Minimizing Task Space Frechet Error via Efficient Incremental Graph Search
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We present an algorithm that generates a collision-free configuration-space path that closely follows, according to the discrete Fréchet metric, a desired path in task space. By leveraging the Fréchet metric and other tools from computational geometry, we approximate the search space using a cross-product graph. This structure allows us to efficiently search for the solution using a simple variant of Dijkstra's graph search algorithm. Additionally, we can incrementally update and improve the solution in an anytime fashion. We compare multiple proposed densification strategies and show that our algorithm outperforms a previously proposed optimization-based approach.
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