Conservative Hypercube Volumes for Compact, Certifiably Continuous Roadmaps

This work presents an analysis of a novel approach to motion planning for serial manipulators, based on an explicit and conservative representation of the configuration space (Cspace). Traditional sampling-based planners typically rely on implicit Cspace representations defined by workspace obstacles, resulting in limitations such as discrete configuration validity checks and the need for dense roadmaps with many samples. We investigate the Free Volume Graph (FVG) planner, which constructs roadmaps using hypercube volumes of verified free Cspace. This method enables a resolution-free certificate of continuous path validity, addressing key challenges in standard planning frameworks. Through a series of case studies involving 6- and 7-DOF manipulators across single and multi-query planning tasks, we evaluate the performance of FVG against Probabilistic Roadmap (PRM) method. Our findings indicate that FVG provides significant benefits in memory efficiency and computation time. Additionally, we examine the applicability of this approach to an open motion planning problem, identifying both its advantages and the remaining challenges in extending the method to broader scenarios.