This paper summarizes our research efforts in robotics. The primary goal is to bring robotics science closer to its goal of task-level planning. We approach this goal through blend of theory, implementation, and experimentation. We have identified several key problem areas on which to concentrate, and are undertaking research on generating assembly strategies from task-level descriptions. Our projects focus on: Algorithmic techniques for modelling 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 modelling of uncertainty and error in sensing, control, and the shape of the manipulated parts. The development of a precise theory of Error Diagnosis and Recovery, and a method for generating sensor-based plans with built-in error detection and recovery. The heart of this research lies in a geometrical planning theory, for reasoning about and manipulating physical systems. We will develop this underlying theory, implement and test the theory in simulation, and conduct robotics laboratory experiments.