一种改进的移动机器人路径规划算法

doi:10.16182/j.issn1004731x.joss.23-0585

摘要/Abstract

摘要：

为解决快速随机扩展树算法(RRT)无效采样以及路径不最优等问题，提出一种基于RRT和A*算法的拟水流避障算法RRT-QSA*。在采样上引入RRT算法规定采样区间来限制采样点，增强采样的目标导向性；遇到障碍物时采用融合了A*算法的拟水流避障算法迅速绕过障碍物；采用路径优化算法对搜索到的路径进行路径优化。仿真结果表明：与RRT算法相比，RRT-QSA*算法的计算时间减少了96.83%~99.88%，搜索节点数减少了86.62%~96.01%，路径长度数减少了9.9%~16.7%，转折角度减少了80.93%~93.04%。随着地图的增大，RRT-QSA*算法比RRT算法计算效率的提升更加明显。

关键词: 移动机器人, 路径规划, 快速随机扩展树, 路径优化, Turtlebot2

Abstract:

To solve the problems of invalid sampling and non-optimal paths of the RRT, the quasi-stream avoidance algorithm is proposed. The RRT algorithm is introduced to specify the sampling interval to limit the sampling points and enhance the goal-oriented nature of sampling. The quasi-stream avoidance algorithm incorporating the A* algorithm (QSA*) is used to quickly bypass the obstacle when it is encountered. A path optimization algorithm is used to smooth the searched path. The simulation results show that compared with the RRT algorithm, the computation time of the RRT-QSA* algorithm is reduced by 96.83%~99.88%, the number of search nodes is reduced by 86.62%~96.01%, the number of path lengths is reduced by 9.9%~16.7%, and the turning angle decreased by 80.93%~93.04%. The RRT-QSA* algorithm shows a more intense improvement in computational efficiency than the RRT algorithm as the map size increases.

Key words: mobile robots, path planning, RRT, path optimization, Turtlebot2

中图分类号:

TP242.6

孙海杰,伞红军,肖乐等 . 一种改进的移动机器人路径规划算法[J]. 系统仿真学报, 2024, 36(9): 2193-2207.

Sun Haijie,San Hongjun,Xiao Le,et al . An Improved Path Planning Algorithm for Mobile Robots[J]. Journal of System Simulation, 2024, 36(9): 2193-2207.

图/表 27

图1

图2

图3

图4

图5

图6

图7

表1

表2

顺时针流动条件对应关系表

流动	模式	极端限定条件	流动条件
$↑$	M1-Fig.6(1)	\	U0, RU1, R0
	M2-Fig.6(5)	\	R1, RU1, U0
	M3-Fig.6(14)	j=0	R1, RU1, U0
	M3-Fig.6(13)	j=0 & i=R	RU1, U0
$↗$	M2-Fig.6(6)	\	R1, U0, RU0
$↗$	M3-Fig.6(14)	j=0	R1, U0, RU0
$→$	M1-Fig.6(2)	\	R0, RD1, D0
	M2-Fig.6(7)	\	D1, RD1, R0
	M3-Fig.6(16)	i=0	D1, RD1, R0
	M3-Fig.6(15)	i=0 & j=0	RD1, R0
$↘$	M2-Fig.6(8)	\	D1, RD0, R0
$↘$	M3-Fig.6(16)	i=0	D1, R0, RD0
$↓$	M1-Fig.6(3)	\	D0, LD1, L0
	M2-Fig.6(9)	\	L1, LD1, D0
	M3-Fig.6(19)	j=C	L1, LD1, D0
	M3-Fig.6(17)	i=0 & j=C	LD1, D0
$↙$	M2-Fig.6(10)	\	L1, D0, LD0
$↙$	M3-Fig.6(19)	j=C	L1, LD0, D0
$←$	M1-Fig.6(3)	\	L0, LU1, U0
	M2-Fig.6(4)	\	U1, LU1, L0
	M3-Fig.6(20)	i=R	U1, LU1, L0
	M3-Fig.6(18)	i=R & j=C	LU1, L0
$↖$	M2-Fig.6(12)	\	U1, L0, LU0
$↖$	M3-Fig.6(20)	i=R	U1, LU0, L0

