  A defining feature of sampling-based motion planning is the reliance on an
implicit representation of the state space, which is enabled by a set of
probing samples. Traditionally, these samples are drawn either
probabilistically or deterministically to uniformly cover the state space. Yet,
the motion of many robotic systems is often restricted to "small" regions of
the state space, due to, for example, differential constraints or
collision-avoidance constraints. To accelerate the planning process, it is thus
desirable to devise non-uniform sampling strategies that favor sampling in
those regions where an optimal solution might lie. This paper proposes a
methodology for non-uniform sampling, whereby a sampling distribution is
learned from demonstrations, and then used to bias sampling. The sampling
distribution is computed through a conditional variational autoencoder,
allowing sample generation from the latent space conditioned on the specific
planning problem. This methodology is general, can be used in combination with
any sampling-based planner, and can effectively exploit the underlying
structure of a planning problem while maintaining the theoretical guarantees of
sampling-based approaches. Specifically, on several planning problems, the
proposed methodology is shown to effectively learn representations for the
relevant regions of the state space, resulting in an order of magnitude
improvement in terms of success rate and convergence to the optimal cost.
