. Any practical model of robotic motion must cope with the uncertainty and imprecision 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 find 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 find efficiently 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 flexibility for considering robots with different capabilities or initial positions in the same environment. Key words. computational geometry, compliant motion, path hull data structure AMS subject ..