Efficient Geometric Predicates for Integrated Task and Motion Planning

“Can’t your robot do this for you?” People have great expectations of what tasks robots can accomplish and have been dreaming of intelligent machines that can understand, perceive, and manipulate. While today’s robot systems may not quite fulfill this dream, research in individual areas on automated planning, path planning, and robot control has made substantial progress. However, integrating these components does not make an intelligent robot. In particular, task planning cannot be solved as a problem separate from motion planning. This thesis approaches the integrated task and motion planning problem from the geometric side. Its main goal is to develop a powerful and efficient interface for the symbolic task planner to query and sample in a continuous-valued, geometric world. To provide more efficient queries without risking collisions, new geometric predicates are proposed that operate on single-sided, ε-precise approximations of the geometry. These single-sided approximations are generated by our new bounding mesh algorithm, which iteratively decimates edges to generate simpler meshes that either enclose or are enclosed by the original geometry. Edge decimations are guided by a quadratic cost function with linear inequalities. Several cost functions are evaluated on a set of robot geometries and further shapes, and experiments indicate that bounding mesh approximation reduces vertex counts by a factor of 10–20 at a good precision. Integration with a convex segmentation algorithm then allows a bounding convex decomposition of the scene, suitable for efficient collision checking routines. Effectively, bounded geometric predicates allow faster collision and inclusion queries, but never overlook a collision or a non-inclusion. Besides these queries, an approach to sampling with geometric constraints is developed to provide a mapping from symbolic preconditions to feasible geometric states. Constraints may be formulated as coincidence, parallelism, and distance relations between shapes of robots and objects, and are solved by projection sampling to cover the constraint space.