Research on Trajectory Planning Control Method of Intelligent Vehicle Based on Velocity Obstacle Model

doi:10.12382/bgxb.2024.0058

Abstract

Abstract:

In order to improve the obstacles avoidance ability of intelligent vehicles,an trajectory planning and control method of intelligent vehicles is proposed based on velocity obstacle model.The proposed method is used to establish a velocity obstacle model for intelligent vehicles by combining the velocity obstacle method and obstacle expansion method,The motion uncertainty of dynamic obstacles in the velocity space is transformed into the positional uncertainty,and the safety margin is adaptively adjusted by obstacle size and relative velocity.To balance trajectory tracking accuracy and driving stability,a fuzzy model predictive controller (FMPC) is designed based on the equation of state for vehicle,the fuzzy control principle and the model predictive control principle.A simulation model is established to verify the effectiveness of the proposed method.The simulated results show that the proposed method can be used to avoid the multiple random static and dynamic obstacles,and the reference trajectory can be quickly and smoothly tracked after obstacles avoidance.Based on the analysis of obstacles avoidance stability,it is concluded that the target speed is 100km/h,the maximum lateral speed is 4.01km/h,the maximum yaw rate is 20.8°/s,and the maximum centroid side slip angle is 2.32°,which meet the requirements of driving stability.The proposed method effectively improves the obstacle avoidance ability and driving stability of intelligent vehicles.

Key words: obstacles avoidance, velocity obstacle, trajectory planning, fuzzy control

CLC Number:

HE Yang, LI Gang. Research on Trajectory Planning Control Method of Intelligent Vehicle Based on Velocity Obstacle Model[J]. Acta Armamentarii, 2025, 46(4): 240058-.

Figures/Tables 23

Fig.1 Vehicle yaw dynamic model

Fig.2 Trajectory tracking error model

Fig.3 Membership functions of input and output

Table 1 Fuzzy rules of τQ

e_φ	e_y
e_φ	NB	NM	NS	ZO	PS	PM	PB
NB	PB	PM	PM	PS	PM	PM	PB
NM	PM	PM	PS	PS	PS	PM	PM
NS	PM	PS	PS	ZO	PS	PS	PM
ZO	PB	PS	PS	ZO	PS	PS	PB
PS	PM	PS	PS	ZO	PS	PS	PM
PM	PM	PM	PS	PS	PS	PM	PM
PB	PB	PM	PS	PS	PS	PM	PB

Table 2 Fuzzy rules of τR

κ_ref	e_y
κ_ref	NB	NM	NS	ZO	PS	PM	PB
ZO	PB	PM	PS	ZO	PS	PM	PB
PS	PM	PS	PS	ZO	PS	PS	PM
PM	PM	PS	PS	PM	PS	PS	PM
PB	PB	PM	PM	PB	PM	PM	PB

Fig.4 Response surface

Fig.5 Vehicle point mass model

Fig.6 Obstacle expansive model

Fig.7 Velocity obstacle model of intelligent vehicle

Fig.8 Logic framework of trajectory planning of intelligent vehicle based on VOM

Table 3 Related parameters of SUV

参数	数值
长×宽×高/m	4.63×1.82×1.71
簧载质量m/kg	1430
转动惯量I_x/(kg·m²)	717.7
转动惯量I_y/(kg·m²)	2059.2
转动惯量I_z/(kg·m²)	2059.2
轴距l/m	2.68
前轮距T_f/m	1.63
后轮距T_r/m	1.64
质心高度h/m	0.61
轮胎纵向刚度C_sf、C_sr/(N·m^-1)	8×10⁵
前轮侧偏刚度 $C α f$ /(N·rad^-1)	7×10⁴
后轮侧偏刚度 $C α r$ /(N·rad^-1)	6.5×10⁴
轮胎规格	235/55 R18

Table 3 Related parameters of SUV

参数	数值
长×宽×高/m	4.63×1.82×1.71
簧载质量m/kg	1430
转动惯量I_x/(kg·m²)	717.7
转动惯量I_y/(kg·m²)	2059.2
转动惯量I_z/(kg·m²)	2059.2
轴距l/m	2.68
前轮距T_f/m	1.63
后轮距T_r/m	1.64
质心高度h/m	0.61
轮胎纵向刚度C_sf、C_sr/(N·m^-1)	8×10⁵
前轮侧偏刚度 $C α f$ /(N·rad^-1)	7×10⁴
后轮侧偏刚度 $C α r$ /(N·rad^-1)	6.5×10⁴
轮胎规格	235/55 R18

