Generation of Configuration Space Obstacles: Moving Algebraic Surfaces

Abstract

We present an algebraic algorithm to generate the boundary of configuration space obstacles arising from the translatory motion of curved convex objects among curved convex obsta cles. Both the boundaries of the objects and obstacles are given by patches of algebraic surfaces. Further, we consider obtaining compliant motion paths where a curved convex object with fixed orientation moves in continuous contact with another curved convex obstacle in three-dimensional space. We also give a method to obtain a piecewise algebraic, ap proximate geodesic path on a curved convex C-space obstacle.