IRIS on a Torus: Growing Convex Sets on Manifolds
My current research focus at MIT is motion planning along manifolds, which we're primarily exploring through the lens of the graph of convex sets framework, abbreviated as GCS. (Refer to a previous blog post for more details, or check out the papers of Marcucci et. al. here and here .) Convexity is a property that is examined through the lens of Euclidean geometry, but it is possible to consider it in the broader context of smooth manifolds. This is reliant on the idea of a geodesic: a shortest path on a manifold. Replacing Euclidean spaces with manifolds and lines with geodesics allows us to consider a graph of geodesically convex sets (GGCS). We've begun laying the groundwork for planning over manifolds with such a tool, and you can read about it in our paper Non-Euclidean Motion Planning with Graphs of Geodesically-Convex Sets , to appear at RSS 2023. (You can read the preprint today on arXiv!) While GGCS assumes the geodesically convex sets are given, computing such set