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A new approach to the kinematic analysis of object motion constrained by mechanical contacts is presented. In robotic manipulation, such as grasping and assembly, robots manipulate objects through mechanical contacts with the grasped object and with the environment. We need to understand the kinematic behavior of the object motion under the constraints by the mechanical contacts in order to find appropriate strategies for manipulation tasks. In this paper, we first show that the constraints by mechanical contacts are generally described by a set of homogeneous linear inequalities. In task planning, it is often necessary for the planner to treat the complex inequalities. Thus, we develop an efficient mathematical tool based on the theory of polyhedral convex cones in order to treat the inequalities in a simple and systematic manner. Furthermore, we develop computation algorithms of the polyhedral convex cones in order to treat the inequalities on a computer. We apply the method to the planning of form-closure grasps, workpiece fixturing, and hybrid position/force control. Several examples demonstrate the usefulness of the algorithms.

Kinematics of Manipulation Using the Theory of Polyhedral Convex Cones and Its Applications to Grasping and Assembly Operations