Energy-Optimal Impedance Control of Cooperative Robot Manipulators

An impedance-based control scheme is introduced for cooperative manipulators grasping a rigid object. The position and orientation of the payload are to be maintained close to the desired trajectory, trading off tracking accuracy by low energy consumption and maintaining stability. To this end, the augmented dynamics of the robots, their actuators, and the payload are formed, and an impedance control is adopted. A virtual control strategy is used to decouple torque control from actuator control. An optimization problem is then formulated using energy balance equations. The optimization finds the damping and stiffness gains of the impedance relation such that the energy consumption is minimized. Furthermore, L2 stability techniques are used to guarantee the stability of the controller. A numerical example is provided to demonstrate the results.