2009 International Conference on Artificial Intelligence and Computational Intelligence

Transcription

1 9 International Conerence on Artiicial Intelligence and Computational Intelligence A Novel Longitudinal Speed imator or Fully Automation Ground Vehicle on Cornering Maneuver Guanyu WANG University o Science and Technology Beijing Beijing, 83, China wgiveny@yahoo.com.cn Shengbo LI Tsinghua University Beijing, 8, China lisb@gmail.com Abstract For a ully automation ground vehicle, the accurate longitudinal speed becomes more and more important due to the increasing demands on tracking o position, velocity and acceleration. Based on low-cost wheel speed encoders, this paper proposes a novel longitudinal speed estimator or vehicles on cornering maneuver. In the estimator, a gain-varying Kalman estimator is designed to output lateral states o vehicle body. On its basis, the side slip dynamics o tyres are modeled and then the relationship between wheel absolute speed and wheel angular speed is obtained. Subsequently, we calculate the longitudinal speed at center o gravity by using a planar vehicle model to describe the kinetic motion o vehicle body. With a passenger car equipped with dierential and other on-board sensors, a series o cornering experiments are carried out and demonstrate the success o the proposed estimator. Keywords-Vehicle; longitudinal speed estimation; cornering; I. Introduction Nowadays, ully automation ground vehicles play a more and more important role on intelligent transportation systems. Apart rom route programming and strategy decision, the autonomous movement o a vehicle lies on an automatic control o vehicle s longitudinal and lateral motions to a certain extent. In the longitudinal control, it is necessary to obtain precise measurement or estimation o vehicle longitudinal kinetic states, e.g. longitudinal speed, in order to realize an accurate tracking o position, velocity and acceleration. Now, there are several measurement methods to implement the acquisition o longitudinal speed, e.g. ive-wheel meter[], [], wheel speed encoder[3] and other non-contact speed sensor[]. The ive-wheel meter has been one o the most popular measurement sensors o vehicle speed beore 99 s[5]. As a speed sensor, the test wheel was not convenient in use, low in precision and narrow in check range. Non-contact measurement techniques, e.g. optical[], inrared, photo-electrical[7], are taking the position o ive-wheel meter. The non-contact method is more accurate, but more expensive and less practical because o bulkiness, complexity, and requent need or cleaning maintenance. The dierential is another eective device to measure vehicle speed. Due to the existence o a base station, its accuracy can be smaller than.m/s[]. But, its high price is not aordable or most o commercial vehicles. Currently, an estimation method based on wheel speed encoder has the most prosperous engineering perspective because o both its low cost and desirable perormance [3]. One o typical applications is in to enhance advanced vehicle dynamics control systems such as anti-lock brake systems (ABS) and auto-traction systems (ATS) control schemes. Those applications ocused on solving the issue caused by slips between the wheels and terrain in straight driving or braking condition. However, a cornering maneuver on curved has been considered by now. In this situation, the side slip o tyres and lateral motion o vehicle body will greatly decrease the estimation accuracy o longitudinal speed. This paper aims to develop a novel longitudinal speed estimator or vehicles on cornering maneuver. First, we use a gain-varying Kalman estimator to obtain the yaw rate and side slip angle o vehicle body. Then, emphasis is given to analyze the side slip dynamics o ront tyres and yaw motion o vehicle body, and the ormula o the longitudinal speed estimator is derived. Finally, its accuracy is veriied by adopting a passenger vehicle equipped with a dierential device. II. Introduction to ground vehicle O G Y X v Gx Y ' O' Fig. Coordinated system o our-wheel vehicle A typical ully automation ground vehicle is shown as Fig.. It s a our-wheel passenger car with rear driven wheels and steerable ront wheels. An ISO coordinate system (X-Y) ixed on vehicle is used to describe vehicle kinetic motions, shown as Fig.. Since the ront wheels can rotate, their coordinate systems are dependent with X-Y system. Similar to the assumption in a bicycle model[], the eect o ackerman steering linkage is neglected and the coordinated system o let ront wheel is assumed to be identical with that o right ront one, that is X - Y coordinate system. The wheel speed encoders are equipped in both ront and rear wheels. They output the angular speed o ront wheels. In order to simply the ollowing context, we deine a new ω * as the product o the angular speed and the wheel radius. In case o any misunderstanding, we still call u * as X ' u * /9 $. 9 IEEE DOI.9/AICI

