Discrete Path Planning for Convex Polyhedra through Edge-Rolling on a Plane

Abstract

This thesis solved the path-planning problem of the Platonic solids and truncated icosahedron through edge-rolling on a plane with obstacle avoidance, which hitherto had not been solved. The BFS-based algorithm found the shortest paths for the Platonic solids on a prescribed plane while the RRT-based algorithm generated feasible paths with efficient tree exploration on a non-prescribed plane. The results can be readily applied to a variety of applications: path planning for general convex polyhedral, dexterous robotic in-hand manipulation, video games, and locomotion of polyhedral tensegrity robots.