A trajectory-tracking controller for improving the safety and stability of four-wheel steering autonomous vehicles
Abstract
To achieve anti-crosswind, anti-sideslip, and anti-rollover in trajectory-tracking for Four-Wheel Steering (4WS) autonomous vehicles, a trajectory-tracking controller based on a four-channel Active Disturbance Rejection Control (ADRC) was used to track the desired lateral displacement, longitudinal displacement, yaw angle, and roll angle, and minimize the tracking errors between the actual output values and the desired values through static decoupling steering and braking systems. In addition, the anti-crosswind, anti-sideslip, and anti-rollover simulations were implemented with CarSim®. Finally, the simulation results showed that the 4WS autonomous vehicle with the controller still has good anti-crosswind, anti-sideslip, and anti-rollover performance in path tracking, even under a small turning radius or lowadhesion curved roads.
First published online 12 March 2021
Keyword : four-wheel steering, curved trajectory-tracking, active disturbance rejection control, anti-crosswind, anti-sideslip, anti-rollover, CarSim®
How to Cite
Liu, R., Wei, M., Sang, N., & Wei, J. (2021). A trajectory-tracking controller for improving the safety and stability of four-wheel steering autonomous vehicles. Transport, 36(2), 147-163. https://doi.org/10.3846/transport.2021.14291
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Hiraoka, T.; Nishihara, O.; Kumamoto, H. 2004. Model-following sliding mode control for active four-wheel steering vehicle, Review of Automotive Engineering 25(3): 305–313.
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Li, B; Yu, F. 2010. Design of a vehicle lateral stability control system via a fuzzy logic control approach, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 224(3): 313–326. https://doi.org/10.1243/09544070JAUTO1279
Li, G.; Hong, W.; Liang, H. 2012. Four-wheel independently driven in-wheel motors electric vehicle AFS and DYC integrated control, SAE Technical Paper 2012-01-0258. https://doi.org/10.4271/2012-01-0258
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Liu, R.; Wei, M.; Sang, N.; Wei, J. 2020. Research on curved path tracking control for four-wheel steering vehicle considering road adhesion coefficient, Mathematical Problems in Engineering 2020: 3108589. https://doi.org/10.1155/2020/3108589
Liu, R.; Wei, M.; Zhao, W. 2018. Trajectory tracking control of four wheel steering under high speed emergency obstacle avoidance, International Journal of Vehicle Design 77(1–2): 1–21. https://doi.org/10.1504/IJVD.2018.098265
MacAdam, C. C. 1980. An optimal preview control for linear systems, Journal of Dynamic Systems, Measurement, and Control 102(3): 188–190. https://doi.org/10.1115/1.3139632
MacAdam, C. C. 1981. Application of an optimal preview control for simulation of closed-loop automobile driving, IEEE Transactions on Systems, Man, and Cybernetics 11(6): 393–399. https://doi.org/10.1109/TSMC.1981.4308705
Maruyama, Y.; Yamazaki, F. 2006. Driving simulator experiment on the moving stability of an automobile under strong crosswind, Journal of Wind Engineering and Industrial Aerodynamics 94(4): 191–205. https://doi.org/10.1016/j.jweia.2005.12.006
Ming, T.; Deng, W.; Zhang, S.; Zhu, B. 2016. MPC-based trajectory tracking control for intelligent vehicles, SAE Technical Paper 2016-01-0452. https://doi.org/10.4271/2016-01-0452
Nagai, M.; Hirano, Y.; Yamanaka, S. 1997. Integrated control of active rear wheel steering and direct yaw moment control, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility 27(5–6): 357–370. https://doi.org/10.1080/00423119708969336
Nagai, M.; Shino, M.; Gao, F. 2002. Study on integrated control of active front steer angle and direct yaw moment, JSAE Review 23(3): 309–315. https://doi.org/10.1016/S0389-4304(02)00189-3
Nikravesh, P.; Lee, J. 1993. Optimal four-wheel steering strategy using nonlinear analytical vehicle models, SAE Technical Paper 931915. https://doi.org/10.4271/931915
Piyabongkarn, D.; Keviczky, T.; Rajamani, R. 2004. Active direct tilt control for stability enhancement of a narrow commuter vehicle, International Journal of Automotive Technology 5(2): 77–88.
