基于速度障碍模型的智能汽车轨迹规划控制方法研究

doi:10.12382/bgxb.2024.0058

摘要/Abstract

摘要：

为提高智能汽车的避障能力,提出一种基于速度障碍模型的智能汽车轨迹规划控制方法。结合速度障碍法和障碍物膨胀法,建立智能汽车的速度障碍模型,将动态障碍物在速度空间中的运动不确定转化为位置不确定,实现安全裕度根据障碍物尺寸和相对速度自适应调整。为兼顾轨迹跟踪精度和行驶稳定性,根据汽车状态方程、模糊控制原理和模型预测控制原理设计智能汽车模糊模型预测控制器(Fuzzy Model Predictive Control,FMPC)。为验证该方法的有效性,采用仿真软件建立其仿真模型。仿真结果表明:对多个随机的静、动态障碍物均可实现避障,且在避障后快速平稳地跟踪参考轨迹。通过避障稳定性分析得出,目标车速为100km/h,其最大横向速度为4.01km/h,最大横摆角速度为20.8°/s,最大质心侧偏角为2.32°,满足汽车行驶稳定性要求,该方法有效提高了智能汽车的避障能力及其行驶稳定性。

关键词: 避障, 速度障碍, 轨迹规划, 模糊控制

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

中图分类号:

何洋, 李刚. 基于速度障碍模型的智能汽车轨迹规划控制方法研究[J]. 兵工学报, 2025, 46(4): 240058-.

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-.

图/表 23

图1 汽车横摆动力学模型

Fig.1 Vehicle yaw dynamic model

图2 轨迹跟踪误差模型

Fig.2 Trajectory tracking error model

图3 输入、输出隶属函数

Fig.3 Membership functions of input and output

表1 τQ模糊规则

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

表2 τR模糊规则

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

图4 响应曲面

Fig.4 Response surface

图5 汽车点质量模型

Fig.5 Vehicle point mass model

图6 障碍物膨胀模型图

Fig.6 Obstacle expansive model

图7 智能汽车速度障碍模型

Fig.7 Velocity obstacle model of intelligent vehicle

图8 基于VOM的智能汽车轨迹规划控制逻辑架构

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

表3 汽车相关参数

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

表3 汽车相关参数

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

图9 仿真模型

Fig.9 Simulation model

图10 转向角响应特性

Fig.10 Response characteristics of steering angle

表4 统计值

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

图11 双移线轨迹跟踪

Fig.11 Double lane change trajectory tracking

表5 轨迹跟踪误差

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

图12 车速60km/h时动、静态障碍物避障

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

图13 车速100km/h时动、静态障碍物避障

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

表6 安全裕度

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

图14 速度跟踪曲线

Fig.14 Speed tracking curve

图15 汽车横摆包络线区域示意图

Fig.15 Schematic diagram of vehicle yaw envelope region

图16 横向速度与横摆角速度变化关系

Fig.16 Relation between lateral velocity and yaw rate

图17 质心侧偏角与横摆角速度变化关系

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

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