On Moving and Orienting Objects

Many problems arising in the area of robotics are directly or indirectly motion related. In order to analyze such problems, it is necessary to incorporate the dynamics with the geometry in the mathematical formulation. With this in view, this thesis deals with two such problems--motion planning in the presence of uncertainty and the automated design of parts orienters. Motion planning for robots with errors in position measurement, velocity and time is considered and shown to be decidable in polynomial time for a large class of inputs. The robot model is then extended to include damping--a limited form of force sensing. Motion planning for point objects in three-dimensional scenes and robots with damping is shown to be PSPACE-hard. A simplified version of the same problem is shown to be PSPACE-complete. The problem of the automated design of parts orienters is rather closely related to motion planning. But the dynamics of the problem is so dominant that similar general formulations seem impossible. In this thesis, the alternative pursued is paradigm-by-paradigm analysis. Three paradigms are presented and analyzed--the "belt", for orienting convex polygons that are infinite in the third dimension, the "pan handler", for flat polygonal objects and the vibratory track for flat, convex polygons. Polynomial time algorithms are developed for the automated design of orienters in each of the paradigms.