  Asymptotically-optimal motion planners such as RRT* have been shown to
incrementally approximate the shortest path between start and goal states. Once
an initial solution is found, their performance can be dramatically improved by
restricting subsequent samples to regions of the state space that can
potentially improve the current solution. When the motion planning problem lies
in a Euclidean space, this region $X_{inf}$, called the informed set, can be
sampled directly. However, when planning with differential constraints in
non-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 as
Hierarchical Rejection Sampling (HRS) may still be slow in high-dimensional
state space. This may cause the planning algorithm to spend most of its time
trying 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 this
problem as one of sampling uniformly within the sub-level-set of an implicit
non-convex function. This recasting enables us to apply Monte Carlo sampling
methods, used very effectively in the Machine Learning and Optimization
communities, to solve our problem. We show for a wide range of scenarios that
using our sampler can accelerate the convergence rate to high-quality solutions
in high-dimensional problems.
