Towards small asymptotically near-optimal roadmaps

An exciting recent development is the definition of sampling-based motion planners which guarantee asymptotic optimality. Nevertheless, roadmaps with this property may grow too large and lead to longer query resolution times. If optimality requirements are relaxed, existing asymptotically near-optimal solutions produce sparser graphs by removing redundant edges. Even these alternatives, however, include all sampled configurations as nodes in the roadmap. This work proposes a method, which can reject redundant samples but does provide asymptotic coverage and connectivity guarantees, while keeping local path costs low. Not adding every sample can significantly reduce the size of the final roadmap. An additional advantage is that it is possible to define a reasonable stopping criterion for the approach inspired by previous methods. To achieve these objectives, the proposed method maintains a dense graph that is used for evaluating the performance of the roadmap with regards to local path costs. Experimental results show that the method indeed provides small roadmaps, allowing for shorter query resolution times. Furthermore, smoothing the final paths results in an even more advantageous comparison against alternatives with regards to path quality.