Homology-Rank-Informed Geometry Score for Configuration Space Reconstruction

Abstract

Accurately reconstructing datasets holds paramount significance in the field of machine learning. In path planning problems, the ability to precisely reconstruct the configuration space (CS) is pivotal for distinguishing between collision-free states and states in collisions. Collision states can be visualized as voids within the CS of a robot. In this paper, we introduce a novel approach to assess the fidelity of the reconstructed distribution of collision-free states by adapting the concept of homology rank of manifolds with a geometry score tailored to the unique characteristics of CS. This scoring mechanism effectively quantifies the degree to which the reconstructed CS faithfully represents the collision-free space and facilitates the identification of collision states. To validate our proposed methodology, extensive simulations were conducted across a range of case studies. The results demonstrate the capability of our approach to measure the resemblance between the original dataset and its regenerated counterpart with an acceptable accuracy.