最小规划裕量优先的多机器人CBS路径规划算法

doi:10.16182/j.issn1004731x.joss.25-0599

摘要/Abstract

摘要：

针对传统CBS(conflict-based search)框架冲突树(conflict tree，CT)扩展存在链式效应、求解效率不足的问题，提出一种基于规划裕量的最小裕量优先CBS算法。在底层 $A *$ 搜索中引入规划裕量的计算，在高层冲突求解中优先处理裕量最小的机器人，在保证路径最优性的同时抑制CT链式扩展。仿真实验表明：所提算法明显减少了CT节点拓展量与根节点冲突数，有效提升了求解效率，验证了算法的有效性与优越性。

关键词: 路径规划, 基于冲突搜索的算法, 规划裕量, 冲突消解

Abstract:

To address the problems of chain effect and insufficient solving efficiency in the conflict tree (CT) expansion of the traditional conflict-based search (CBS) framework, a minimum-margin-first CBS algorithm based on planning margin was proposed. The calculation of planning margin was introduced into the underlying A* search, and the robots with the minimum margin were prioritized in the high-level conflict resolution, to suppress the chain expansion of the CT while ensuring path optimality. Simulation experiments show that the proposed algorithm significantly reduces the amount of CT node expansion and the number of root node conflicts and effectively improves the solving efficiency, verifying the effectiveness and superiority of the algorithm.

Key words: path planning, conflict-based search algorithm, planning margin, conflict resolution

中图分类号:

TP242

梁隆硝,毛剑琳,王妮娅等 . 最小规划裕量优先的多机器人CBS路径规划算法[J]. 系统仿真学报, 2026, 38(5): 1159-1173.

Liang Longxiao,Mao Jianlin,Wang Niya,et al . Multi-agent CBS Path Planning Algorithm Based on Minimum Planning Margin First[J]. Journal of System Simulation, 2026, 38(5): 1159-1173.

图/表 14

图1

图2

图3

表1

机器人路径规划

路径	t=0	t=1	t=2	t=3	t=4	t=5	t=6
$p 1 . r o o t$	(0,3)	(1,3)	(2,3)	(3,3)	(3,2)	(3,1)	(3,0)
$p 2 . r o o t$	(2,1)	(2,2)	(2,3)	(2,4)
$p 1.1$	(0,3)	(1,3)	(1,2)	(1,1)	(1,0)	(2,0)	(3,0)
$p 3 . r o o t$	(0,3)	(3,1)	(2,1)	(1,1)	(1,0)
$p 1.3$	(4,1)	(1,3)	(1,2)	(2,2)	(3,2)	(3,1)	(3,0)
$p 4 . r o o t$	(0,3)	(2,4)	(3,4)	(3,3)	(3,2)
$p 1.5$	(0,3)	(1,3)	(1,2)	(2,2)	(2,1)	(2,0)

表1

图4

图5

图6

图7

表2

表3

表4

图8

图9

表5

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地图	机器人数量	HCA*	LaCAM*	PBS	MMF-CBS-DS
random-64-64-10	10	430.8	439.4	429.9	429.9
	20	864.3	901.1	863.0	863.0
	30	1 268.1	1 337.2	1 267.5	1 267.5
	40	1 701.4	1 811.1	1 700.0	1 691.5
	50	2 149.8	2 270.5	2 137.9	2 111.7
	60	2 593.0	2 754.4	2 576.9	2 532.9
	70	3 031.5	3 287.8	3 006.5	3 150.8
	80	3 456.0	3 762.3	3 431.7	3 374.8
random-64-64-20	10	457.0	463.8	456.1	456.1
	20	918.4	934.9	906.2	906.2
	30	1 354.2	1 411.1	1 332.5	1 332.4
	40	1 810.2	1 910.2	1 777.3	1 777.2
	50	2 278.3	2 386.0	2 213.0	2 212.9
	60	2 735.4	2 900.0	2 632.6	2 632.3
	70	3 200.2	3 443.0	3 076.0	3 062.7
random-32-32-10	10	222.8	229.2	222.4	222.4
	20	448.4	477.1	447.2	447.2
	30	670.8	737.8	664.3	664.1
	40	896.8	999.6	887.3	887.1
	50	1 132.2	1 286.5	1 092.0	1 091.0
	60	1 365.4	1 507.8	1 276.5	1 215.3

地图	机器人数量	CBS	CBS-DS	MMF-CBS-DS
random-64-64-10	10	1.6	1.6	1.2
	20	4.6	4.5	3.4
	30	355.7	49.4	40.3
	40	2 134.3	327	108.3
	50	32 644.0	2 095.0	290.7
	60	31 133.6	4 632.8	410.6
	70	54 797.0	4 608.0	566.5
	80	31 797.7	4 755.7	2 999.8
random-64-64-20	10	1.2	1.2	1.4
	20	21.6	11.4	11.0
	30	426.0	136.1	78.1
	40	21 166.8	2 412.0	690.1
	50	22 588.4	6 559.5	2 648.7
	60	438 308.1	57 003.9	5 491.0
	70	525 043.7	71 492.3	70 817.7
random-32-32-10	10	15.6	6.3	6.5
	20	49.3	19.0	16.5
	30	46 735.5	1 286.7	383.6
	40	211 694.2	11 066.5	3 057.3
	50	236 498.5	28 155.9	4 887.0
	60	4 997.0	2 668.5	487.0

地图	机器人数量	CBS	CBS-DS	MMF-CBS-DS
random-64-64-10	10	1.7	1.7	0.88
	20	4.4	4.3	4.7
	30	1 722.0	181.5	170.7
	40	5 103.3	703.0	242.9
	50	126 960.1	8 197.8	689.8
	60	111 600.8	16 178.3	987.4
	70	169 686.6	10 306.5	1 095.7
	80	40 658.4	7 363.9	4 558.8
random-64-64-20	10	0.88	1.2	0.88
	20	53.1	99.2	17.7
	30	1 099.1	655.1	327.5
	40	66 633.8	6 251.8	4 363.4
	50	37 193.2	24 750.2	12 293.2
	60	891 989.6	791 882.1	106 313.1
	70	832 745.8	918 059.7	110 843.1
random-32-32-10	10	63.8	19.4	22.8
	20	149.5	49.4	47.0
	30	224 965.4	4 852.1	1 240.5
	40	501 823.9	18 364.6	7 332.8
	50	498 414.6	50 606.5	4 887.0
	60	6 861.8	3 461.3	585.5