  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 present the
multi-robot motion explorer, an algorithm which extends previous results on
multilevel Morse theory by introducing a component-based framework, where we
reduce multi-robot configuration spaces by reducing each robots component space
using fiber bundles. Our algorithm exploits this component structure to search
for and visualize local minima. A user of the algorithm can specify a
multilevel abstraction and an optimization algorithm. We use this information
to incrementally build a local minima tree for a given problem. We demonstrate
this algorithm on several multi-robot systems of up to 20 degrees of freedom.
