A Local Collision Avoidance Method for Non-strictly Convex Polyhedra

Abstract

This paper proposes a local collision avoidance method for non-strictly convex polyhedra with continuous velocities. The main contribution of the method is that non-strictly convex polyhedra can be used as geometric models of the robot and the environment without any approximation. The problem of the continuous interaction generation between polyhedra is reduced to the continuous constraints generation between polygonal faces and the continuity of those constraints are managed by the combinatorics based on Voronoi regions of a face. A collision-free motion is obtained by solving an optimization problem defined by an objective function which describes a task and linear inequality constraints which do geometrical constraints to avoid collisions. The proposed method is examined using example cases of simple objects and also applied to a humanoid robot HRP-2.