采用RRT*算法和椭圆先验的机械臂约束规划研究

doi:10.16182/j.issn1004731x.joss.24-0545

摘要/Abstract

摘要：

对约束规划问题中应用均匀采样策略的传统RRT*算法存在采样点非精确转向引导以及非必要的节点代价比较导致增加额外时间成本的问题，提出一种利用投影采样点启发式函数代价进行采样点椭圆先验判断的改进RRT*算法。基于椭圆先验判断采样点是否能够优化路径，缩短了规划时间。使用测地线进一步对投影采样点的当前代价进行预估。仿真结果表明：改进后的RRT*算法规划的路径相较于传统RRT*算法时间代价平均减少了73.27%，相较于将椭圆先验直接引入的RRT*算法路径代价平均减少4.49%。

关键词: 机械臂, 采样点, 约束规划, RRT*, 椭圆先验, 测地线, 时间代价, 路径代价

Abstract:

There are problems in the traditional RRT* algorithm using a uniform sampling strategy applied in constrained programming problems, such as inaccurate turning guidance of sampling points and unnecessary node cost comparisons, which lead to an increase in additional time costs. To address these issues, an improved RRT* algorithm was proposed. This algorithm leveraged a heuristic function cost of the projected sampling points to make an ellipse prior judgment on the sampling points. Based on the ellipse prior, the sampling points were judged to determine whether they could optimize the path and shorten the programming time. The geodesics were used to further estimate the current cost of the projected sampling points. Simulation results show that the planned path by the improved RRT* algorithm has an average time cost reduction of 73.27% compared to that by the traditional RRT* algorithm and an average path cost reduction of 4.49% compared to the RRT* algorithm that directly incorporates the ellipse prior.

Key words: manipulator, sampling point, constraint programming, RRT*, ellipse prior, geodesic, time cost, path cost

中图分类号:

TP391.9

杨震,苏丽,成治雨 . 采用RRT*算法和椭圆先验的机械臂约束规划研究[J]. 系统仿真学报, 2025, 37(10): 2643-2651.

Yang Zhen,Su Li,Cheng Zhiyu . Research on Constrained Programming of Manipulator Using RRT* Algorithm and Ellipse Prior[J]. Journal of System Simulation, 2025, 37(10): 2643-2651.

图/表 11

图1

图2

图3

图4

表1

UR5机械臂DH参数

自由度	$a i$	$α i$	$d i$	$θ i$
1	0	90	89.2	$θ 1$
2	-425	0	0	$θ 2$
3	-392.2	0	0	$θ 3$
4	0	90	109.3	$θ 4$
5	0	-90	94.65	$θ 5$
6	0	0	82.3	$θ 6$

表1

图5

表2

改进RRT*算法参数

参数	三维数学空间
最大步长 $α$	1.0
目标偏置概率 $β$	0.1
约束投影阈值 $ϵ$	0.01
采样点数目m	2 000
目标阈值e	0.1

表2

表3

图6

图7

图8

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算法	成功比例	路径代价	规划时间/s
约束RRT*	10/10	11.17±0.16	10.55±3.21
先验约束RRT*	10/10	11.81±0.51	2.23±0.35
改进约束RRT*	10/10	11.28±0.13	2.82±0.43