Path Planning Method Integrating Curve Combination and Numerical Optimization for Parallel Parking on Narrow Road

doi:10.12141/j.issn.1000-565X.240581

Abstract

Abstract:

To address the challenges of abrupt curvature changes, high collision risks, and repeated adjustments in parallel parking within narrow urban passages, this study proposes a three-segment one-step path planning method integrating curve combination and numerical optimization to enhance vehicle’s steering performance and dynamic obstacle avoidance capabilities, and to improve the parking efficiency and safety. Firstly, based on the curvature characteristics of arcs and spiral curves, two types of curve combinations, namely CAC (Clothoid Curve-Arc-Clothoid Curve) and CC (Clothoid Curve-Clothoid Curve), are designed. Secondly, the parking process is reversed, and the CAC curve combination is used to design the path of the end section. Then, a constrained optimization model based on the CC curve combination is constructed to plan the path of the starting section, and the middle section path is designed by introducing the quintic polynomial curve. Finally, multi-condition simulation tests are carried out in the quasi-feasible area through Matlab. The results show that the proposed method can plan a collision-free and continuously curved feasible path in a narrow scene with a channel width of only 3 meters, without occupying wide channel. Comparative analysis reveals significant advantages of the proposed method over quintic polynomial curve and arc-clothoid curve-straight methods in terms of path smoothness, obstacle avoidance and space utilization efficiency. Model predictive control validation confirms that the vehicle adopting the proposed method is of precise path tracking performance with continuous front-wheel steering angle changes. The proposed three-segment one-step path planning method provides an efficient and safe solution to narrow-space parallel parking, and effectively improves the parking efficiency, thus alleviating road congestion caused by roadside parking operations and improving urban traffic efficiency.

Key words: automatic parking, path planning, clothoid curve, numerical optimization

CLC Number:

U491.7

CHENG Guozhu, XUE Daoan, GU Shuang. Path Planning Method Integrating Curve Combination and Numerical Optimization for Parallel Parking on Narrow Road[J]. Journal of South China University of Technology(Natural Science Edition), 2025, 53(11): 77-89.

Figures/Tables 18

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Table 1

Table 2

Fig.9

Table 3

Solution parameters of path planning"

起点坐标/m	C₁₂/m^-2	C₂₃/m^-2	$k P 2$ /m^-1	$y A, m a x$ /m
（8.950 0，3.622 5）	0.179 1	0.287 1	0.205 3	5.123 2
（8.950 0，3.825 5）	0.287 1	0.229 1	0.238 1	5.356 5
（9.450 0，3.622 5）	0.080 7	0.287 1	0.148 7	5.137 7
（9.450 0，3.825 5）	0.193 2	0.206 4	0.238 1	5.241 3

Table 3

Fig.10

Table 4

Parking conditions of the comparison methods"

方法	起点坐标/m	是否满足碰撞约束	是否满足曲率约束	$y A, m a x$ /m
方法1	（8.108 2，3.622 5）	是	否	5.299 4
方法1	（8.407 4，3.822 5）	否	否	5.501 2
方法2	（8.108 2，3.622 5）	是	是	5.362 5
方法2	（8.407 4，3.822 5）	否	是	5.559 5

