Internal force-based impedance control for cooperating manipulators

An internal force-based impedance control scheme for cooperating manipulators is introduced which controls the motion of the objects being manipulated and the internal force on the objects. The controller enforces a relationship between the velocity of each manipulator and the internal force on the manipulated objects. Each manipulator is directly given the properties of an impedance by the controller; thus, eliminating the gain limitation inherent in the structure of previously proposed schemes. The controller uses the forces sensed at the robot end effectors to compensate for the effects of the objects' dynamics and to compute the internal force using only kinematic relationships. Thus, knowledge of the objects' dynamics is not required. Stability of the system is proven using Lyapunov theory and simulation results are presented validating the proposed concepts. The effect of computational delays in digital control implementations is analyzed vis-a-vis stability and a lower bound derived on the size of the desired manipulator inertia relative to the actual manipulator endpoint inertia. The bound is independent of the sample time.