The physics of motion of a sliding object can be used to plan sensorless robot manipulation strategies. Prediction of a sliding object’s motion is difficult because the object’s distribution of support on the surface, and the resulting frictional forces, are in general unknown. This paper describes a new approach to the analysis of sliding motion, which finds the set of object motions for all distributions of support. The analysis results in the definition of discrete regions of guaranteed sticking and slipping behavior which lend themselves to use in planning. Unlike previous work our approach produces quantitative bounds on the rate at which predicted motions can occur. To illustrate a manipulation plan which requires quantitative information for its construction, we consider a strategy based on "herding" a sliding disk toward a central goal by moving a robot finger in a decreasing spiral about the goal. The optimal spiral is constructed, and its performance discussed.