assumed to be homogeneous with rictional coeicient.7. Fig. 4 shows the vehicle motion induced by the crash impact without any mitigating driving, braking, or steering control actions. Heading angle [ (deg) ] Yaw rate [ z (deg/s) ] F yf & F yr (N) M Friction (Nm) deg 36deg x 14 F yf F yr x Time (s) Fig. 4. Simulated vehicle motion ater a collision Let Fy and F yr to denote the tire lateral orces at the ront and rear axles, respectively. M Friction is the induced yaw moment calculated rom the tire lateral orces, then we have M Friction afyf b FyR (8) This induced moment acts as a counter reaction against the moment rom the collision impact and shows remarkable eects when the vehicle heading angle crosses 18 and 36. As shown in the tire model (Fig. 3), lateral orce changes with slip angle quickly around or multiples o 18 angles, especially when tires are rolling ( ). Since the lateral orces o the ront and rear tires switch signs at slightly dierent time (due to the act the distances rom the center o gravity to the axles are dierent), this transitional phase introduces large yaw moment when the lateral orces at the two axles are o opposite signs. Thereore, the yaw rate is signiicantly reduced when the vehicle heading angle crosses through 18 and Prediction Results The proposed impulse estimation and vehicle motion estimation algorithms are validated using Carsim simulations in Fig..

4 Fig.. Comparison o actual and projected impulse and impact orces ( o represents the projection point) The impact starts at 2 seconds and the impulse is estimated with measured signals and the equation o motion in subsection 2.1. The linearly extrapolated result rom the impulses estimated rom three measurements projects the impulse at the hal-way point o the crash duration. And the predicted orces are obtained by calculating the height o the assumed triangle with an area that is twice the size o the projected impulse magnitude. The predicted vehicle dynamic response to the projected impact orces is shown in Fig. 6. Yaw rate (deg/s) 1 Actual response Predicted response 18deg 36deg Heading angle (deg) Fig. 6. Comparison o actual and predicted response o the struck vehicle The yaw rate peaks at 89 /s and the vehicle keeps spinning and drops quickly at each 18 crossover. The prediction results seem to be accurate enough to be used or control interventions. 3. VEHICLE TRAJECTORY STUDY Based on the predicted vehicle motion, the desired inal heading angle can be determined. The hypothesis is that it will be beneicial to reach a inal heading angle o 18 or 36 (or multiples o 18 thereater) with respect to the lanes to avoid side impact rom another bullet vehicle, and to avoid large lateral displacement so that the vehicle does not encroaching excessively into the adjacent lanes. Once the inal heading angle is identiied, control actions will then be computed to stabilize vehicle motions to the desired heading angle. 3.1 Vehicle Model in the Global Coordinate Fig. 7. Top view o the vehicle in the global coordinate Since the relative motion o the vehicle with respect to the road is o interest, the motion vectors need to be F x F y transormed into the global coordinate system as shown in Fig. 7: ( Fx Fxr ) cos ( Fy Fyr ) sin VX (9) m ( Fx Fxr ) sin ( Fy Fyr ) cos VY m (1) v V cos V sin (11) x X Y v V sin V cos (12) y X Y where ψ is the heading angle, the angle between the vehicle centerline and the road tangent line, and is the ront wheel steering angle. The coordinate system (X, Y) is ixed on the ground, serving as a rame o reerence or vehicle motion on the road. The body ixed coordinate system is denoted by (x, y) with its origin located at the center o gravity (CG) o the vehicle. To track the side slip angle even at magnitudes above 9, the longitudinal and lateral velocity vectors in vehicle coordinates are determined by the velocities in the global coordinates and heading angles during spinning. The vehicle side slip angle ( ) and tire side slip angles (, r ) are determined rom the ollowing equations: atan2( vy, vx) (13) atan2 vy a z, vx (14), r y z x atan2 v b v (1) where atan2 is the our-quadrant inverse tangent unction that produces results in the range (-π, π]. To avoid singularities o this calculation, the magnitude o longitudinal velocity ( v x ) is limited when it is near zero [14]. In addition, lateral vehicle position during spinning is obtained by integrating the lateral velocity in the global coordinate system. 