Efficiently Planning Compliant Motion in the Plane

Any practical model of robotic motion must cope with the uncertainty and impre-cision inherent in real robots. One important model is compliant motion, in which a robot that encounters an obstacle obliquely may slide along the obstacle. In this paper, we start by investigating the geometry of compliant motion in the plane under perfect control and nd a compact data structure encoding all paths to a goal. When we introduce uncertainty in control and position sensing, the same data structure allows us to nd eeciently a compliant motion that reaches the goal if one exists, to compute the boundary of the non-directional backprojection of the goal, and to compute multi-step plans for sensorless robots. Our preprocessing and query approach has advantages of speed for on-line queries and exibility for considering robots with diierent capabilities or initial positions in the same environment.