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Multi-Agent Goal Assignment with Finite-Time Path Planning

Tony A. WoodMaryam Kamgarpour
Dec 2022
摘要
Minimising the longest travel distance for a group of mobile robots withinterchangeable goals requires knowledge of the shortest length paths betweenall robots and goal destinations. Determining the exact length of the shortestpaths in an environment with obstacles is challenging and cannot be guaranteedin a finite time. We propose an algorithm in which the accuracy of the pathplanning is iteratively increased. The approach provides a certificate when theuncertainties on estimates of the shortest paths become small enough toguarantee the optimality of the goal assignment. To this end, we apply resultsfrom assignment sensitivity assuming upper and lower bounds on the length ofthe shortest paths. We then provide polynomial-time methods to find such boundsby applying sampling-based path planning. The upper bounds are given byfeasible paths, the lower bounds are obtained by expanding the sample set andleveraging knowledge of the sample dispersion. We demonstrate the applicationof the proposed method with a multi-robot path-planning case study.
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