2 the wheel speed. Here, the subscript * is L or R, representing let wheel or right wheel. The vehicle longitudinal speed to be estimated, notated as v Gx, is deined as the X-axis component o vehicle speed at the center o gravity (CG). In Fig., the CG is donated by a circle point. Besides wheel speed encoders, a steering angle sensor and raw rate sensor are also equipped in the passenger vehicle. Additionally, the absolute speed o vehicle at the wheels o ront axes is notated by v *. In order to distinguish rom wheel speed, we call it wheel absolute speed. III. System coniguration o longitudinal speed estimator In a driving scenario, the ront tyres slip approximates zero because they are in driven wheels, but the rear tyres slip always exists. Thereore, only the ront wheel encoders are adopted to calculate the vehicle longitudinal velocity. When the ront steering angle is zero in a straight road, the X -Y system coincides with X-Y system. The v Gx can be easily calculated by either u L or u R. However, on a curved road, things change a lot. The v Gx is no longer equal to either o u L or u R due to the existence o tyre side slip angle and the yaw motion o vehicle body. It is demonstrated in Fig., in which red/blue lines represent wheel speeds and black line represent the actual vehicle longitudinal speed measured by a dierential. Fig. 3 is the corresponding steering angle. Compared with result, the wheel speeds have considerable discrepancy in a cornering maneuver. Long. speed ( m/s) Steer angle(rad) 5 5 Let Wheel Right Wheel 3 Fig. Wheel speed and longitudinal speed Fig. 3 Steering angle In order solve the issue, we proposed a novel longitudinal speed estimator, shown as Fig.. It consists o our components: pre-estimator o longitudinal speed, wheel absolute speed calculator, lateral state estimator and longitudinal speed calculator. The pre-estimator o longitudinal speed is used to calculate an approximation o longitudinal speed, notated as u Gx. The u Gx is outputted into the lateral state estimator so as to enhance its estimating precision o lateral states, e.g. the yaw rate ω r and side slip angle at CG β. On its basis, the wheel absolute speed calculator is used to compute the v L and v R on the ends o ront axes. Combined v L, v R, ω r and β together, the last component completes the calculation o the longitudinal speed. u L u R r m β r ω v L v R Gx Fig. System coniguration o longitudinal speed estimator IV. Synthesis o vehicle longitudinal speed estimator A. Pre-estimator o longitudinal speed Wheel speed encoders equipped on let and right ront axle output tick numbers in each sampling time and consequently give the inormation o their rotating speeds. The angular speed o wheel is calculated by counting the amount o tick numbers in each sampling period. By multiplying the wheel radius, the wheel speeds u L and u R are calculated: ul = ωl rw () ur = ωr rw Where r w is the wheel radius, ω L and ω R are the angular speed o wheels. We deine a pre-estimator o longitudinal speed as: ul + ur = () Where u Gx is the pre-estimation o longitudinal speed. The estimation u Gx will be outputted into the lateral state estimator. B. Design o lateral state estimator For a vehicle as a rigid body, side slip angle β and yaw rate ω r at CG determines its main lateral states. This indicates that they are two important variables or accurate estimation o longitudinal vehicle since the estimating discrepancy o v Gx is closely related to the lateral motion o vehicle. It is assumed that: () Vehicle is laterally symmetric; () Roll motion is neglected; (3) The lateral acceleration is below. g; () No urgent accelerating or decelerating conditions; (5) There is no vertical motion. The assumption simpliies a vehicle to be a bicycle model, shown as Fig. 5. 3

