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Speed-Varying Path Tracking Based on Model Predictive Control for Autonomous Vehicles

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Abstract

In order to improve autonomous vehicles path-tracking accuracy and stability, a lateral–longitudinal coordination path-tracking control method is proposed. The proposed coordination control consists of path-tracking control and speed tracking control. First, the desired safety speed is planned according to the known road curvature and adhesion coefficient in order to prevent the tire force saturation. Based on the three-degree-of-freedom (3DOF) vehicle dynamic model and the preview tracking error model, model predictive control (MPC) theory is adopted to design the speed-varying vehicle path-tracking controller. Then, the quadratic programming (QP) method is used to solve the objective function with constraints, which calculates the steering angle to control the vehicle track the reference path. In addition, a PID speed controller is designed to calculate the torque of each wheel to track the desired speed. Finally, according to the yaw rate error and the vehicle slip angle error, a yaw moment stability controller based on the fuzzy logic control theory is designed to balance the vehicle stability and motility. The simulation results based on a Matlab/Carsim platform show that the coordination path-tracking control method proposed in this paper can effectively improve the vehicle tracking accuracy and the stability on different roads.

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Data available on request from the authors.

References

  • Chen, T., Xu, X., Chen, L., Jiang, H. B., Cai, Y. F., & Li, Y. (2018). Estimation of longitudinal force, lateral vehicle speed and yaw rate for four-wheel independent driven electric vehicles. Mechanical Systems and Signal Processing, 101, 377–388.

    Article  Google Scholar 

  • Cheng, S., Li, L., Guo, H. Q., Chen, Z. G., & Song, P. (2020). Longitudinal collision avoidance and lateral stability adaptive control system based on mpc of autonomous vehicles. IEEE Transactions on Intelligent Transportation Systems, 21(6), 2376–2385.

    Article  Google Scholar 

  • Choi, M., & Choi, S. B. (2016). MPC for vehicle lateral stability via differential braking and active front steering considering practical aspects. Proc IMechE, Part d: Journal of Automobile Engineering, 230, 459–469.

    Article  Google Scholar 

  • Gruyer, D., Magnier, V., Hamdi, K., Claussmann, L., Orfila, O., & Rakotonirainy, A. (2017). Perception, information processing and modeling: Critical stages for autonomous driving applications. Annual Reviews in Control, 44, 323–341.

    Article  Google Scholar 

  • Guo, J. H., Luo, Y. G., & Li, K. Q. (2017). An Adaptive hierarchical trajectory following control approach of autonomous four-wheel independent drive electric vehicles. IEEE Transactions on Intelligent Transportation Systems, 19(8), 2482–2492.

    Article  Google Scholar 

  • Guo, J. H., Luo, Y. G., Li, K. Q., & Dai, Y. F. (2018a). Coordinated path-following and direct yaw-moment control of autonomous electric vehicles with sideslip angle estimation. Mechanical Systems and Signal Processing, 105, 183–199.

    Article  Google Scholar 

  • Guo, H. Y., Liu, J., Cao, D. P., Chen, H., Yu, R., & Lv, C. (2018b). Dual-envelop-oriented moving horizon path tracking control for fully automated vehicles. Mechatronics, 50, 422–433.

    Article  Google Scholar 

  • Gutjahr, B., Gröll, L., & Werling, M. (2017). Lateral vehicle trajectory optimization using constrained linear time varying MPC. IEEE Trans. Intelligent Transportation Systems, 18(6), 1586–1595.

    Google Scholar 

  • Hang, P., & Chen, X. B. (2019). Integrated chassis control algorithm design for path tracking based on four-wheel steering and direct yaw-moment control. Proc IMechE Part i: J Systems and Control Engineering, 233(6), 625–641.

    Google Scholar 

  • Hang, P., Xia, X., Chen, G., & Chen, X. B. (2022). Active safety control of automated electric vehicles at driving limits: A tube-based MPC approach. IEEE Transactions on Transportation Electrification, 8(1), 1338–1349.

    Article  Google Scholar 

  • Ji, J., Khajepour, A., Melek, W., & Huang, Y. (2017). Path planning and tracking for vehicle collision avoidance based on model predictive control with multiconstraints. IEEE Transactions on Vehicular Technology, 66(2), 952–964.

    Article  Google Scholar 

  • Li, H. L., & Luo, Y. T. (2020). Integrated coordination control for distributed drive electric vehicle trajectory tracking. International Journal of Automotive Technology, 21(4), 1047–1060.

    Article  Google Scholar 

  • Li, K. Q., Guo, J. H., & Luo, Y. G. (2019). Design of robust output-feedback-based automatic steering controller for unmanned electric vehicles. International Journal of Vehicle Design, 79(1), 63–83.

    Article  Google Scholar 

  • Lin, F., Wang, S. B., Zhao, Y. Q., & Cai, Y. Z. (2021). Research on autonomous vehicle path tracking control considering roll stability. Proc IMechE, Part d: Journal of Automobile Engineering, 235(1), 199–210.

