A sampling and learning framework to prove motion planning infeasibility

Abstract

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.

A Novel Narrow Region Detector for Sampling-Based Planners' Efficiency: Match Based Passage Identifier

“…Sample Driven Connectivity Learning (SDCL) (Li & Dantam, 2023) is a new learning-based method for the narrow passage problem. In this method, firstly, the regions that make PRM roadmaps difficult to connect are learned and then these regions are sampled.…”

Motion Planning (In)feasibility Detection using a Prior Roadmap via Path and Cut Search

“…Step 3 of the learning framework introduced in Section I aims to convert cut edges into (d − 1)-dimensional hyperplanes to ensure infeasibility in the continuous C-space. The method [31] can be invoked in this step to learn a separating hyperplane that disconnects the start and goal. Figure 3 shows the time comparison of Dijkstra's and the Push-relabel algorithms as the number of vertices and edges in G increases.…”

“…The work [4], [37] uses support vector machines (SVM) to learn a feasibility classifier for multi-step planning, such as task and motion planning. The work [31] learns a separating manifold between a start and a goal using radial basis function kernel SVM. To deal with image inputs, the work [38]- [41] designs convolutional neural network-based feasibility classifiers.…”