Scaling Infeasibility Proofs via Concurrent, Codimension-One, Locally-Updated Coxeter Triangulation

Achieving a complete motion planner that guarantees a plan or infeasibility proof in finite time is challenging, especially in high-dimensional spaces. Previous efforts have introduced asymptotically complete motion planners capable of providing a plan or infeasibility proof given long enough time. The algorithm trains a manifold using configuration space samples as data and triangulates the manifold to ensure its existence in the obstacle region of the configuration space. In this letter, we extend the construction of infeasibility proofs to higher dimensions by adapting Coxeter triangulation's manifold tracing and cell construction procedures to concurrently triangulate the configuration space codimension-one manifold, and we apply a local elastic update to fix the triangulation when part of it is in the free space. We perform experiments on 4-DOF and 5-DOF serial manipulators. Infeasibility proofs in 4D are two orders of magnitude faster than previous results. Infeasibility proofs in 5D complete within minutes.