Fig.9 Simulation model

Fig.10 Response characteristics of steering angle

Table 4 Statistical values

参数	车速/(km·h^-1)	MPC	FMPC	FMPC优化量/%
超调量/%	60	12.2	7.9	4.3
超调量/%	100	27.1	14.7	12.4
上升时间/s	60	0.43	0.35	18.6
上升时间/s	100	0.44	0.37	15.9
峰值时间/s	60	0.93	0.71	23.6
峰值时间/s	100	0.95	0.81	14.7
过度时间/s	60	1.92	0.98	48.9
过度时间/s	100	2.27	1.21	46.7

Fig.11 Double lane change trajectory tracking

Table 5 Trajectory tracking error m

车速/(km·h^-1)	MPC	FMPC	FMPC优化量/%
60	0.23	0.10	56.5
100	0.69	0.31	55.1

Fig.12 Dynamic and static obstacles avoidance at 60km/h

Fig.13 Dynamic and static obstacles avoidance at 100km/h

Table 6 Safety margin

障碍物	方向	车速/(km·h^-1)
障碍物	方向	60	100
A	纵向	14.3	16.2
A	横向	1.22	2.36
B	纵向	8.13	11.7
B	横向	1.03	1.85
C	纵向	5.29	14.3
C	横向	1.02	1.47
D	纵向	8.22	16.1
D	横向	1.17	1.22
E	纵向	8.17	10.6
E	横向	1.09	1.49

