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Asymptotically-optimal motion planners such as RRT* have been shown toincrementally approximate the shortest path between start and goal states. Oncean initial solution is found, their performance can be dramatically improved byrestricting subsequent samples to regions of the state space that canpotentially improve the current solution. When the motion planning problem liesin a Euclidean space, this region $X_{inf}$, called the informed set, can besampled directly. However, when planning with differential constraints innon-Euclidean state spaces, no analytic solutions exists to sampling $X_{inf}$directly.  State-of-the-art approaches to sampling $X_{inf}$ in such domains such asHierarchical Rejection Sampling (HRS) may still be slow in high-dimensionalstate space. This may cause the planning algorithm to spend most of its timetrying to produces samples in $X_{inf}$ rather than explore it. In this paper,we suggest an alternative approach to produce samples in the informed set$X_{inf}$ for a wide range of settings. Our main insight is to recast thisproblem as one of sampling uniformly within the sub-level-set of an implicitnon-convex function. This recasting enables us to apply Monte Carlo samplingmethods, used very effectively in the Machine Learning and Optimizationcommunities, to solve our problem. We show for a wide range of scenarios thatusing our sampler can accelerate the convergence rate to high-quality solutionsin high-dimensional problems.

Generalizing Informed Sampling for Asymptotically Optimal Sampling-based Kinodynamic Planning via Markov Chain Monte Carlo