Robot Task and Motion Planning with Sets of Convex Polyhedra

Geometric volumes can be used as an intermediate representation for bridging the gap between task planning, with its symbolic preconditions and effects, and motion planning, with its continuous-space geometry. In this work, we use sets of convex polyhedra to represent the boundaries of objects, robot manipulators, and swept volumes of robot motions. We apply efficient algorithms for convex decomposition, conservative swept volume approximation and collision detection, and integrate these methods into our existing "knowledge of volumes" approach to robot task planning called KVP. We demonstrate and evaluate our approach in several task planning scenarios, including a bimanual robot platform.