3 ω r β Fig. 5 Sketch o bicycle model α Its linear state space equation is expressed as β β = A B ω ω + r r (3) β ωrm = C + w ω r Where ω rm is measurement o yaw rate, w is measurement noise, A and B are matrices o system equation, C is matrix o output equation. They are deined as: C + Cr ac bcr C m mu Gx m A, B, C ac ac bcr a C b C () + r I I z Iz z In equation (), m is vehicle mass, C and C r are the cornering stiness o ront and rear tyres, a is the distance rom CG to ront axes, b is the distance rom CG to rear axes, I z is the moment o inertial around Z-axis. Today, a gain-constant Kalman estimator has been used widely, e.g. [8]. One o its shortcomings is that the longitudinal speed must be constant. In such situations as accelerating and decelerating, it is unsatisactory since the u Gx is time-varying. At this moment, equation (3) is a nonlinear model due to its time-varying system matrix. Thereore, we design a Kalman estimator with its gain varying because o the longitudinal speed: β β = Au ( Gx ) Lu ( Gx ) C Bu ( Gx ) + ω ω r r (5) + L u r ( ) Gx m Where L is the estimator gain. It, together with A, B and C, are unctions o u Gx. imator Gain 5 3 log(l()) log(l()) 5 5 u Gx (m/s) Fig. imator gain o lateral state estimator At dierent vehicle speed point, the estimator gain L is calculated according to Kalman ilter theory. It orms a - mapping between L and u Gx, shown as Fig.. In Fig., the solid line and dash line represent the irst element and second element o log(l) in gain-varying Kalman estimator. The star and circle point represent that o log(l) in gain-constant Kalman ilter in a nominal speed u Gx =m/s. C. Design o wheel absolute speed calculator In this section, wheel absolute speed is calculated rom wheel angular speed considering the tyre s side slip. With similar assumption in section 3., except the term (), we have a planar kinetic model o vehicle, shown as Fig. 7. In Fig. 7, α is side slip angle o ront tyres, v G is vehicle speed at CG, v Gx and v Gy are its components in X-axis and Y-axis, v L is the absolute speed o wheel and u L is its component in X -axis. vl ul α v G v Gy vr β v Gx ur α ω r Fig. 7 Schematic graph o planar vehicle model Since the wheel speed is a component o wheel absolute speed, their relationship is ormulated as: vl = ul /cosα () vr = ur /cosα In equation (), the side slip angle o let and right ront tyres are identical with each other. It is expressed as: a α = β (7) In equation (7), α is side slip angle o ront tyres. D. Longitudinal speed calculator Due to the lateral motion o vehicle body, the wheel absolute speed still can t be regarded as the vehicle longitudinal speed. Given that the planar vehicle model in Fig. 7, the relationship between vehicle speed at CG and wheel absolute speed is: tw vl = vg z a x+ y (8) tw vr = vg z a x y Where v L and v R are vectors o wheel absolute speed, 35

4 v G is vector o vehicle speed at CG., x, y, z are unit vectors o X-axis, Y-axis and Z-axis, respectively. They all are deined in vehicle coordinate system. Since the α, β and related the above vectors are accessible, equation (8) can be rewritten into a scalar orm, yielding: tw ( ) GxL = vl vgy a (9) tw = v + ω a ω ( ) GxR R Gy r r Where v GxL and v GxR are the estimated values o v Gx according to let and right wheels speed, respectively, Gy is an estimation o lateral speed at CG, deined as: v Gy = u Gx β () Given equal emphasis to measurements o let wheel and right wheel, we average the estimated values o v Gx in equation (9), having the longitudinal speed: GxR + vgxl Gx = () Equation () is the estimation o longitudinal speed considering side slip o ront tyres and lateral motion o vehicle body. V. Experiment veriication The experiment platorm is a passenger car with.l engine, automatic transmission, ABS and ESP. It is originally equipped with angular speed encoders o ront wheels, yaw rate sensor and steering angle o handle wheel. It must be noted that the steering angle o handle wheel is transormed into the steering angle o ront wheels by using a constant gain o steering system. The experiment is carried out on a proving ground. Drivers are instructed to turn in dierent radius just like on curved road. Additionally, a dierential device is also equipped. Its signals are recorded simultaneously to provide precise inormation o vehicle states. The outputs