Motion Planning Explorer: Visualizing Local Minima using a Local-Minima Tree

Abstract: Motion planning problems often have many local minima. Those minima are important to visualize to let a user guide, prevent or predict motions. Towards this goal, we develop the motion planning explorer, an algorithm to let users interactively explore a tree of local-minima. Following ideas from Morse theory, we define local minima as paths invariant under minimization of a cost functional. The local-minima are grouped into a local-minima tree using lower-dimensional projections specified by a user. The user can then interactively explore the local-minima tree, thereby visualizing the problem structure and guide or prevent motions. We show the motion planning explorer to faithfully capture local minima in four realistic scenarios, both for holonomic and certain non-holonomic robots.