3.2 Vehicle Motion Analysis with Brake Action As shown in the tire model (Fig. 3), longitudinal and lateral orces are unctions o side slip angles and longitudinal slip ratios o the individual tire. The simulation results in this subsection show that the combination o tire orces generates dierent vehicle yaw motions. Lateral disp.[y(m)] Longitudinal disp.[x(m)] Fig. 8. Projected vehicle position and motion without any mitigating brake action (*: indicates lane boundary crossing)

5 V [m/s] It is assumed that the vehicle is initially running with a longitudinal speed o 3m/s with zero heading angle. It is also assumed that the lateral speed (3m/s) and yaw rate (1 /s) are the initial state generated rom a side impact. Fig. 8 and 9 show the predicted vehicle state trajectories on the heading angle / yaw rate phase plane, and the longitudinal vehicle speed without any mitigating actions. Although the results show that the heading angle almost reaches 36 (which is desirable), its lateral deviation is over 2m. So, the lateral displacement needs to be reduced with proper control actions. In Fig. 1, the eects o dierent braking control actions in the phase plane are shown. Since the tire orces are aected signiicantly by the wheel slip ratio, the vehicle yaw rate and heading angle are quite dierent or the three braking actions. (a) (b) (c) 4 3 V X V Y Time [sec] Fig. 9. Directional vehicle velocity on the global axis without any mitigating brake action Fig. 1. Comparison o braking actions with the initial state V X =3m/s and z =1 /s. (a) 4wheel brake lock. (b) Rear 2wheel brakes lock. (c) Front 2wheel brake lock. 4. CONTROL SIGNALS WITH THE OPTIMIZER 4.1 Optimization Problem A gradient descent approach is used to ind possible control signals to balance between minimum lateral deviation and sae heading angle. The MATLAB s toolbox (the routine mincon ) is used or this constrained optimization problem. The objective unction is chosen to minimize lateral deviation while achieving desirable heading angles with the ollowing orm: N N 2 2 J w1ys i Yp i w2 mod i (16) i1 i1 where Y s is the lateral displacement rom the Earth-ixed X axis, Y p is the lateral road center position with respect to the Earth-ixed X axis, mod is the modulo operation o heading angles with ( mod mod, ), and w1, w2are weighting actors. The objective unction is composed o two terms. The equation sums up the square o lateral deviations rom the course and sums up the square o angle dierences toward to the multiples o 18 along the time span. As the objective unction gets minimized, the lateral deviations get decreased and, at the same time, the heading angles get approached to multiples o 18. A trade-o between small lateral deviations and the sae heading angles can be made by adjusting the weights on each term in the objective unction. Sequential control inputs, which are longitudinal slip ratios o each tire, are ound so that the objective unction can be minimized under the slip ratio range constraints: min J, r subject to 1, r, (17) r Here, we assume that the tire orces are algebraic unctions o these tire slip ratios. 4.2 Simulation Results The results in this section show possible brake control actions perormed by the optimization scheme under the same vehicle condition in Fig 8-9. In this simulation, all measurements such as position, speed, yaw rate, and heading angle are assumed to be available and accurate, and no actuator dynamics are included in the simulation model. Fig. 11 and Fig. 12 show an example o a trade-o between the lateral displacement and the heading angle with dierent weighting actors. The result in Fig. 11 achieves 18 heading angle with one lane oset rom the course, while the weighing actors in Fig. 12 brings the vehicle to the original lane with 36 turn. So, i the vehicle is ree rom the secondary collision at least