are regarded as true values so as to veriy the precision o our estimator. A. Experiment veriication with lateral state estimator In order to veriy the perormance o lateral state estimator, we employed the experiment data in a multi-cornering scenario. The proile o steering angle is shown as Fig. 3. The proile o longitudinal speed is shown as Fig.. Both the gain-varying and gain-constant Kalman estimators are tested. Their results are shown as Fig. 8 and Fig. 9, respectively. In Fig. 8 and Fig. 9, black lines donate the output o, red lines donate the estimation. Shown by Fig. 8 and Fig. 9, both the two estimators output an accurate yaw rate value. This is because the yaw rate is a measurable variable in (3) and its estimation won t deviate rom its measurement. However, it shows obvious dierence when estimating side slip angle. In the right o Fig. 8, the estimation accords with output in most o the time. With respect to the gain-constant estimator, the longitudinal speed orm sec to 5 sec is low and a time-invariant estimator in u Gx =m/s can t depict the dynamics o vehicle lateral dynamics in low speed. It leads to large discrepancy in side slip angle. But as the longitudinal speed increases ater 5 sec, its dynamic begins to approach the actual one. So, the estimation precision o β increases somewhat. Yaw rate (rad/s) Side slip angle (rad) Fig. 8 imation o gain-varying Kalman estimator Yaw rate (rad/s) Side slip angle (rad) Fig. 9 imation o gain-constant Kalman estimator B. Experiment result o the whole longitudinal speed estimator Two sections o experiment data are employed to 3

5 demonstrate the perormance o longitudinal speed estimator. The proiles o steering angle are shown as Fig. 3 and Fig.. The corresponding estimation results are shown as Fig. and Fig.. Steer angle(rad) Fig. Steering angle o ront wheel In Fig. and Fig., represents the longitudinal speed estimator proposed in this paper and represents the pre-estimator o longitudinal speed in section 3.. Long. speed(m/s) Speed error (m/s) Long. speed(m/s) (a) Longitudinal speed (b) Speed error Fig. imation results o section I (a) Longitudinal speed Speed error (m/s) (b) Speed error Fig. imation result o section II Compared with the pre-estimator o longitudinal speed, it is ound that the whole estimator has a higher estimating precision, especially on an urgent cornering maneuver. That is because the latter considers the side slip characteristics o ront tyres and eliminate the inluence o lateral motion o vehicle body. Thereore, it can be concluded that the proposed estimation method in this paper can have a higher estimation precision. It is more applicable to the cornering maneuver on a curved road. VI. Conclusions () On a curved road, the side slip dynamics o ront tyres and lateral motion o vehicle body are the key issue to induce discrepancy between linear speed o ront wheels and longitudinal speed o vehicle at CG. () The proposed estimator has a more accurate estimation o vehicle longitudinal speed on a cornering maneuver. Reerences [] T. Gillepie. Fundamentals o Vehicle Dynamics. Society o Automotive Engineers, Inc., Warrendate, PA, U.S.A., 99. [] J. Ryu and J. Gerdes. Integrating Inertial Sensors with or Vehicle Dynamics Control. Journal o Dynamic Systems, Measurement, and Control, Vol., No., pp.3-5,. [3] K. Kobayashi, K. CheoP, K. Watanabe. imation o Absolute Vehicle Speed using Fuzzy Logic Rule-Based Kalman Filter. Proc. o American Control Conerence, Seatile, Washington, USA, 995. [] C. Pelczar, K. Sung, J. Kim, B. Jang. Vehicle speed measurement using wireless sensor nodes. Proc. o 8 IEEE Intl. Con. on Vehicle Electronics and Saety, Columbus, USA, 8. [5] L. Zhang, B. Qi, D Zhao. Fundamentals and perormance comparison o several vehicle speed measurements. Highways & Automotive Applications, No., pp. -, 8. [] B. Lin, H, Cheng, B, Shaw, J. Palen. Optical and electronic design or a ield prototype o a laser-based vehicle delineation detection system. Optics and Lasers in Engineering, No. 3, pp. -7,. [7] Z. Chen, Z. Yang. Development o a new type non-contact speedometer. Transactions o the Chinese Society o Agricultural Machinery, vol. 3, no., pp. 8-88,. [8] T. Zhu, H. Zheng. Application o Unscented Kalman Filter to Vehicle State imation. International Colloquium on Computing, Communication, Control, and Management, Vol., pp , 8. 37