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In this extended abstract, we report on ongoing work towards an approximatemultimodal optimization algorithm with asymptotic guarantees. Multimodaloptimization is the problem of finding all local optimal solutions (modes) to apath optimization problem. This is important to compress path databases, ascontingencies for replanning and as source of symbolic representations.Following ideas from Morse theory, we define modes as paths invariant underoptimization of a cost functional. We develop a multi-mode estimation algorithmwhich approximately finds all modes of a given motion optimization problem andasymptotically converges. This is made possible by integrating sparse roadmapswith an existing single-mode optimization algorithm. Initial evaluation resultsshow the multi-mode estimation algorithm as a promising direction to study pathspaces from a topological point of view.

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