Dynamic Manipulability for Cooperating Multiple Robot Systems with Frictional Contacts

This paper presents a strategy for finding feasible acceleration range, i.e., dynamic manipulability, of multiple robotic systems with frictional contacts between robot end-effectors and object. The frictional contact conditions are generally described by Coulomb´s Law which requires each contact force to lie within a friction cone. Since the friction cones are described by nonlinear inequality constraints, it is not easy to handle the constraint in manipulability analysis. To include the frictional contact condition into the conventional manipulability, we approximate the friction cone to a pyramid which is described by linear inequality constraints. And then achievable acceleration boundaries of manipulated object are calculated by conventional linear programming technique under constraints for torque capability of each robot and the approximated contact condition. With the proposed method we find some solution to which conventional approaches did not reach. Also, case studies will be presented to illustrate the correctness of the proposed approach for two robot systems of simple planar robots and PUMA560 robots