Visualizing Local Minima in Multi-Robot Motion Planning using Multilevel Morse Theory
This addresses the need to understand and debug multi-robot systems, but it is incremental as it extends prior work on multilevel Morse theory.
The paper tackles the problem of visualizing local minima in multi-robot motion planning by presenting the multi-robot motion explorer algorithm, which builds a local minima tree for systems with up to 20 degrees of freedom.
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.