Simultaneous planning of sampling and optimization: study on lazy evaluation and configuration free space approximation for optimal motion planning algorithm

recent trend in optimal motion planning has broadened the research area toward the hybridization of sampling, optimization, and grid-based approaches. A synergy from such integrations can be expected to bring the overall performance improvement, but seamless integration and generalization is still an open problem. In this paper, we suggest a hybrid motion planning algorithm utilizing both sampling and optimization techniques, while simultaneously approximating a configuration-free space. Unlike conventional optimization-based approaches, the proposed algorithm does not depend on a priori information or resolution-complete factors, e.g., a distance field. Ours instead learns spatial information on the fly by exploiting empirical collisions found during the execution, and decentralizes the information over the constructed graph for an efficient reference. With the help of the learned information, we associate the constructed search graph with the approximate configuration-free space so that our optimization-based local planner exploits the local area to identify the connectivity of free space without depending on the precomputed workspace information. To show the novelty of the proposed algorithm, we apply the proposed idea to asymptotic optimal planners with lazy collision checking; lazy PRM ^* and Batch Informed Tree ^* , and evaluate them against other state-of-the-arts in both synthetic and practical benchmarks with varying degrees of freedom. We also discuss the performance analysis, properties of different algorithm frameworks of lazy collision checking and our approximation method.