Computing the Possible Rest Configurations of Two Interacting Polygons

Abstract

An algorithm that constructs the set of all possible equilibrium configurations for two interacting polygonal objects is described. Given two polygons, associated friction properties, and an applied force, the algorithm constructs the set of all configurations where the contact reaction force can balance the applied force, obeying friction constraints. The algorithm explicitly includes uncertainty in friction, applied force, and mass properties of the polygons. The algorithm has been implemented, and physical experiments have been performed to test the validity of the algorithm's predictions. The algorithm may be applied to a variety of physical systems to determine the possible rest states: examples include a part falling into a fixture and an object being pushed by a robot end-effector.