Distributively controlling two robots handling an object in the task space without any communication

Two distributed cooperation controllers are presented for trajectory tracking of two manipulators which are cooperatively handling an object. The controllers control the positions of the robots distributively by using the trajectory error of the object in the task space. In the first controller, the internal force between the object and a manipulator is controlled only by a feedforward of the desired force. The second controller uses a force feedback. No communication is required between the manipulators in both the controllers. Their globally and exponentially asymptotic stabilities are guaranteed by Lyapunov functions