Towards Kinematic Actionable Infeasibility Detection in Motion Planning

This paper presents a geometry-driven framework for certifying infeasibility in motion planning through an explicit resolution-dependent analysis of configuration space topology. The method traces separating manifolds induced by obstacle boundaries directly in configuration space, enabling both infeasibility detection and identification of geometric causes. A parallel frontier-expansion algorithm is developed for efficient simplicial reconstruction in high-dimensional spaces, validated on 4-DOF and 5-DOF robot scenarios.