Abstract
This paper addresses the multirobot path planning problem using Petri net (PN) models, integrating insights from linear integer programming with a focus on totally unimodular matrices. Initially, we establish theoretical foundations linking optimal solutions of linear integer problems to their relaxed counterparts. Subsequently, we adapt these findings to robot path planning. The core contribution lies in the introduction of an innovative algorithm designed to iteratively converge on the optimal solution by solving successive continuous linear problems. A key feature of this algorithm is its proven efficiency, which converges to the optimal solution of the integer problem within a theoretically established finite number of iterations. Empirical validation is achieved through the resolution of 300 different path planning scenarios, which include varying numbers of robots, maps, and missions. These cases, solved using both the proposed method and existing techniques, demonstrate the superiority of the proposed method in performance.
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