Local Path Planning for Unmanned Ground Vehicles Based on Improved Artificial Potential Field Method in Frenet Coordinate System

doi:10.12382/bgxb.2023.0305

Abstract

Abstract:

The artificial potential field method is widely used in the local path planning for unmanned ground vehicle (UGV) due to its small amount of computation and high accuracy. For the problems of target unreachability, local minimum and falling into U-shaped obstacles existing in the conventional artificial potential field method, a local path planning algorithm based on the improved artificial potential field method in Frenet coordinate system is proposed. In this paper, the Frenet coordinate system is used to describe the UGV’s obstacle avoidance movement, which simplifies the planning model and addresses the difficulty in expressing the relative position of UGV and the road during path planning. A safety ellipse model and the concept of prediction distance are proposed to adjust the influence area of the potential field. Additionally, the repulsive field function is improved by adding the reference line potential field and the dynamic velocity potential field based on the Frenet coordinate system. These modifications enable the UGVs to avoid obstacles under both static and dynamic conditions. The path planning methods are proposed to launch the static and dynamic obstacle avoidance simulation experiments with different vehicle speeds in straight and curved road scenarios using mathematical simulation software. The results demonstrate that the front wheel turning angle and traverse angular velocity at different vehicle speeds are controlled within a small range, and the improved algorithm can effectively solve the defects of the conventional artificial potential field method. Besides, compared with the rapidly-exploring random tree(RRT) algorithm, the computational efficiency of path planning of the improved algorithm in the obstacle avoidance process is improved by 42.8%, and achieves better computational performance.

Key words: unmanned ground vehicle, local path planning, artificial potential field method, Frenet coordinate system

CLC Number:

JI Peng, GUO Minghao. Local Path Planning for Unmanned Ground Vehicles Based on Improved Artificial Potential Field Method in Frenet Coordinate System[J]. Acta Armamentarii, 2024, 45(7): 2097-2109.

Figures/Tables 29

Fig.1 Establishment of Frenet coordinate system

Fig.2 Description of path diagram in Cartesian coordinate system(Left:the depiction of vehicle trajectory on the roadway; Right:the actual mapping of vehicle trajectory in Cartesian coordinate system)

Fig.3 Description of path diagram in Frenet coordinate system(Left: the depiction of vehicle trajectory on the roadway; Right: the actual mapping of vehicle trajectory in Frenet coordinate system)

Fig.4 Trajectory generation in Frenet coordinate system

Table 1 The parameters and meanings of Cartesian coordinate system

参数	含义
r_h/m	车辆的位置矢量
v_h/(m·s^-1)	车辆的速度矢量
a_h/(m·s^-2)	车辆的加速度矢量
k_h/m^-1	车的位置在车轨迹上的曲率
τ_h	车轨迹切线上的单位向量
n_h	车轨迹法线上的单位向量

Table 2 The parameters and meanings of Frenet coordinate system

参数	含义
r_r/m	车辆投影的位置矢量
$s ·$ /(m·s^-1)	纵向速度
$s · ·$ /(m·s^-2)	纵向加速度
k_r/m^-1	投影的位置矢量在道路几何上的曲率
$l ·$ /(m·s^-1)	横向速度
$l · ·$ /(m·s^-2)	横向加速度
τ_r	投影在道路几何上切线的单位向量
n_r	投影在道路几何上法线的单位向量
l'	横向位移对弧长的1阶导数
l″	横向位移对弧长的2阶导数

Table 2 The parameters and meanings of Frenet coordinate system

参数	含义
r_r/m	车辆投影的位置矢量
$s ·$ /(m·s^-1)	纵向速度
$s · ·$ /(m·s^-2)	纵向加速度
k_r/m^-1	投影的位置矢量在道路几何上的曲率
$l ·$ /(m·s^-1)	横向速度
$l · ·$ /(m·s^-2)	横向加速度
τ_r	投影在道路几何上切线的单位向量
n_r	投影在道路几何上法线的单位向量
l'	横向位移对弧长的1阶导数
l″	横向位移对弧长的2阶导数

Fig.5 Potential field diagram of artificial potential field method

Fig.6 Vehicle obstacle avoidance sketch

Fig.7 Safe elliptic graph

Fig.8 Addressing the middle equilibrium point

Fig.9 Solving the problem of long paths

Fig.10 Solving the problem of unreachable targets

Fig.11 Flow chart of prediction distance algorithm

Fig.12 Solving the problem of U-shaped obstacles

Fig.13 Comparison of the proposed algorithm and the algorithm in Ref.[6]