    Article  Google Scholar 

  • Liu, K., Gong, J. W., Kurt, A., Chen, H. Y., & Ozguner, U. (2018). Dynamic Modeling and Control of High-speed Automated Vehicles for Lane Change Maneuver. IEEE Transactions on Intelligent Vehicles, 3(3), 329–339.

    Article  Google Scholar 

  • Liu, W., Wang, R. C., Xie, C. Y., & Ye, Q. (2020). Investigation on adaptive preview distance path tracking control with directional error compensation. Proc IMechE, Part d: Journal of Automobile Engineering, 234(4), 484–500.

    Google Scholar 

  • Norouzi, A., Kazemi, R., & Azadi, S. (2018). Vehicle lateral control in the presence of uncertainty for lane change maneuver using adaptive sliding mode control with fuzzy boundary layer. Proc IMechE Part i: Journal of Systems and Control Engineering, 232(1), 12–28.

    Google Scholar 

  • Peng, H. N., Wang, W. D., An, Q., Xiang, C. L., & Li, L. (2020). Path tracking and direct yaw moment coordinated control based on robust MPC with the finite time horizon for autonomous independent-drive vehicles. IEEE Transactions on Vehicular Technology, 69(6), 6053–6066.

    Article  Google Scholar 

  • Ren, Y., Zheng, L., & Khajepour, A. (2019). Integrated model predictive and torque vectoring control for path tracking of 4-wheel-driven autonomous vehicles. IET Intelligent Transport Systems, 13(1), 98–107.

    Article  Google Scholar 

  • Tan, Q. F., Shi, L. L., & Katupitiya, J. (2019). A novel control approach for path tracking of a force-controlled two-wheel-steer four-wheel-drive vehicle. Proc IMechE, Part d: Journal of Automobile Engineering, 233(6), 1480–1494.

    Article  Google Scholar 

  • Tavan, N., Tavan, M., & Hosseini, R. (2015). An optimal integrated longitudinal and lateral dynamic controller development for vehicle path tracking. Latin American Journal of Solids and Structures, 12(6), 1006–1023.

    Article  Google Scholar 

  • Xia, Y. Q., Pu, F., Li, S. F., & Gao, Y. (2016). Lateral path tracking control of autonomous land vehicle based on adrc and differential flatness. IEEE Transactions on Industrial Electronics, 63(5), 3091–3099.

    Article  Google Scholar 

  • Xiang, C. L., Peng, H. N., Wang, W. D., Li, L., An, Q., & Cheng, S. (2021). Path tracking coordinated control strategy for autonomous four in-wheel-motor independent-drive vehicles with consideration of lateral stability. Proc IMechE, Part d: Journal of Automobile Engineering, 235(4), 1023–1036.

    Article  Google Scholar 

  • Xie, J., Xu, X., Wang, F., Tang, Z., & Chen, L. (2021). Coordinated control based path following of distributed drive autonomous electric vehicles with yaw-moment control. Control Engineering Practice, 106, 104659.

    Article  Google Scholar 

  • Yu, J. X., Guo, X. X., Pei, X. F., Chen, Z. F., Zhou, W., Zhu, M. L., & Wu, C. X. (2020). Path tracking control based on tube MPC and time delay motion prediction. IET Intelligent Transport Systems, 14(1), 1–12.

    Article  Google Scholar 

  • Zhang, H., Shi, Y., Wang, J. M., & Chen, H. (2018). A New Delay-compensation Scheme for Networked Control Systems in Controller Area Networks. IEEE Transactions on Industrial Electronics, 65(9), 7239–7247.

    Article  Google Scholar 

  • Zhang, B., Zong, C. F., Chen, G. Y., & Li, G. Y. (2019). An adaptive-prediction-horizon model prediction control for path tracking in a four-wheel independent control electric vehicle. Proc IMechE, Part d: Journal of Automobile Engineering, 233(12), 3246–3262.

    Article  Google Scholar 

  • Zhang, Z. Q., Zhang, L., Wang, C., Wang, M. Q., Cao, D. P., & Wang, Z. P. (2023). Integrated Decision Making and Motion Control for Autonomous Emergency Avoidance Based on Driving Primitives Transition. IEEE Transactions on Vehicular Technology, 72(4), 4207–4221.

    Article  Google Scholar 

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Acknowledgements

The authors appreciate the financial support from the National Natural Science Foundation of China (Grant No. 51305472).

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Authors and Affiliations

  1. School of Mechatronics and Vehicle Engineering, Chongqing Jiaotong University, Chongqing, 400074, People’s Republic of China

    Shuang Tang & Jun Li

  2. Faculty of Intelligence Manufacturing, Yibin University, Yibin, 644000, People’s Republic of China

    Wei Zhou

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  1. Shuang Tang
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  2. Jun Li
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Correspondence to Jun Li.

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Tang, S., Li, J. & Zhou, W. Speed-Varying Path Tracking Based on Model Predictive Control for Autonomous Vehicles. Int.J Automot. Technol. 25, 399–411 (2024). https://doi.org/10.1007/s12239-024-00033-7

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  • DOI: https://doi.org/10.1007/s12239-024-00033-7

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