Learning Proofs of Motion Planning Infeasibility

Abstract

We present a learning-based approach to prove infeasibility of kinematic motion planning problems. Samplingbased 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 propose a combination of bidirectional samplingbased planning (such as RRT-connect) and machine learning to construct an infeasibility proof alongside the two search trees. 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 learning hyper-parameters and robustness of configuration space optimization, the output is either an infeasibility proof or a motion plan. We demonstrate proof construction for 3-DOF and 4-DOF manipulators and show improvement over a previous algorithm.

A sampling and learning framework to prove motion planning infeasibility

“…In this experiment, we use a primitive shape collision geometry model of the Jaco arm for computing configuration space penetration depth. This is why the experiment takes significantly less time than in Li and Dantam (2020) and Li and Dantam (2021) (with average running time of 457.5s and 177.36 s, respectively). The use of parallel computing also greatly benefits running time.…”

“…An initial version of this work appeared in Li and Dantam (2021). We now extend that work to improve generality and efficiency as follows:…”

“…An initial version of this work appeared in Li and Dantam (2021). We now extend that work to improve generality and efficiency as follows:• generalizing to configuration spaces with multiple, disconnected free space components by using a Probabilistic Roadmap (PRM) instead of a bidirectional rapidly exploring random tree (RRT-connect);• parallelization of parts of the algorithm to reduce overall running time;• more efficient checking of polytope facets using a minimum enclosing ball;• more efficient handling of triangulation and facet checking failures;• additional experiments on up to 4-DOF configuration spaces to show scalability of our algorithm.…”

A Survey on the Integration of Machine Learning with Sampling-based Motion Planning

“…• Planner selection (Morales et al, 2005;Choudhury et al, 2015) • Connection strategy selection (Ekenna et al, 2013;Uwacu et al, 2016) • Sampler selection (Hsu et al, 2005) • Paths & parameter selection (Chamzas et al, 2021a;Moll et al, 2021) • Meta-reasoning (Li and Dantam, 2021;Sung et al, 2021)…”

“…Given the intuition that search trees rooted at the start and goal of a planning problem form two separate classes in C, recent work has proposed learning a manifold that separates these classes (Li and Dantam, 2021). Points are then sampled on the manifold, and a closed polytope is constructed to approximate it.…”