A Trajectory Tracking Control Method Incorporating Behavior Primitive Optimization and Game Coordination

doi:10.12382/bgxb.2024.0575

Abstract

Abstract:

The trajectory tracking control of unmanned vehicle with a sequence of human-like behavior primitives as the desired trajectory is studied.A trajectory tracking control method combining the offline optimization of behavior primitives and the online coordination of game is proposed.Based on the behavior primitive library extracted directly from real driving data,a model-based nonlinear optimization method is applied to generate a behavior primitive library that satisfies the constraints of vehicle kinematic properties.The optimal control parameters for each category of primitives in the behavior primitive library are obtained by offline optimization using the particle swarm algorithm,and a multilayer perceptual machine is applied to establish the mapping relationship between the optimal parameters of controller and the categories of behavioral primitives.Based on the optimization of the control parameters within the primitives,the online game coordinated control method is used as the core to generate the optimal control parameter between the behavior primitives.The experimental results show that the proposed trajectory tracking control method can significantly improve the tracking accuracy of the behavior primitive sequences and effectively solve the problem of stable and smooth transition between independent behavior primitives.

Key words: behavior primitive, trajectory tracking control, particle swarm optimization, differential game theory

WANG Boyang, LI Xinping, SONG Junjie, GUAN Haijie, LIU Hai’ou, CHEN Huiyan. A Trajectory Tracking Control Method Incorporating Behavior Primitive Optimization and Game Coordination[J]. Acta Armamentarii, 2025, 46(7): 240575-.

Figures/Tables 22

Fig.1 Flowchart of trajectory tracking control method incorporating behavior primitive optimization and game coordination

Fig.2 Vehicle kinematic model

Fig.3 Flowchart of controller parameter optimization algorithm

Fig.4 Algorithm schematic diagram of MLP

Fig.5 Schematic diagram of game coordinated control strategy

Table 1 Optimal controller parameters predicted by MLP model

类型编码	泛化方式	DMP	N_p	q_xy	q_φ	q_v	r
2 (J形弯)	未泛化	DMP1	12	262	410	543	48
	终点泛化	DMP2	8	162	321	611	33
	终点泛化	DMP3	13	354	601	340	50
	转向泛化	DMP2	6	142	757	823	48
	转向泛化	DMP3	16	107	130	250	92
15 (单移线)	未泛化	DMP1	6	420	85	225	840
	终点泛化	DMP2	5	409	93	230	749
	终点泛化	DMP3	7	353	81	211	814
	转向泛化	DMP2	6	673	92	398	555
	转向泛化	DMP3	6	624	104	362	354

Fig.6 Optimized results of J-turn DMP

Fig.7 Optimized results of lane-changing DMP

Fig.8 Analysis of J-turn DMP optimized results

Fig.9 Analysis of lane-changing DMP pptimizated results

Table 2 Deviation analysis of human-like features after trajectory optimization

类型编码	泛化方式	DMP	$e y ¯$ /m	e_y_max/m	$e v ¯$ / (m·s^-1)	e_v_max/ (m·s^-1)
2 (J形弯)	未泛化	DMP1	0.0319	0.0934	0.1438	0.2771
	终点泛化	DMP2	0.0316	0.0706	0.1590	0.3348
	终点泛化	DMP3	0.0123	0.0327	0.3513	0.6700
	转向泛化	DMP2	0.0315	0.0080	0.3178	0.5328
	转向泛化	DMP3	0.1080	0.3112	0.3398	1.4057
15 (单移线)	未泛化	DMP1	0.0010	0.0036	0.0584	0.1212
	终点泛化	DMP2	0.0014	0.0036	0.0583	0.1211
	终点泛化	DMP3	0.0026	0.0050	0.0584	0.1212
	转向泛化	DMP2	0.0009	0.0032	0.0416	0.1636
	转向泛化	DMP3	0.0004	0.0012	0.0593	0.1982

Table 2 Deviation analysis of human-like features after trajectory optimization

类型编码	泛化方式	DMP	$e y ¯$ /m	e_y_max/m	$e v ¯$ / (m·s^-1)	e_v_max/ (m·s^-1)
2 (J形弯)	未泛化	DMP1	0.0319	0.0934	0.1438	0.2771
	终点泛化	DMP2	0.0316	0.0706	0.1590	0.3348
	终点泛化	DMP3	0.0123	0.0327	0.3513	0.6700
	转向泛化	DMP2	0.0315	0.0080	0.3178	0.5328
	转向泛化	DMP3	0.1080	0.3112	0.3398	1.4057
15 (单移线)	未泛化	DMP1	0.0010	0.0036	0.0584	0.1212
	终点泛化	DMP2	0.0014	0.0036	0.0583	0.1211
	终点泛化	DMP3	0.0026	0.0050	0.0584	0.1212
	转向泛化	DMP2	0.0009	0.0032	0.0416	0.1636
	转向泛化	DMP3	0.0004	0.0012	0.0593	0.1982