Table 3 Comparison of U-shaped obstacle algorithms

参数	传统人工势场法	文献[6]算法	本文改进人工势场法
步数	-	71	62
路径长/m	-	7.1	5.6
时间/s	-	0.1114	0.036

Fig.14 Vehicle speed diagram

Fig.15 Schematic diagram of avoiding dynamic obstacles

Fig.16 Path planning effects of different methods

Table 4 Comparison of algorithm simulation data

算法	仿真时间/s	仿真步长	路径长度/m
RRT算法	0.92	0.5	1652
传统人工势场法	0.40	0.5
改进人工势场法	0.47	0.5	1476

Fig.17 Schematic diagram of automatic driving system

Fig.18 Moving trajectory during static obstacle avoidance(Left:preparing for obstacle avoidance; Middle:avoiding obstacles; Right:obstacle avoidance completed)

Fig.19 Simulation path tracking effect

Fig.20 Moving trajectory during dynamic obstacle avoidance(Left:preparing for obstacle avoidance; Middle:Avoiding obstacles; Right:obstacle avoidance completed)

Fig.21 Joint simulation path tracking effect

Fig.22 Simulation process of avoiding U-shaped obstacles (Left:preparing for obstacle avoidance;Middle:avoiding obstacles; Right:obstacle avoidance completed)

Fig.23 Simulation process of avoiding dynamic obstacles (Left:preparing for obstacle avoidance;Middle:avoiding obstacles; Right:obstacle avoidance completed)

Fig.24 Simulation process of avoiding dynamic obstacles under large curvature(Left:preparing for obstacle avoidance; Middle:avoiding obstacles; Right:obstacle avoidance completed)

