A sampling and learning framework to prove motion planning infeasibility

We present a learning-based approach to prove infeasibility of kinematic motion planning problems. Sampling-based motion planners are effective in high-dimensional spaces but are only probabilistically complete. Consequently, these planners cannot provide a definite answer if no plan exists, which is important for high-level scenarios, such as task-motion planning. We apply data generated during multi-directional sampling-based planning (such as PRM) to a machine learning approach to construct an infeasibility proof. An infeasibility proof is a closed manifold in the obstacle region of the configuration space that separates the start and goal into disconnected components of the free configuration space. We train the manifold using common machine learning techniques and then triangulate the manifold into a polytope to prove containment in the obstacle region. Under assumptions about the hyper-parameters and robustness of configuration space optimization, the output is either an infeasibility proof or a motion plan in the limit. We demonstrate proof construction for up to 4-DOF configuration spaces. A large part of the algorithm is parallelizable, which offers potential to address higher dimensional configuration spaces.