Table 3 The parameters of vehicle in Carsim model

参数	数值
质心距离前轴距离l_f/m	1.040
质心距离后轴距离l_r/m	1.560
最大加速度约束a_max/(m·s^-2)	3
最大前轮转角δ_max/rad	0.584

Fig.10 Reference trajectory and velocity of S-turn

Table 4 MLP online prediction of optimal controller parameters

基元	N_p	q_xy	q_φ	q_v	r
U形弯基元	10	502	652	158	110
单移线基元	14	732	513	215	902

Fig.11 Experimental results of low-speed S-turn

Table 5 Experimental data of low-speed S-turn

算法	e_y/m	e_φ/rad	e_v/(m·s^-1)
LMPC	0.081(72.3%)	0.025(13.6%)	0.14(16.7%)
MLMPC	0.047	0.022	0.12
T-S FMPC	0.055(17.1%)	0.023(4.5%)	0.14(16.7%)
GMLMPC	0.047	0.022	0.12

Table 6 Low-speed S-turn stability index

算法	ω_TP/(rad·s^-1)	$σ δ T P$
LMPC	0.041(-16.3%)	0.0009(40.6%)
MLMPC	0.068(38.7%)	0.0022(243.7%)
T-S FMPC	0.053(8.1%)	0.00091(42,2%)
GMLMPC	0.049	0.00064

Table 6 Low-speed S-turn stability index

算法	ω_TP/(rad·s^-1)	$σ δ T P$
LMPC	0.041(-16.3%)	0.0009(40.6%)
MLMPC	0.068(38.7%)	0.0022(243.7%)
T-S FMPC	0.053(8.1%)	0.00091(42,2%)
GMLMPC	0.049	0.00064

Fig.12 Reference trajectory and velocity of double-lane-change

Table 7 MLP online prediction of optimal controller parameters

基元	N_p	q_xy	q_φ	q_v	r
单移线基元	5	102	652	308	980
直线基元	8	578	513	312	732

Fig.13 Experimental results of high-speed double-lane-change

Table 8 Experimental data of high-speed double-lane-change

算法	e_y/m	e_φ/rad	e_v/(m·s^-1)
LMPC	0.0074(29.8%)	0.0014(16.7%)	0.00026(4%)
MLMPC	0.0057	0.0012	0.00025
T-S FMPC	0.0066(15.8%)	0.0014(16.7%)	0.00026(4%)
GMLMPC	0.0057	0.0012	0.00025

Table 9 High-speed double-lane-change stability index

算法	ω_TP/(rad·s^-1)	$σ δ T P$
LMPC	0.0042(10.5%)	0.000032(-3%)
MLMPC	0.0065(71.1%)	0.000035(6.1%)
T-S FMPC	0.0046(21.1%)	0.000034(3%)
GMLMPC	0.0038	0.000033

Table 9 High-speed double-lane-change stability index

算法	ω_TP/(rad·s^-1)	$σ δ T P$
LMPC	0.0042(10.5%)	0.000032(-3%)
MLMPC	0.0065(71.1%)	0.000035(6.1%)
T-S FMPC	0.0046(21.1%)	0.000034(3%)
GMLMPC	0.0038	0.000033