Ren, D. B.; Zhang, J. Y.; Zhang, J. M.; Cui, S. M. 2011. Trajectory planning and yaw rate tracking control for lane changing of intelligent vehicle on curved road, Science China Technological Sciences 54(3): 630–642. https://doi.org/10.1007/s11431-010-4227-6
Sang, N.; Wei, M.; Bai, Y. 2015. Control of vehicle active front steering based on active disturbance rejection feedback controller, Transactions of Nanjing University of Aeronautics and Astronautics 32(4): 461–468.
Sano, S.; Furukawa, Y.; Shiraishi, S. 1986. Four wheel steering system with rear wheel steer angle controlled as a function of steering wheel angle, SAE Technical Paper 860625. https://doi.org/10.4271/860625
Shibahata, Y.; Irie, N.; Itoh, H.; Nakamura, K. 1986. The development of an experimental four-wheel-steering vehicle, SAE Technical Paper 860623. https://doi.org/10.4271/860623
Sirou, M.; Galtier, L. 1991. Rear Steering Control System for a Motor Vehicle with Four Steered Wheels. EP0418115A1. European Patent Office. Available from Internet: https://patents.google.com/patent/EP0418115A1/en
Solmaz, S.; Corless, M.; Shorten, R. 2007. A methodology for the design of robust rollover prevention controllers for automotive vehicles with active steering, International Journal of Control 80(11): 1763–1779. https://doi.org/10.1080/00207170701473987
Song, J. 2012. Integrated control of brake pressure and rearwheel steering to improve lateral stability with fuzzy logic, International Journal of Automotive Technology 13(4): 563–570. https://doi.org/10.1007/s12239-012-0054-z
Sun, C.; Zhang, X.; Xi, L.; Tian, Y. 2018. Design of a path-tracking steering controller for autonomous vehicles, Energies 11(6): 1451. https://doi.org/10.3390/en11061451
Sun, T.; Guo, H.; Cao, J.-Y.; Chai, L.-J.; Sun, Y.-D. 2013. Study on integrated control of active front steering and direct yaw moment based on vehicle lateral velocity estimation, Mathematical Problems in Engineering 2013: 275269. https://doi.org/10.1155/2013/275269
Tajima, J.; Yuhara, N.; Sano, S.; Takimoto, S. 1999. Effects of steering system characteristics on control performance from the viewpoint of steer-by-wire system design, SAE Technical Paper 1999-01-0821. https://doi.org/10.4271/1999-01-0821
Urmson, C.; Baker, C.; Dolan, J.; Rybski, P.; Salesky, B.; Whittaker, W.; Ferguson, D.; Darms, M. 2009. Autonomous driving in traffic: boss and the urban challenge, AI Magazine 30(2): 17–28. https://doi.org/10.1609/aimag.v30i2.2238
Wu, Y.; Wang, L.; Li, F. 2018. Research on variable steering ratio control strategy of steer-by-wire system, SAE Technical Paper 2018-01-1583. https://doi.org/10.4271/2018-01-1583
Xia, Y.; Pu, F.; Li, S.; 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. https://doi.org/10.1109/TIE.2016.2531021
Yang, J.; Bao, H.; Ma, N.; Xuan, Z. 2017. An algorithm of curved path tracking with prediction model for autonomous vehicle, in 2017 13th International Conference on Computational Intelligence and Security (CIS), 15–18 December 2017, Hong Kong, China, 405–408. https://doi.org/10.1109/CIS.2017.00094
Yim, S.; Jeon, K.; Yi, K. 2012. An investigation into vehicle rollover prevention by coordinated control of active anti-roll bar and electronic stability program, International Journal of Control, Automation and Systems 10(2): 275–287. https://doi.org/10.1007/s12555-012-0208-9
Zeyada, Y.; Karnopp, D.; El-Arabi, M.; El-Behiry, E. S. 1998. A combined active-steering differential-braking yaw rate control strategy for emergency maneuvers, SAE Technical Paper 980230. https://doi.org/10.4271/980230
Zhang, J.; Zheng, H.; Zhao, M. 2018. Analysis of vehicle steering stability of nonlinear four wheel steering based on sliding mode control, SAE Technical Paper 2018-01-1593. https://doi.org/10.4271/2018-01-1593
Zhao, J.; Taheri, S. 2012. A multi-objective LMI-based antiroll control system, SAE International Journal of Commercial Vehicles 5(2): 421–428. https://doi.org/10.4271/2012-01-1904
