Accelerating Motion Planning via Optimal Transport
Keywords: Motion Planning, Trajectory Optimization, Optimal Transport
TL;DR: The paper proposes a highly parallelizable, efficient gradient-free update rule formulated as an Optimal Transport problem, applying to trajectory optimization for optimizing a batch of high-dimensional trajectories on multiple non-convex objectives.
Abstract: Motion planning is still an open problem in robotics. A class of methods striving to provide smooth solutions is gradient-based trajectory optimization. However, those methods might suffer from bad local minima, while for many settings, they may be inapplicable due to the absence of access to objectives-gradients. In response to these issues, we introduce Motion Planning via Optimal Transport (MPOT) - a *gradient-free* method that optimizes a batch of smooth trajectories over highly nonlinear costs, even for high-dimensional tasks, while imposing smoothness through a Gaussian Process trajectory prior that serves as cost. To facilitate batch trajectory optimization, we introduce an original zero-order and highly-parallelizable update rule -- the Sinkhorn Step, which uses the regular polytope family for its search directions; each regular polytope, centered on trajectory waypoints, serves as a local neighborhood, effectively acting as a trust region, where the Sinkhorn Step *transports* local waypoints toward low-cost regions. With these properties, MPOT solves batch planning tasks even with narrow passages in *less than a second*, finding locally optimal solutions. We show the efficiency of MPOT in a range of problems from low-dimensional point-mass navigation to high-dimensional whole-body robot motion planning, evincing its superiority compared with popular motion planners and paving the way for new applications of optimal transport in motion planning.
Submission Number: 1