An extended Jacobian matrix and multirate control for bilateral control between different time resolution systems

In this paper, a way to obtain bilateral control between different time resolution systems is proposed. Bilateral control enables communication of information regarding our tactile sense. A master (local) robot is manipulated by an operator and a slave (remote) robot tracks the position of the master while the reaction force of the slave is fed back to the master. Conventionally, there have been few studies about the difference of time resolution and feedback gains between master and slave systems. First, an extended Jacobian matrix is proposed to describe the dynamics of bilateral control taking time resolution difference into account. The fast (master) and slow (slave) systems are transformed to other fast and slow systems in modal space, which the dynamics of the position accordance and force regulation are described in. Then, a multirate controller is designed to couple the fast system with high feedback gain and the slow system with low feedback gain. The validity of the proposed method is confirmed by simulations and experiments.