Zhou, L.; Ou, L.; Wang, C. 2009. A simulation of the four-wheel steering vehicle stability based on DYC control, in 2009 International Conference on Measuring Technology and Mechatronics Automation, 11–12 April 2009, Zhangjiajie, Hunan, China, 189–193. https://doi.org/10.1109/ICMTMA.2009.469
Zhu, T.; Zong, C. 2009. Research on control algorithm for DYC and integrated control with 4WS, in 2009 International Conference on Computational Intelligence and Natural Computing, 6–7 June 2009, Wuhan, China, 166–169. https://doi.org/10.1109/CINC.2009.91
Boada, B. L.; Boada, M. J. L.; Díaz, V. 2005. Fuzzy-logic applied to yaw moment control for vehicle stability, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility 43(10): 753–770. https://doi.org/10.1080/00423110500128984
Braghin, F.; Cheli, F.; Corradi, R.; Tomasini, G.; Sabbioni, E. 2008. Active anti-rollover system for heavy-duty road vehicles, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility 46: 653–668. https://doi.org/10.1080/00423110802033064
Cao, J.; Jing, L.; Guo, K.; Yu, F. 2013. Study on integrated control of vehicle yaw and rollover stability using nonlinear prediction model, Mathematical Problems in Engineering 2013: 643548. https://doi.org/10.1155/2013/643548
Chen, X.; Zhang, J.; Yang, M.; Zhong, L.; Dong, J. 2018. Continuous-curvature path generation using Fermat’s spiral for unmanned marine and aerial vehicles, in 2018 Chinese Control And Decision Conference (CCDC), 9–11 June 2018, Shenyang, China, 4911–4916. https://doi.org/10.1109/CCDC.2018.8407982
Cheng, J.; Zhang, Y.; Wang, Z. 2011. Curve path tracking control for tractor-trailer mobile robot, in 2011 Eighth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD), 26–28 July 2011, Shanghai, China, 502–506. https://doi.org/10.1109/FSKD.2011.6019497
Chiu, J.; Solmaz, S.; Corless, M.; Shorten, R. 2010. A methodology for the design of robust rollover prevention controllers for automotive vehicles using differential braking, International Journal of Vehicle Autonomous Systems 8(2–4): 146–170. https://doi.org/10.1504/IJVAS.2010.035794
Demirci, M.; Gokasan, M. 2013. Adaptive optimal control allocation using Lagrangian neural networks for stability control of a 4WS–4WD electric vehicle, Transactions of the Institute of Measurement and Control 35(8): 1139–1151. https://doi.org/10.1177/0142331213490597
Duong, M.-T.; Do, T.-D.; Le, M.-H. 2018. Navigating self-driving vehicles using convolutional neural network, in 2018 4th International Conference on Green Technology and Sustainable Development (GTSD), 23–24 November 2018, Ho Chi Minh, Vietnam, 607–610. https://doi.org/10.1109/GTSD.2018.8595533
Furukawa, Y.; Yuhara, N.; Sano, S.; Takeda, H.; Matsushita, Y. 1989. A review of four-wheel steering studies from the viewpoint of vehicle dynamics and control, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility 18(1–3): 151–186. https://doi.org/10.1080/00423118908968917
Guo, J.; Chu, L.; Liu, H.; Shang, M.; Fang, Y. 2010. Integrated control of active front steering and electronic stability program, in 2010 2nd International Conference on Advanced Computer Control, 27–29 March 2010, Shenyang, China, 449–453. https://doi.org/10.1109/ICACC.2010.5486880
Han, J. 2009. From PID to active disturbance rejection control, IEEE Transactions on Industrial Electronics 56(3): 900–906. https://doi.org/10.1109/TIE.2008.2011621
Hiraoka, T.; Nishihara, O.; Kumamoto, H. 2004. Model-following sliding mode control for active four-wheel steering vehicle, Review of Automotive Engineering 25(3): 305–313.
Hoffmann, G. M.; Tomlin, C. J.; Montemerlo, M.; Thrun, S. 2007. Autonomous automobile trajectory tracking for off-road driving: controller design, experimental validation and racing, in 2007 American Control Conference, 9–13 July 2007, New York, NY, USA, 2296–2301. https://doi.org/10.1109/ACC.2007.4282788
J3087_201710. Automatic Emergency Braking (AEB) System Performance Testing. SAE Standard.