Fig.14 Speed tracking curve

Fig.15 Schematic diagram of vehicle yaw envelope region

Fig.16 Relation between lateral velocity and yaw rate

Fig.17 Relation between centroid side slip angle and yaw rate

References 31

[1]	龚建伟, 龚乘, 林云龙, 等. 智能车辆规划与控制策略学习方法综述[J]. 北京理工大学学报, 2022, 42(7):665-674.
	GONG J Y, GONG C, LIN Y L, et al. Review on machine learning methods for motion planning and control policy of intelligent vehicles[J]. Transactions of Beijing Institute of Technology, 2022, 42(7):665-674. (in Chinese)
[2]	WANG J S, WANG J, HAN Q L. Receding-horizon trajectory planning for under-actuated autonomous vehicles based on collaborative neurodynamic optimization[J]. IEEE/CAA Journal of Automatica Sinica, 2022, 9(11):1909-1923.
[3]	李新凯, 虎晓诚, 马萍, 等. 基于改进DDPG的无人驾驶避障跟踪控制[J]. 华南理工大学学报(自然科学版), 2023, 51(11):44-55. doi: 10.12141/j.issn.1000-565X.220747
	LI X K, HU X C, MA P, et al. Driverless obstacle avoidance and tracking control based on improved DDPG[J]. Journal of South China University of Technology(Natural Science Edition), 2023, 51(11):44-55. (in Chinese) doi: 10.12141/j.issn.1000-565X.220747
[4]	ZHANG X L, ZHANG W X, ZHAO Y Q, et al. Personalized motion planning and tracking control for autonomous vehicles obstacle avoidance[J]. IEEE Transactions on Vehicular Technology, 2022, 71(5):4733-4747.
[5]	王国栋, 刘立, 孟宇, 等. 一体式车辆避撞轨迹规划与跟踪控制[J]. 交通运输系统工程与信息, 2022, 22(2):127-136.
	WANG G D, LIU L, MENG Y, et al. Integrated control of trajectory planning and tracking for vehicle collision avoidance[J]. Journal of Transportation Systems Engineering and Information Technology, 2022, 22(2):127-136. (in Chinese)
[6]	李耀华, 范吉康, 刘洋, 等. 自适应双时域参数MPC的智能车辆路径规划与跟踪控制[J]. 汽车安全与节能学报, 2021, 12(4):528-539.
	LI Y H, FAN J K, LIU Y, et al. Path planning and path tracking control for autonomous vehicle based on MPC with adaptive dual-horizon-parameters[J]. Automotive Safety and Energy, 2021, 12(4):528-539. (in Chinese)
[7]	WANG P W, GAO S, LI L, et al. Obstacle avoidance path planning design for autonomous driving vehicles based on an improved artificial potential field algorithm[J]. Energies, 2019, 12(12):2342.
[8]	李军, 周伟, 唐爽. 基于自适应拟合的智能车换道避障轨迹规划[J]. 汽车工程, 2023, 45(7):1174-1183.
	LI J, ZHOU W, TANG S. Lane change and obstacle avoidance trajectory planning of intelligent vehicle based on adaptive fitting[J]. Automotive Engineering, 2023, 45(7):1174-1183. (in Chinese)
[9]	方秋雨, 张蕴霖, 麻壮壮, 等. 未知环境下基于控制障碍函数的无人车轨迹规划[J]. 兵工学报, 2023, 44(增刊2):90-100.
	FANG Q Y, ZHANG Y L, MA Z Z, et al. Control barrier functions-based trajectory planning for unmanned ground vehicles in unknown environment[J]. Acta Armamentarii, 2023, 44(S2):90-100. (in Chinese) doi: 10.12382/bgxb.2023.0882
[10]	王明强, 王震坡, 张雷. 基于碰撞风险评估的智能汽车局部路径规划方法研究[J]. 机械工程学报, 2021, 57(10):28-40. doi: 10.3901/JME.2021.10.028
	WANG M Q, WANG Z P, ZHANG L. Local path planning for intelligent vehicles based on collision risk evaluation[J]. Journal of Mechanical Engineering, 2021, 57(10):28-40. (in Chinese) doi: 10.3901/JME.2021.10.028
[11]	QIN P, LIU F, GUO Z Z, et al. Hierarchical collision-free trajectory planning for autonomous vehicles based on improved artificial potential field method[J]. Transactions of the Institute of Measurement and Control, 2022, 46(4):799-812.
[12]	ZHOU X Z, PEI X F, YANG B. Hierarchical hybrid trajectory planning for autonomous vehicle considering multiple road types[J]. Proceedings of the Institution of Mechanical Engineers, 2023, 237(9):2217-2230.
[13]	张利鹏, 苏泰, 严勇. 基于采样区域优化的智能车辆轨迹规划方法[J]. 机械工程学报, 2022, 58(14):276-287. doi: 10.3901/JME.2022.14.276
	ZHANG L P, SU T, YAN Y. Trajectory planning method of intelligent vehicle based on sampling area optimization[J]. Journal of Mechanical Engineering, 2022, 58(14):276-287. (in Chinese) doi: 10.3901/JME.2022.14.276
[14]	杨彬, 宋学伟, 高振海. 考虑车辆运动约束的最优避障轨迹规划算法[J]. 汽车工程, 2021, 43(4):562-570.
	YANG B, SONG X W, GAO Z H. Optimal obstacle avoidance trajectory planning algorithm considering vehicle motion constraints[J]. Automotive Engineering, 2021, 43(4):562-570. (in Chinese)
[15]	肖宏宇, 付志强, 陈慧勇. 面向低速自动驾驶车辆的避障规划研究[J]. 同济大学学报(自然科学版), 2019, 47(增刊1):164-170.
