The overall objective of this research is to develop a task level geometrical planning theory for representing, reasoning about, and manipulating physical systems. A specific goal of this work is the generation of assembly strategies from task - level descriptions. The investigation will concentrate on the following problems: + Algorithmic techniques for modeling geometric constraints, and the planning of robot motions using these constraints. + The synthesis of compliant motion programs using the geometric constraints imposed by the task. + The explicit modeling of uncertainty and error is sensing, control, and the shape of the manipulated part. + The development of a precise theory of error diagnosis and recovery, and a method for generating sensor-based plans with built-in detection and recovery.