Approximate Topological Optimization using Multi-Mode Estimation for Robot Motion Planning

In this extended abstract, we report on ongoing work towards an approximate\nmultimodal optimization algorithm with asymptotic guarantees. Multimodal\noptimization is the problem of finding all local optimal solutions (modes) to a\npath optimization problem. This is important to compress path databases, as\ncontingencies for replanning and as source of symbolic representations.\nFollowing ideas from Morse theory, we define modes as paths invariant under\noptimization of a cost functional. We develop a multi-mode estimation algorithm\nwhich approximately finds all modes of a given motion optimization problem and\nasymptotically converges. This is made possible by integrating sparse roadmaps\nwith an existing single-mode optimization algorithm. Initial evaluation results\nshow the multi-mode estimation algorithm as a promising direction to study path\nspaces from a topological point of view.\n