Ji, Y.; Guo, H.; Chen, H. 2014. Integrated control of active front steering and direct yaw moment based on model predictive control, in The 26th Chinese Control and Decision Conference (2014 CCDC), 31 May – 2 June 2014, Changsha, China, 2044–2049. https://doi.org/10.1109/CCDC.2014.6852504
Kazemi, M.; Shirazi, K. H. 2012. Handling enhancement of a sliding-mode control assisted four-wheel steer vehicle, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 226(2): 234–246. https://doi.org/10.1177/0954407011416552
Larish, C.; Piyabongkarn, D.; Tsourapas, V.; Rajamani, R. 2013. A New Predictive Lateral Load Transfer Ratio for Rollover Prevention Systems, IEEE Transactions on Vehicular Technology 62(7): 2928–2936. https://doi.org/10.1109/TVT.2013.2252930
Lee, A. 1996. Performance of driver-vehicle in aborted lane change maneuvers, SAE Technical Paper 960516. https://doi.org/10.4271/960516
Li, B; Yu, F. 2010. Design of a vehicle lateral stability control system via a fuzzy logic control approach, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 224(3): 313–326. https://doi.org/10.1243/09544070JAUTO1279
Li, G.; Hong, W.; Liang, H. 2012. Four-wheel independently driven in-wheel motors electric vehicle AFS and DYC integrated control, SAE Technical Paper 2012-01-0258. https://doi.org/10.4271/2012-01-0258
Li, J.; Gao, L. 2006. Neural network control approach of vehicle active yaw moment, in 2006 Chinese Control Conference, 7–11 August 2006, Harbin, China, 1714–1717. https://doi.org/10.1109/CHICC.2006.280829
Liu, R.; Wei, M.; Sang, N.; Wei, J. 2020. Research on curved path tracking control for four-wheel steering vehicle considering road adhesion coefficient, Mathematical Problems in Engineering 2020: 3108589. https://doi.org/10.1155/2020/3108589
Liu, R.; Wei, M.; Zhao, W. 2018. Trajectory tracking control of four wheel steering under high speed emergency obstacle avoidance, International Journal of Vehicle Design 77(1–2): 1–21. https://doi.org/10.1504/IJVD.2018.098265
MacAdam, C. C. 1980. An optimal preview control for linear systems, Journal of Dynamic Systems, Measurement, and Control 102(3): 188–190. https://doi.org/10.1115/1.3139632
MacAdam, C. C. 1981. Application of an optimal preview control for simulation of closed-loop automobile driving, IEEE Transactions on Systems, Man, and Cybernetics 11(6): 393–399. https://doi.org/10.1109/TSMC.1981.4308705
Maruyama, Y.; Yamazaki, F. 2006. Driving simulator experiment on the moving stability of an automobile under strong crosswind, Journal of Wind Engineering and Industrial Aerodynamics 94(4): 191–205. https://doi.org/10.1016/j.jweia.2005.12.006
Ming, T.; Deng, W.; Zhang, S.; Zhu, B. 2016. MPC-based trajectory tracking control for intelligent vehicles, SAE Technical Paper 2016-01-0452. https://doi.org/10.4271/2016-01-0452
Nagai, M.; Hirano, Y.; Yamanaka, S. 1997. Integrated control of active rear wheel steering and direct yaw moment control, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility 27(5–6): 357–370. https://doi.org/10.1080/00423119708969336
Nagai, M.; Shino, M.; Gao, F. 2002. Study on integrated control of active front steer angle and direct yaw moment, JSAE Review 23(3): 309–315. https://doi.org/10.1016/S0389-4304(02)00189-3
Nikravesh, P.; Lee, J. 1993. Optimal four-wheel steering strategy using nonlinear analytical vehicle models, SAE Technical Paper 931915. https://doi.org/10.4271/931915
Piyabongkarn, D.; Keviczky, T.; Rajamani, R. 2004. Active direct tilt control for stability enhancement of a narrow commuter vehicle, International Journal of Automotive Technology 5(2): 77–88.
Ren, D. B.; Zhang, J. Y.; Zhang, J. M.; Cui, S. M. 2011. Trajectory planning and yaw rate tracking control for lane changing of intelligent vehicle on curved road, Science China Technological Sciences 54(3): 630–642. https://doi.org/10.1007/s11431-010-4227-6
Sang, N.; Wei, M.; Bai, Y. 2015. Control of vehicle active front steering based on active disturbance rejection feedback controller, Transactions of Nanjing University of Aeronautics and Astronautics 32(4): 461–468.