表2

表3

逆时针流动条件对应关系表

流动	模式	极端限定条件	流动条件
$↓$	M1-Fig.7(1)	\	D0, RD1, R0
	M2-Fig.7(5)	\	R1, RD1, D0
	M3-Fig.7(14)	j=0	R1, RD1, D0
	M3-Fig.7(13)	j=0 & i=0	RD1, D0
$↘$	M2-Fig.7(6)	\	R1, RD0, D0
$↘$	M3-Fig.7(14)	j=0	R1, D0, RD0
$→$	M1-Fig.7(2)	\	R0, RU1, U0
	M2-Fig.7(7)	\	U1, RU1, R0
	M3-Fig.7(16)	i=R	U1, RU1, R0
	M3-Fig.7(15)	i=R & j=0	RU1, R0
$↗$	M2-Fig.7(8)	\	U1, R0, RU0
$↗$	M3-Fig.7(16)	i=R	U1, R0, RU0
$↑$	M1-Fig.7(3)	\	U0, LU1, L0
	M2-Fig.7(9)	\	L1, LU1, U0
	M3-Fig.7(19)	j=C	L1, LU1, U0
	M3-Fig.7(17)	i=R & j=C	LU1, U0
$↖$	M2-Fig.7(10)	\	L1, U0, LU0
$↖$	M3-Fig.7(19)	j=C	L1, LU0, U0
$←$	M1-Fig.7(3)	\	L0, LD1, D0
	M2-Fig.7(4)	\	D1, LD1, L0
	M3-Fig.7(20)	i=0	D1, LD1, L0
	M3-Fig.7(18)	i=0 & j=C	LD1, L0
$↙$	M2-Fig.7(12)	\	D1, L0, LD0
$↙$	M3-Fig.7(20)	i=0	D1, LD0, L0

表3

图8

图9

图10

图11

图12

图13

表4

图14

表5

图15

表6

表7

在不同地图中各算法数据对比

参数	算法	50×50	100×100	150×150	200×200
时间/s	RRT	0.41 $±$ 0.34	3.39 $±$ 3.08	32.62 $±$ 21.39	102.39 $±$ 79.16
	RRT-QSA*	0.013 $±$ 0.01	0.07 $±$ 0.03	0.14 $±$ 0.05	0.16 $±$ 0.04
	A*	0.013 $±$ 0.02	0.04 $±$ 0.02	0.07 $±$ 0.01	0.12 $±$ 0.08
转折点数	RRT	553 $±$ 129	1 714 $±$ 674	5 074 $±$ 1529	9 331 $±$ 2 546
	RRT-QSA*	74 $±$ 46	183 $±$ 253	269 $±$ 57	372 $±$ 26
	A*	225 $±$ 0	431 $±$ 0	680 $±$ 0	951 $±$ 0
路径长度	RRT	94.1 $±$ 6.04	183.67 $±$ 10.69	283.78 $±$ 10.41	349.82 $±$ 18.34
	RRT-QSA*	78.3 $±$ 4.31	159.39 $±$ 6.19	244.71 $±$ 9.70	315.18 $±$ 10.68
	A*	76.9 $±$ 0	173.39 $±$ 0	242.93 $±$ 0	299.59 $±$ 0
转折角度/(°)	RRT	1 767 $±$ 133.84	3 440 $±$ 253.66	5 383 $±$ 302.93	6 713 $±$ 513.79
	RRT-QSA*	337 $±$ 8.99	290 $±$ 13.74	599 $±$ 73.86	467 $±$ 79.16
	A*	279 $±$ 0	242 $±$ 0	451.9 $±$ 0	448.21 $±$ 0

表7

图16

图17

图18

图19

表8

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流动条件	含义	符号
field [i, j+1]	向右搜索	R
field [i+1, j]	向下搜索	D
field [i, j-1]	向左搜索	L
field [i-1, j]	向上搜索	U
field [i+1, j+1]	向右下搜索	RD
field [i-1, j+1]	向右上搜索	RU
field [i+1, j-1]	向左下搜索	LD
field [i-1, j-1]	向左上搜索	LU
= 0	搜索结果为可通行区域	0
= 1	搜索结果为可障碍物	1

指标	RRT
指标	时间/s	路径长度	节点数	转折角度/(°)
均值	0.25	87.74	483.80	1 861.75
标准差	0.26	3.27	206.32	251.30
最大值	0.87	110.65	878	2 252.23
最小值	0.02	72.15	185	1 513.73
指标	RRT-QSA*
指标	时间/s	路径长度	节点数	转折角度/(°)
均值	0.004	42.86	50.67	305.51
标准差	0.003	1.79	2.72	6.95
最大值	0.015	46.45	53	308.99
最小值	0.002	41.96	45	291.59

指标	RRT				RRT-QSA*
指标	时间/s	路径长度	节点数	转折角度/(°)	时间/s	路径长度	节点数	转折角度/(°)
均值	0.20	89.89	387.80	1 804.36	0.03	81.91	74.40	377.35
标准差	0.16	3.27	81.42	114.65	0.01	2.09	47.36	42.26
最大值	0.66	95.09	547	1 988.53	0.03	86.35	216	470.11
最小值	0.05	84.61	243	1 632.59	0.02	78.52	53	321.51

指标	RRT				RRT-QSA*
指标	时间/s	路径长度	节点数	转折角度/(°)	时间/s	路径长度	节点数	转折角度/(°)
均值	6.20	279.82	2 205.86	4 639.15	0.013	203.76	312.50	438.32
标准差	5.50	16.66	728.86	387.67	0.002	2.36	9.20	6.95
最大值	21.49	309.60	3 745	5 363.13	0.017	208.87	326	490.75
最小值	1.64	250.98	1 217	4 064.18	0.001	201.45	297	419.63

算法	S1-G1	S2-G2
RRT	1.5309	2.0347
RRT-QSA*	0.0326	0.0365