Towards Constructing Finer then Homotopy Path Classes

This work presents a new path classification criterion to distinguish paths geometrically and topologically from the workspace, which is divided through cell decomposition, generating a medial-axis-like skeleton structure. We use this information as well as the topology of the robot to bound and classify different paths in the configuration space. We show that the path class found by the proposed method is equivalent to and finer than the path class defined by the homotopy of paths. The proposed path classes are easy to compute, compare, and can be used for various planning purposes. The classification builds heavily upon the topology of the robot and the geometry of the workspace, leading to an alternative fiber-bundle-based description of the configuration space. We introduce a planning framework to overcome obstacles and narrow passages using the proposed path classification method and the resulting path classes.