Adaptively Exploits Local Structure With Generalised Multi-Trees Motion Planning

Tin Lai, Fabio Ramos

Abstract: Sampling-based motion planners perform exceptionallywell in robotic applications that operate in high-dimensional spaces. However, most previous works often constrain the planning workspace rooted at some fixed locations, do not adaptively reason on strategies for narrow passages, and ignore valuable local structure information. In this letter, we propose Rapidly-exploring Random Forest ( <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rrf</small> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">*</sup> )—a generalised multi-trees motion planner that combines the rapid exploring property of tree-based methods and adaptively learns to deploys a Bayesian local sampling strategy in regions that are deemed to be bottlenecks. Local sampling exploits the local-connectivity of spaces via Markov Chain random sampling, which is updated sequentially with a Bayesian proposal distribution to learn the local structure from past observations. The trees selection problem is formulated as a multi-armed bandit problem, which efficiently allocates resources to the most promising tree accelerating planning runtime. <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rrf</small> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">*</sup> learns the region that is difficult to perform tree extensions and adaptively deploys local sampling in those regions to maximise the benefit of exploiting local structure. We provide rigorous proofs of completeness and almost-surely asymptotic optimal convergence, and experimentally demonstrate that the effectiveness of <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rrf</small> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">*</sup> ’s adaptive multi-trees approach allows it to perform well in a wide range of problems.