  To control how a robot moves, motion planning algorithms must compute paths
in high-dimensional state spaces while accounting for physical constraints
related to motors and joints, generating smooth and stable motions, avoiding
obstacles, and preventing collisions. A motion planning algorithm must
therefore balance competing demands, and should ideally incorporate uncertainty
to handle noise, model errors, and facilitate deployment in complex
environments. To address these issues, we introduce a framework for robot
motion planning based on variational Gaussian processes, which unifies and
generalizes various probabilistic-inference-based motion planning algorithms,
and connects them with optimization-based planners. Our framework provides a
principled and flexible way to incorporate equality-based, inequality-based,
and soft motion-planning constraints during end-to-end training, is
straightforward to implement, and provides both interval-based and
Monte-Carlo-based uncertainty estimates. We conduct experiments using different
environments and robots, comparing against baseline approaches based on the
feasibility of the planned paths, and obstacle avoidance quality. Results show
that our proposed approach yields a good balance between success rates and path
quality.
