VRT*: Optimal Sampling-Based Multi-Robot Path Planning via Voronoi-Inspired Filtering Framework

Extensive workspace traversal by multiple robots may compromise planning efficiency due to over-exploration and redundant calculations in inefficient regions, while trying to ensure the optimality of motion planning in multi-robot systems (MRS). This paper proposes a Voronoi-inspired random tree (VRT*), to improve planning efficiency in MRS by mitigating inefficient workspace exploration and reducing redundant computations. In particular, generalized Voronoi graph (GVG) is used to transform workspace into searchable objects. Subsequently, a voronoi guide tree is constructed to capture the connectivity and optimization potential of workspace, enabling the identification of critical workspace and facilitating the planning of heuristic paths. Through integrating the Expansion direction selection strategy into a discrete rapidly-exploring random tree, optimal solutions can be achieved by VRT* while minimizing redundant computations. Robust theoretical proofs and extensive experimental validations show that VRT* efficiently focuses computational resources on critical workspace in MRS planning, rapidly capturing high-quality initial solutions and reliably converging to optimal path.