Table 4

Fig.11

Fig.12

Fig.13

Fig.14

References 16

[1]	张家旭，赵健，施正堂，等．基于回旋曲线的平行泊车路径规划和跟踪控制［J］．吉林大学学报（工学版），2020，50（6）：2247-2257．
	ZHANG Jia-xu， ZHAO Jian， SHI Zheng-tang，et al ．Path planning and tracking control for parallel parking based on clothoid curve［J］．Journal of Jilin University （Engineering and Technology Edition），2020，50（6）：2247-2257．
[2]	YU L， CAI Y， FENG X，et al ．Parallel parking path planning and tracking control based on simulated annealing algorithm［J］．International Journal of Automotive Technology，2024，25（4）：867-880．
[3]	CAI L， GUAN H， ZHOU Z，et al ．Parking planning under limited parking corridor space［J］．IEEE Transactions on Intelligent Transportation Systems，2023，24（2）：1962-1981．
[4]	胡杰，朱令磊，陈瑞楠，等．狭小车位平行泊车路径规划方法研究［J］．汽车工程，2022，44（7）：1040-1048．
	HU Jie， ZHU Linglei， CHEN Ruinan，et al ．Research on parallel parking path planning method for narrow parking space［J］．Automotive Engineering，2022，44（7）：1040-1048．
[5]	刘平，陈卓，刘明杰，等．阶段约束下Gauss配点离散化平行车位自动泊车轨迹规划［J］．汽车工程，2023，45（7）：1163-1173．
	LIU Ping， CHEN Zhuo， LIU Mingjie，et al ．Gauss allocation points parameterization parallel automatic parking trajectory planning for vehicle under multi-stage constraints［J］．Automotive Engineering，2023，45（7）：1163-1173．
[6]	陈晓明，李柏，范丽丽，等．基于半空间约束理论的自动泊车高性能轨迹优化方法［J］．机械工程学报，2024，60（10）：273-288．
	CHEN Xiaoming， LI Bai， FAN Lili，et al ．High-performance trajectory optimization for automated parking via half-space constraining theory［J］．Journal of Mechanical Engineering，2024，60（10）：273-288．
[7]	秦东晨，张文灿，王婷婷，等．受限泊车通道下自动驾驶平行泊车的路径规划方法［J］．郑州大学学报（工学版），2024，45（5）：1-7．
	QING Dongchen， ZHANG Wencan， WANG Tingting，et al ．Path planning method for automated parallel parking in restricted parking lanes［J］．Journal of Zhengzhou University （Engineering Science），2024，45（5）：1-7．
[8]	任秉韬，王淅淅，邓伟文，等．基于混合A^*和可变半径RS曲线的自动泊车路径优化方法［J］．中国公路学报，2022，35（7）：317-327．
	REN Bing-tao， WANG Xi-xi， DENG Wei-wen，et al ．Path optimization algorithm for automatic parking based on hybrid A^* and Reeds-Shepp curve with variable radius［J］．China Journal of Highway and Transport，2022，35（7）：317-327．
[9]	曹彦博，颜京才，李旭升，等．基于改进混合A*算法的自动泊车系统路径搜索方法［J］．汽车技术，2023（6）：37-41．
	CAO Yanbo， YAN Jingcai， LI Xusheng，et al ．A method of path search for automatic parking system based on improved hybrid A* algorithm［J］．Automobile Technology，2023（6）：37-41．
[10]	胡杰，张敏超，徐文才，等．自动驾驶车辆的平行泊车轨迹规划［J］．汽车工程，2022，44（3）：330-339．
	HU Jie， ZHANG Minchao， XU Wencai，et al ．Parallel parking trajectory planning for autonomous vehicles［J］．Automotive Engineering，2022，44（3）：330-339．
[11]	姚智龙，张小俊，王金刚．改进Bi-RRT*算法的自动泊车路径规划［J］．机械科学与技术，2024，43（6）：1063-1071．
	YAO Zhilong， ZHANG Xiaojun， WANG Jingang ．Automatic parking path planning with improved Bi-RRT* algorithm［J］．Mechanical Science and Technology for Aerospace Engineering，2024，43（6）：1063-1071．
[12]	张家旭，刘晔，郭崇，等．基于批处理先验知识树的自主代客泊车路径规划［J］．华中科技大学学报（自然科学版），2021，49（9）：77-82．
	ZHANG Jiaxu， LIU Ye， GUO Chong，et al ．Autonomous valet parking path planning based on batch informed tree［J］．Journal of Huazhong University of Science and Technology （Nature Science Edition），2021，49（9）：77-82．
[13]	SUN Hongwei， CHEN Hui， SONG Shaoyu ．A motion planning method based on reinforcement learning for automatic parallel parking in small slot［J］．Automobile Technology，2021（9）：17-26．
	孙宏伟，陈慧，宋绍禹．一种基于强化学习的小库位自动平行泊车运动规划方法［J］．汽车技术，2021（9）：17-26．
[14]	ZHANG J， CHEN H， SONG S，et al ．Reinforcement learning-based motion planning for automatic parking system［J］．IEEE Access，2020，8：154485-154501．
[15]	CHAI R， LIU D， LIU T，et al ．Deep learning-based trajectory planning and control for autonomous ground vehicle parking maneuver［J］．IEEE Transactions on Automation Science and Engineering，2023，20（3）：1633-1647．
[16]	程国柱，冯思鹤，冯天军．占用车行道的路内停车泊位设置条件［J］．吉林大学学报（工学版），2019，49（6）：1858-1864．
	CHENG Guo-zhu， FENG Si-he， FENG Tian-jun ．Setting condition of on-street parking space occupied vehicle lane［J］．Journal of Jilin University （Engineering and Technology Edition），2019，49（6）：1858-1864．

参数	描述
点P₃和P₄的坐标	起终点后轴中心位置
点P₃和P₄的一阶导数	起终点车辆的航向角
点P₃和P₄的二阶导数	起终点等效前轮转角

参数	数值
车辆宽度W/m	1.645
轴距L/m	2.405
前悬长度L_f/m	0.800
后悬长度L_r/m	0.950
最大等效前轮转角δ_max/rad	0.520
最大前轮转向角速度ω_max/（rad·s^-1）	0.520
最小转弯半径R_min/m	4.200