阶段约束下Gauss配点离散化平行车位自动泊车轨迹规划

doi:10.19562/j.chinasae.qcgc.2023.07.007

Abstract

Abstract:

A trajectory optimization algorithm combining multi-stage division with non-uniform Gauss collocation parameterization is proposed for vehicle high-precision trajectory planning of parallel parking space. Firstly， a mathematical model of parallel automatic parking is established based on the dynamic equation of vehicle parking and constraint conditions. Then， according to the parking process， it is proposed to divide the parking process into five parking stages including parking start， parking space approaching， parking space entering， parking position adjustment and parking landing and corresponding inequality constraints are established for each stage. Furthermore， multiple stage local Gauss discrete strategy is proposed under pseudo-spectral approach frame to achieve independent allocation in each stage so as to improve the precision and adaptivity of trajectory planning. Finally， simulation tests are carried out on a general car model for long and short parking space to verify the performance of the proposed method in accuracy and adaptivity. The test results show that the proposed method can efficiently obtain smooth parking trajectory and averagely decrease parking time by 2.976 s when compared with the piecewise Gaussian pseudo-spectral method， with 21.7% improvement of parking time performance， which indicates the effectiveness of the proposed algorithm.

Key words: automatic parking, parallel parking space, trajectory optimization, stage division, Gauss allocation parameterization

Ping Liu, Zhuo Chen, Mingjie Liu, Changhao Piao, Soohyun Jang, Kailin Wan. Gauss Allocation Points Parameterization Parallel Automatic Parking Trajectory Planning for Vehicle Under Multi-Stage Constraints[J].Automotive Engineering, 2023, 45(7): 1163-1173.

Figures/Tables 16

参数	物理意义	数值	参数	物理意义	数值
L	轴距	2.560 m	$v m a x$	最大行驶速度	3.0 m/s
$f$	车辆前悬	0.902 m	$a m a x$	最大加速度	0.75 m/s²
$r$	车辆后悬	0.883 m	$φ m a x$	最大前轮摆角	0.56 rad
$d$	车身宽度	1.765 m	$ω m a x$	最大前轮摆角角速度	0.56 rad/s

初始值		终端约束
$v$ （0）	0 m/s	$v$ （t_f）	0 m/s
$a$ （0）	0 m/s²	$a$ （t_f）	0 m/s²
$θ$ （0）	$0 o$	$θ$ （t_f）	$0 o$
$φ$ （0）	0 rad	$φ$ （t_f）	0 rad
$ω$ （0）	0 rad/s	$ω$ （t_f）	0 rad/s

阶段	配点数	车位类型
阶段	配点数	长车位	窄车位
N1	$K 1$	6	10
N2	$K 2$	12	6
N3	$K 3$	12	16
N4	$K 4$	6	14
N5	$K 5$	4	6

车位长度/m	研究方法	目标函数 $t f$ /s	泊车时间减少比例/%
7.8	分区域伪谱法^［18］	11.363	21.8
7.8	本文方法	8.879	21.8
6.8	分区域伪谱法^［18］	11.816	14.0
6.8	本文方法	10.16	14.0
5.8	分区域伪谱法^［18］	16.337	29.3
5.8	本文方法	11.547	29.3

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Gauss Allocation Points Parameterization Parallel Automatic Parking Trajectory Planning for Vehicle Under Multi-Stage Constraints

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