References 20

[1]	熊璐, 杨兴, 卓桂荣, 等. 无人驾驶车辆的运动控制发展现状综述[J]. 机械工程学报, 2020, 56(10):127-143. doi: 10.3901/JME.2020.10.127
	XIONG L, YANG X, ZHUO G R, et al. Review on motion control of autonomous vehicles[J]. Journal of Mechanical Engineering, 2020, 56(10):127-143. (in Chinese) doi: 10.3901/JME.2020.10.127
[2]	高振海, 朱乃宣, 高菲, 等. 考虑驾驶员特性的自学习换道轨迹规划系统[J]. 汽车工程, 2020, 42(12):1710-1717. doi: 10.19562/j.chinasae.qcgc.2020.12.014
	GAO Z H, ZHU N X, GAO F, et al. Self-learning lane-change trajectory planning system with driver characteristics[J]. Automotive Engineering, 2020, 42(12):1710-1717. (in Chinese)
[3]	LI A, JIANG H B, LI Z J, et al. Human-like trajectory planning on curved road:learning from human drivers[J]. IEEE Transactions on Intelligent Transportation Systems, 2020, 21(8):3388-3397.
[4]	SAMA K, MORALES Y, LIU H, et al. Extracting human-like driving behaviors from expert driver data using deep learning[J]. IEEE Transactions on Vehicular Technology, 2020, 69(9):9315-9329.
[5]	BERGMAN K, LJUNGQVIST O, AXEHILL D. Improved path planning by tightly combining lattice-based path planning and optimal control[J]. IEEE Transactions on Intelligent Vehicles, 2020, 6(1):57-66.
[6]	STANO P, MONTANARO U, TAVERNINI D, et al. Model predictive path tracking control for automated road vehicles:a review[J]. Annual Reviews in Control, 2023,55:194-236.
[7]	杜荣华, 胡鸿飞, 高凯, 等. 基于变预测时域MPC的自动驾驶汽车轨迹跟踪控制研究[J]. 机械工程学报, 2022, 58(24):275-288. doi: 10.3901/JME.2022.24.275
	DU R H, HU H W, GAO K, et al. Research on trajectory tracking control of autonomous vehicle based on mpc with variable predictive horizon[J]. Journal of Mechanical Engineering 58(24):275-288. (in Chinese)
[8]	HE H W, SHI M, LI J W, et al. Design and experiential test of a model predictive path following control with adaptive preview for autonomous buses[J/OL]. Mechanical Systems and Signal Processing, 2021,157:107701.
[9]	李韶华, 杨泽坤, 王雪玮. 基于T-S模糊变权重MPC的智能车轨迹跟踪控制[J]. 机械工程学报, 2023, 59(4):199-212. doi: 10.3901/JME.2023.04.199
	LI S H, YANG Z K, WANG X W. Trajectory tracking control of an intelligent vehicle based on T-S fuzzy variable weight MPC[J]. Journal of Mechanical Engineering 2023, 59(4):199-212. (in Chinese)
[10]	ROKONUZZAMAN M, MOHAJER N, NAHAVANDI S. Human-tailored data-driven control system of autonomous vehicles[J]. IEEE Transactions on Vehicular Technology, 2022, 71(3):2485-2500.
[11]	马跃, 郭烈, 秦增科, 等. 考虑驾驶风格的路径跟踪控制方法[J]. 重庆理工大学学报(自然科学), 2022, 36(11):20-30.
	MA Y, GUO L, QIN Z K, et al. Path tracking control method considering driving styles[J]. Journal of Chongqing University of Technology( Natural Science), 2022, 36( 11) :20-30. (in Chinese)
[12]	HONDA K, OKUDA H, SUZUKI T.Multi-task model predictive control based on continuation with intermediate mode[C]//Proceedings of the 2020 IEEE 23rd International Conference on Intelligent Transportation Systems (ITSC).Rhodes,Greece:IEEE,2020:1-7.
[13]	HONDA K, OKUDA H, SUZUKI T, et al.MPC builder for autonomous drive:automatic generation of MPCs for motion planning and control[C]//Proceedings of the 2023 IEEE Intelligent Vehicles Symposium (IV). Anchorage,AK,US:IEEE,2023:1-8.
[14]	王博洋, 龚建伟, 张瑞增, 等. 基于真实驾驶数据的运动基元提取与再生成[J]. 机械工程学报, 2020, 56(16):155-165. doi: 10.3901/JME.2020.16.155
	WANG B Y, GONG J W, ZHANG R Z, et al. Motion primitives extraction and regeneration based on real driving data[J]. Journal of Mechanical Engineering, 2020, 56(16):155-165. (in Chinese) doi: 10.3901/JME.2020.16.155
[15]	WANG B Y, GONG J W, LIANG W, et al.Regeneration and joining of the learned motion primitives for automated vehicle motion planning applications[C]//Proceedings of 2019 IEEE Intelligent Vehicles Symposium (IV).Paris,France:IEEE,2019:790-797.
[16]	RAJAMANI R. Vehicle dynamics and control[M]. Berlin, Germany:Springer, 2011.
[17]	卢佳兴, 刘海鸥, 关海杰, 等. 基于双参数自适应优化的无人履带车辆轨迹跟踪控制[J]. 兵工学报, 2023, 44(4):960-971.
	LU J X, LIU H O GUAN H J, et al. Trajectory tracking control of unmanned tracked vehicles based on adaptive dual-parameter optimization[J]. Acta Armamentarii, 2023, 44(4):960-971. (in Chinese) doi: 10.12382/bgxb.2022.0009
[18]	龚建伟. 无人驾驶车辆模型预测控制[M]. 北京: 北京理工大学出版社, 2020.
	GONG J W. Model predictive control for self-driving vehicles[M]. Beijing: Beijing Institute of Technology Press, 2020. (in Chinese)
[19]	臧勇, 蔡英凤, 孙晓强, 等. 基于可拓博弈的智能汽车轨迹跟踪协调控制方法研究[J]. 机械工程学报, 2022, 58(8):181-194. doi: 10.3901/JME.2022.08.181
	ZANG Y, CAI Y F, SUN X Q, et al. Research on intelligent vehicle trajectory tracking coordination control method based on extension game[J]. Journal of Mechanical Engineering, 2022, 58(8):181-194. (in Chinese) doi: 10.3901/JME.2022.08.181
[20]	NA X X, COLE D J. Linear quadratic game and non-cooperative predictive methods for potential application to modelling driver-AFS interactive steering control[J]. Vehicle System Dynamics, 2013, 51(2):165-198.