Globally Optimal Motion Planning for Mobile Robots via Topology-Aware Divide-and-Conquer

Sampling-based motion planning methods have become widely adopted for motion planning due to their effectiveness in high-dimensional and complex environments. However, existing methods often prioritize planning efficiency and tend to get trapped in local optima. To overcome this limitation, we propose a divide-and-conquer hybrid sampling planning framework (DCH-RRT*), which decomposes the overall planning problem into topology-constrained subspaces for parallel exploration under the guidance of topological structure. DCH-RRT* first constructs a Connectivity Roadmap (CRM) and explores diverse topologies based on CRM to perform topology-aware decomposition, enabling an effective partitioning of the entire configuration space. A hybrid sampling strategy is then introduced to guide efficient exploration and accelerate convergence within the topology-informed, nonuniform sampling space. Theoretical analysis confirms that the proposed framework retains asymptotic optimality, while extensive experiments demonstrate that it consistently achieves high-quality paths with competitive computational efficiency compared to existing methods.