Constructing an Approximate Representation of a Configuration Space Without Using Any Intersection Check

摘要

This paper introduces a concept of configuration patch (C-patch) for representing configurations of a polyhedral robot in a point-point contact with polyhedral obstacles, and proposes an approach called inverse mapping method for computing an approximate representation using cubic cells of a configuration space (C-space). A configuration patch has a simple geometry if it is represented in a local coordinate system defined in this paper. The inverse mapping method constructs the approximated C-space by quantizing the C-patches in the local coordinate system and mapping the discrete points to configurations of the robot. It never checks any intersection among the robot and the obstacles. The only process in this algorithm is a coordinate transformation from discrete points on the C-patches to configurations of the robot. Finally, its efficiency is shown by simulations.