during spinning to 36, the result in Fig. 12 will be preerred. On the contrary, i the vehicle is expected to have a secondary collision during spinning, keeping the angle to 18 as the trajectory in Fig. 11 might be saer than exposing the side o the vehicle to the collision. Typically, vehicle stability control actions try to reduce vehicle states quickly. However, i ast stabilizing control action results in a inal heading angle o, say, 9, the vehicle exposes its side to approaching vehicles. In this case, allowing a larger yaw rate may be the right thing to do. Also, i larger yaw rate results in small lateral deviation, it is also desirable. Thereore, it can be seen that this optimization might sometimes produce results against common intuition. I the host vehicle or the inrastructure can acquire inormation about the surrounding vehicles, a beneicial heading angle among, 18, or 36 (or multiples o 1/ 2

6 Lateral disp.[y(m)] V [m/s] Longitudinal disp.[x(m)] Time [sec] Fig. 11. Projected vehicle position on the road and yaw motion with weightings w1 1, w2 1 Lateral disp.[y(m)] V [m/s] Longitudinal disp.[x(m)] V X V Y Time [sec] Fig. 12. Projected vehicle position on the road and yaw motion with weightings w1 1, w thereater) could be determined. For example, i the environmental sensor indicates a possible crash near 6m downstream rom the initial (primary) crash, the control action in Fig. 12 is not a good choice. Instead, the vehicle trajectory shown in Fig. 11 is preerred.. CONCLUSIONS In this paper, impact orce and motion prediction algorithms were developed based on a 4DOF vehicle model. A crash impact strength projection algorithm that estimates the impact and vehicle motion beore the crash ends were presented. A constrained minimization problem is ormulated which allows a trade-o between small lateral deviation and sae heading angle. V X V Y Simulation results show that the combination o dierent braking actions can lead a vehicle to a desired heading angle and reduce the lateral deviation rom the original (unmitigated) trajectory. Studies on the combination o weighting actors and the development o a eedback control algorithm are ongoing works. REFERENCES [1] NHTSA. Traic Saety Facts 29, DOT HS , 21. [2] Zhou, J. "Active Saety Measures or Vehicles Involved in Light Vehicle-to-Vehicle Impacts," Ph. D. Dissertation, University o Michigan, Ann Arbor, 28. [3] Langwieder, K., Sporner, A., and Hell. W. RESICO Retrospective Saety Analysis o Car Collisions Resulting in Serious Injuries, GDV 981, Munich, Germany, [4] NHTSA. Problem Deinition or Pre-Crash Sensing Advanced Restraints, DOT HS , 29. [] Piao, J., and Mcdonald, M. Advanced Driver Assistance Systems rom Autonomous to Cooperative Approach, Transport Reviews, vol.28, p.69, 28. [6] Dang, J. N. Preliminary Results Analyzing the Eectiveness o Electronic Stability Control (ESC) Systems, DOT HS 89 79, 24. [7] Chan, C.-Y., and Tan, H.-S. Feasibility Analysis o Steering Control as a Driver-Assistance Function in Collision Situations, IEEE Trans. On Intelligent Transportation Systems, pp. 1 9, 21. [8] Robert Bosch GmbH. Secondary Collision Mitigation, rom [9] Yang, D., Gordon, T., et al. Post-Impact Vehicle Path Control by Optimization o Individual Wheel Braking Sequences, Proc. o AVEC 21, pp [1] Yang, D., Gordon, T., et al. Optimized Brake-based Control o Path Lateral Deviation or Mitigation o Secondary Collisions, Proc. o the Institution o Mechanical Engineers, Part D: Journal o Automobile Engineering, vol. 22, no. 12, pp , 21. [11] Zhou, J., Peng, H., and Lu, J. Collision Model or Vehicle Motion Prediction ater Light Impacts, Vehicle System Dynamics, 46, 1, pp [12] Zhou, J., Lu, J., and Peng, H. Vehicle stabilization in response to exogenous impulsive disturbances to the vehicle body, In Proc. o the American Control Conerence, St. Louis, MO, pp , 29, [13] Huang, M. Vehicle Crash Mechanics, CRC Press, Boca Raton, FL 2. [14] Hac, A., et al. Estimation o Vehicle Roll Angle and Side Slip or Crash Sensing, SAE Technical Paper [1] Pacejka, H. B. Tire and Vehicle Dynamics (Second edition), SAE International, 2. [16] Mechanical Simulation Corporation.