	XIAO H Y, FU Z Q, CHEN H Y. Obstacle avoidance planning for low-speed autonomous ground vehicles[J]. Journal of Tongji University(Natural Science), 2019, 47(S1):164-170. (in Chinese)
[16]	TANG W B, ZHOU Y, ZHANG T W, et al. Cooperative collision avoidance in multirobot systems using fuzzy rules and velocity obstacles[J]. Robotica, 2022, 41(2):668-689.
[17]	XI Z M, TORKAMANI E A. Analytic velocity obstacle for efficient collision avoidance computation and a comparison study with sampling and optimization-based approaches[J]. Journal of Autonomous Vehicles and Systems, 2022, 2(1):011001.
[18]	ZHAO J W, LI S H, FAN H Y. Model predictive coordinated control of heavy-duty vehicle using non-linear three-directional coupled model[J]. IET Intelligent Transport Systems, 2020, 14(4):257-265.
[19]	NGUYEN A T, SENTOUH C, ZHANU H, et al. Fuzzy static output feedback control for path following of autonomous vehicles with transient performance improvements[J]. IEEE Transactions on Intelligent Transportation Systems, 2020, 21(7):3069-3079.
[20]	陈虹, 申忱, 郭洪艳, 等. 面向动态避障的智能汽车滚动时域路径规划[J]. 中国公路学报, 2019, 32(1):162-172.
	CHEN H, SHEN C, GUO H Y, et al. Moving horizon path planning for intelligent vehicle considering dynamic obstacle avoidance[J]. China Journal Highway and Transport, 2019, 32(1):162-172. (in Chinese)
[21]	FUNKE J, BROWN M, ERLIEN S M, et al. Collision avoidance and stabilization for autonomous vehicles in emergency scenarios[J]. IEEE Transactions on Control Systems Technology, 2017, 25(4):1204-1216.
[22]	YE X Y, ZHU S P, CHEN S. Research on model predictive trajectory following control of automatic vehicle considering prediction[J]. International Journal of Wireless and Mobile Computing, 2021, 21(1):52-58.
[23]	LIANG Y, LI Y, KHAJEPOUR A, et al. Holistic adaptive multi-model predictive control for the path following of 4WID autonomous vehicles[J]. IEEE Transactions on Vehicular Technology, 2021, 70(1):69-81.
[24]	DONG H X, ZHUANG W C, YIN G D, et al. Energy-optimal braking control using a double-layer scheme for trajectory planning and tracking of connected electric vehicles[J]. Chinese Journal of Mechanical Engineering, 2021, 34(5):60-71.
[25]	裴红蕾. 智能汽车换道避障路径规划与跟踪方法[J]. 中国安全科学学报, 2018, 28(9):26-32. doi: 10.16265/j.cnki.issn1003-3033.2018.09.005
	PEI H L. Method of path planning and tracking for intelligent vehicle obstacle avoidance by lane changing[J]. China Safety Science Journal, 2018, 28(9):26-32. (in Chinese) doi: 10.16265/j.cnki.issn1003-3033.2018.09.005
[26]	HAO X, DONG W C, ZHUANG G D, et al. Energy-optimal braking control using a double-layer scheme for trajectory planning and tracking of connected electric vehicles[J]. Chinese Journal of Mechanical Engineering, 2021, 34(5):60-71.
[27]	邓海鹏, 麻斌, 赵海光, 等. 自主驾驶车辆紧急避障的路径规划与轨迹跟踪控制[J]. 兵工学报, 2020, 41(3):585-594. doi: 10.3969/j.issn.1000-1093.2020.03.020
	DENG H P, MA B, ZHAO H G, et al. Path planning and tracking control of autonomous vehicle for obstacle avoidance[J]. Acta Armamentarii, 2020, 41(3):585-594. (in Chinese) doi: 10.3969/j.issn.1000-1093.2020.03.020
[28]	王嘉文, 孙晨晨, 赵靖, 等. 交通事件下路段通行能力多层模糊估计方法[J]. 交通运输系统工程与信息, 2023, 23(6):100-110.
	WANG J W, SUN C C, ZHAO J, et al. Multilayer fuzzy estimation method for road traffic capacity affected by traffic incidents[J]. Journal of Transportation Systems Engineering and Information Technology, 2023, 23(6):100-110. (in Chinese)
[29]	AREFNEZHAD S, GHAFFAI A, KHODAYARI A, et al. Modeling of double lane change maneuver of vehicles[J]. International Journal of Automotive Technology, 2018, 19(2):271-279.
[30]	FUNK J, BROWN J, ERLIEN S M, et al. Collision avoidance and stabilization for autonomous vehicles in emergency scenarios[J]. IEEE Transactions on Control Systems Technology, 2017, 25(4):1204-1216.
[31]	刘凯, 龚建伟, 陈舒平, 等. 高速无人驾驶车辆最优运动规划与控制的动力学建模分析[J]. 机械工程学报, 2018, 54(14):141-151. doi: 10.3901/JME.2018.14.141
	LIU K, GONG J W, CHEN S P, et al. Dynamic modeling analysis of optimal motion planning and control for high-speed self-driving vehicles[J]. Journal of Mechanical Engineering, 2018, 54(14):141-151. (in Chinese) doi: 10.3901/JME.2018.14.141