Visualizing Local Minima in Multi-Robot Motion Planning using Morse Theory

Multi-robot motion planning problems often have many local minima. It is essential to visualize those local minima such that we can better understand, debug and interact with multi-robot systems. Towards this goal, we use previous results combining Morse theory and fiber bundles to organize local minima into a local minima tree. We extend this local minima tree to multi-robot systems by introducing fiber bundle diagrams and devising a new algorithm to compute, project and sample from fiber bundles. We demonstrate this algorithm on several multi-robot systems of up to 20 degrees of freedom.