Sano, S.; Furukawa, Y.; Shiraishi, S. 1986. Four wheel steering system with rear wheel steer angle controlled as a function of steering wheel angle, SAE Technical Paper 860625. https://doi.org/10.4271/860625
Shibahata, Y.; Irie, N.; Itoh, H.; Nakamura, K. 1986. The development of an experimental four-wheel-steering vehicle, SAE Technical Paper 860623. https://doi.org/10.4271/860623
Sirou, M.; Galtier, L. 1991. Rear Steering Control System for a Motor Vehicle with Four Steered Wheels. EP0418115A1. European Patent Office. Available from Internet: https://patents.google.com/patent/EP0418115A1/en
Solmaz, S.; Corless, M.; Shorten, R. 2007. A methodology for the design of robust rollover prevention controllers for automotive vehicles with active steering, International Journal of Control 80(11): 1763–1779. https://doi.org/10.1080/00207170701473987
Song, J. 2012. Integrated control of brake pressure and rearwheel steering to improve lateral stability with fuzzy logic, International Journal of Automotive Technology 13(4): 563–570. https://doi.org/10.1007/s12239-012-0054-z
Sun, C.; Zhang, X.; Xi, L.; Tian, Y. 2018. Design of a path-tracking steering controller for autonomous vehicles, Energies 11(6): 1451. https://doi.org/10.3390/en11061451
Sun, T.; Guo, H.; Cao, J.-Y.; Chai, L.-J.; Sun, Y.-D. 2013. Study on integrated control of active front steering and direct yaw moment based on vehicle lateral velocity estimation, Mathematical Problems in Engineering 2013: 275269. https://doi.org/10.1155/2013/275269
Tajima, J.; Yuhara, N.; Sano, S.; Takimoto, S. 1999. Effects of steering system characteristics on control performance from the viewpoint of steer-by-wire system design, SAE Technical Paper 1999-01-0821. https://doi.org/10.4271/1999-01-0821
Urmson, C.; Baker, C.; Dolan, J.; Rybski, P.; Salesky, B.; Whittaker, W.; Ferguson, D.; Darms, M. 2009. Autonomous driving in traffic: boss and the urban challenge, AI Magazine 30(2): 17–28. https://doi.org/10.1609/aimag.v30i2.2238
Wu, Y.; Wang, L.; Li, F. 2018. Research on variable steering ratio control strategy of steer-by-wire system, SAE Technical Paper 2018-01-1583. https://doi.org/10.4271/2018-01-1583
Xia, Y.; Pu, F.; Li, S.; 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. https://doi.org/10.1109/TIE.2016.2531021
Yang, J.; Bao, H.; Ma, N.; Xuan, Z. 2017. An algorithm of curved path tracking with prediction model for autonomous vehicle, in 2017 13th International Conference on Computational Intelligence and Security (CIS), 15–18 December 2017, Hong Kong, China, 405–408. https://doi.org/10.1109/CIS.2017.00094
Yim, S.; Jeon, K.; Yi, K. 2012. An investigation into vehicle rollover prevention by coordinated control of active anti-roll bar and electronic stability program, International Journal of Control, Automation and Systems 10(2): 275–287. https://doi.org/10.1007/s12555-012-0208-9
Zeyada, Y.; Karnopp, D.; El-Arabi, M.; El-Behiry, E. S. 1998. A combined active-steering differential-braking yaw rate control strategy for emergency maneuvers, SAE Technical Paper 980230. https://doi.org/10.4271/980230
Zhang, J.; Zheng, H.; Zhao, M. 2018. Analysis of vehicle steering stability of nonlinear four wheel steering based on sliding mode control, SAE Technical Paper 2018-01-1593. https://doi.org/10.4271/2018-01-1593
Zhao, J.; Taheri, S. 2012. A multi-objective LMI-based antiroll control system, SAE International Journal of Commercial Vehicles 5(2): 421–428. https://doi.org/10.4271/2012-01-1904
Zhou, L.; Ou, L.; Wang, C. 2009. A simulation of the four-wheel steering vehicle stability based on DYC control, in 2009 International Conference on Measuring Technology and Mechatronics Automation, 11–12 April 2009, Zhangjiajie, Hunan, China, 189–193. https://doi.org/10.1109/ICMTMA.2009.469
Zhu, T.; Zong, C. 2009. Research on control algorithm for DYC and integrated control with 4WS, in 2009 International Conference on Computational Intelligence and Natural Computing, 6–7 June 2009, Wuhan, China, 166–169. https://doi.org/10.1109/CINC.2009.91