Fig.25 Avoid dynamic obstacle path tracking effect

References 20

[1]	翟丽, 张雪莹, 张闲, 等. 基于势场法的无人车局部动态避障路径规划算法[J]. 北京理工大学学报, 2022, 42(7):696-705.
	ZHAI L, ZHANG X Y, ZHANG X, et al. Local dynamic obstacle avoidance path planning algorithm for unmanned vehicles based on potential field method[J]. Transactions of Beijing Institute of Technology, 2022, 42(7):696-705. (in Chinese)
[2]	牛秦玉, 李美凡, 赵勇. 改进人工势场法的AGV路径规划算法研究[J]. 机床与液压, 2022, 50(17):19-24. doi: 10.3969/j.issn.1001-3881.2022.17.004
	NIU Q Y, LI M F, ZHAO Y. Research on AGV path planning algorithm based on improved artificial potential field method[J]. Machine and Hydraulic, 2022, 50(17):19-24. (in Chinese)
[3]	YUAN C C, WENG S F, SHEN J, et al. Research on active collision avoidance algorithm for intelligent vehicle based on improved artificial potential field model[J]. International Journal of Advanced Robotic Systems, 2020, 17(3):172988 142091123.
[4]	修彩靖, 陈慧. 基于改进人工势场法的无人驾驶车辆局部路径规划的研究[J]. 汽车工程, 2013, 35(9):808-811.
	XIU C J, CHEN H. Research on local path planning of autonomous vehicles based on improved artificial potential field method[J]. Automotive Engineering, 2013, 35(9): 808-811. (in Chinese)
[5]	陈相茹. 基于人工势场理论的车辆行驶路径建模研究[D]. 长春: 吉林大学, 2020.
	CHEN X R. Research on vehicle driving path modeling based on artificial potential field theory[D]. Changchun: Jilin University, 2020. (in Chinese)
[6]	李二超, 王玉华. 改进人工势场法的移动机器人避障轨迹研究[J]. 计算机工程与应用, 2022, 58(6):296-304. doi: 10.3778/j.issn.1002-8331.2108-0122
	LI E C, WANG Y H. Research on obstacle avoidance trajectory of mobile robot based on improved artificial potential field method[J]. Computer Engineering and Application, 2022, 58(6):296-304. (in Chinese)
[7]	孙鹏耀, 黄炎焱, 潘尧. 基于改进势场法的移动机器人路径规划[J]. 兵工学报, 2020, 41(10):2106-2121. doi: 10.3969/j.issn.1000-1093.2020.10.021
	SUN P Y, HUANG Y Y, PAN Y. Mobile robot path planning based on improved potential field method[J]. Acta Armamentarii, 2020, 41(10):2106-2121. (in Chinese)
[8]	HOU P Q, PAN H, GUO C. Simulation research for mobile robot path planning based on improved artificial potential field method recommended by the AsiaSim[J]. International Journal of Modeling, Simulation and Scientific Computing (English), 2017(2):008.
[9]	王沙晶, 陈建业. 基于Frenet坐标系的智能车运动规划研究[J]. 移动电源与车辆, 2019, 195(1):22-29.
	WANG S J, CHEN J Y. Research on motion planning of intelligent vehicle based on Frenet coordinate system[J]. Mobile Power and Vehicle, 2019, 195(1):22-29. (in Chinese)
[10]	魏民祥, 滕德成, 吴树凡. 基于Frenet坐标系的自动驾驶轨迹规划与优化算法[J]. 控制与决策, 2021, 36(4):815-824.
	WEI M X, TENG D C, WU S F. Autonomous driving trajectory planning and optimization algorithm based on Frenet coordinate system[J]. Control and Decision, 2021, 36(4):815-824. (in Chinese)
[11]	刘冰雁, 叶雄兵, 方胜良, 等. 基于Frenet和改进人工势场的在轨规避路径自主规划[J]. 北京航空航天大学学报, 2021, 47(4):731-741.
	LIU B Y, YE X B, FANG S L, et al. On-orbit avoidance path autonomous planning based on Frenet and improved artificial potential field[J]. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(4):731-741. (in Chinese)
[12]	王威, 陈慧岩, 马建昊, 等. 基于Frenet坐标系和控制延时补偿的智能车辆路径跟踪[J]. 兵工学报, 2019, 40(11):2336-2351. doi: 10.3969/j.issn.1000-1093.2019.11.019
	WANG W, CHEN H Y, MA J H, et al. Intelligent vehicle path tracking based on Frenet coordinate system and control delay compensation[J]. Acta Armamentarii, 2019, 40(11):2336-2351. (in Chinese) doi: 10.3969/j.issn.1000-1093.2019.11.019
[13]	袁春, 龚城, 何成诚, 等. Frenet坐标系及凸近似避障原理的无人车局部路径规划[J]. 重庆理工大学学报(自然科学), 2022, 36(4):59-67.
	YUAN C, GONG C, HE C C, et al. Frenet coordinate system and convex approximation obstacle avoidance principle of unmanned vehicle local path planning[J]. Journal of Chongqing University of Technology(Natural Science), 2022, 36(4):59-67. (in Chinese)
[14]	李萌. 基于Frenet坐标系的智能车辆多场景轨迹规划研究[D]. 哈尔滨: 哈尔滨工业大学, 2021.
	LI M. Research on multi-scenario trajectory planning of intelligent vehicles based on Frenet coordinate system[D]. Harbin: Harbin Institute of Technology, 2021. (in Chinese)
[15]	WERLING M, ZIEGLER J, KAMMEL S, et al. Optimal trajectory generation for dynamic street scenarios in a Frenét Frame[C/OL]//Proceedings of 2010 IEEE International Conference on Robotics and Automation. Anchorage, AK, US:IEEE, 2010.
[16]	陈天德, 黄炎焱, 沈炜. 基于虚拟障碍物法的无震荡航路规划[J]. 兵工学报, 2019, 40(3):651-658. doi: 10.3969/j.issn.1000-1093.2019.03.025
	CHEN T D, HUANG Y Y, SHEN W. Shock-free route planning based on virtual obstacle method[J]. Acta Armamentarii, 2019, 40(3):651-658. (in Chinese)
[17]	韩宇洪. 基于改进人工势场法的无人车避障路径规划研究[D]. 重庆: 重庆理工大学, 2020.
	HAN Y H. Research on obstacle avoidance path planning of unmanned vehicles based on improved artificial potential field method[D]. Chongqing: Chongqing University of Technology, 2020. (in Chinese)
[18]	朱伟达. 基于改进型人工势场法的车辆避障路径规划研究[D]. 镇江: 江苏大学, 2017.
	ZHU W D. Research on vehicle obstacle avoidance path planning based on improved artificial potential field method[D]. Zhenjiang: Jiangsu University, 2017. (in Chinese)
[19]	范世鹏, 祁琪, 路坤锋, 等. 基于改进人工势场法的巡航导弹自主避障技术[J]. 北京理工大学学报, 2018, 38(8):828-834.
	FAN S P, QI Q, LU K F, et al. Autonomous obstacle avoidance technology of cruise missile based on improved artificial potential field method[J]. Transactions of Beijing Institute of Technology, 2018, 38(8):828-834. (in Chinese)
[20]	RASEKHIPOUR Y, KHAJEPOUR A, CHEN S K, et al. A potential field-based model predictive path-planning controller for autonomous road vehicles[J]. IEEE Transactions on Intelligent Transportation Systems, 2017, 18(5):1255.