Sampling-based algorithms solve the path planning problem by generating random samples in the searchspace and incrementally growing a connectivity graph or a tree. Conventionally, the sampling strategy used in these algorithms is biased towards exploration to acquire information about the search-space. In contrast, this work proposes an optimization-based procedure that generates new samples so as to improve the cost-to-come value of vertices in a given neighborhood. The application of the proposed algorithm adds an exploitativebias to sampling and results in a faster convergence to the optimal solution compared to other state-of-the-art sampling techniques. This is demonstrated using benchmarking experiments performed for 7 DOF Panda and 14 DOF Baxter robots.

Asymptotically optimal sampling-based planners require an intelligent exploration strategy to accelerate convergence. After an initial solution is found, a necessary condition for improvement is to generate new samples in the so-called "Informed Set". However, Informed Sampling can be ineffective in focusing search if the chosen heuristic fails to provide a good estimate of the solution cost. This work proposes an algorithm to sample the "Relevant Region" instead, which is a subset of the Informed Set. The Relevant Region utilizes cost-to-come information from the planner's tree structure, reduces dependence on the heuristic, and further focuses the search. Benchmarking tests in uniform and general cost-space settings demonstrate the efficacy of Relevant Region sampling.

Efficient exploration of the search space is crucial for faster convergence in sampling-based motion planning. An effective sampling method must first concentrate on quickly finding a good initial solution and then focus the search on regions that can potentially improve the current best solution. In this paper, we propose a non-parametric exploration technique that addresses these challenges. The proposed algorithm prioritizes search by utilizing heuristics. After an initial solution is found, the method generates samples in the “$L_{2} -$informed set”, while leveraging collision data to reduce the number of samples in the obstacle space. We demonstrate the efficiency of the proposed approach with several benchmarking experiments.