Towards Kinematic Actionable Infeasibility Detection in Motion Planning

2026-09-26

AI Summary

This study addresses the challenge of certifying infeasibility within finite time for high-dimensional motion planning by proposing a geometry-driven infeasibility detection framework. The method performs explicit resolution-dependent topological analysis of the configuration space to track separating manifolds, integrating signed distance field representations, simplicial reconstruction, and a GPU-accelerated parallel frontier expansion algorithm to overcome high-dimensional computational bottlenecks. This enables rapid infeasibility detection and root-cause localization. Experimental results demonstrate that the proposed framework completes certification within seconds for 4-DOF scenarios and under four minutes for 5-DOF robotic setups. By significantly reducing computation time while ensuring reliability, this work establishes an efficient and robust new paradigm for infeasibility determination in high-dimensional motion planning.

Abstract

Motion planning in robotics requires not only computing collision-free paths but also certifying infeasibility when no such path exists. Complete methods are limited to low-dimensional spaces, while sampling-based planners scale efficiently but cannot provide finite-time infeasibility certificates, leaving this problem largely unresolved in high-dimensional spaces. In this letter, we present a geometry-driven framework for certifying infeasibility through an explicit resolution-dependent analysis of configuration space topology. Leveraging signed distance field representations, the proposed method traces separating manifolds induced by obstacle boundaries directly in configuration space, enabling both detection of infeasibility and identification of the specific geometric cause. To address computational challenges, we develop a parallel frontier-expansion algorithm that exploits GPU acceleration for efficient simplicial reconstruction in high-dimensional spaces. We validate the approach on 4-DOF and 5-DOF robot scenarios, certifying infeasibility within seconds for 4-DOF cases and under four minutes for 5-DOF cases. We further discuss avenues for improving scalability to higher-dimensional spaces.

Problem

• Motion Planning
• Infeasibility Detection
• Configuration Space
• High-dimensional Spaces
• Robotics

Innovation

• Motion Planning
• Infeasibility Detection
• Signed Distance Field
• GPU Acceleration
• Configuration Space Topology