A study on passivity of flexible master-slave manipulators

In this paper we study on the passivity of one degree-of freedom flexible master-slave manipulators (FMSM) with symmetric bilateral control. First, we derive dynamic equations of the FMSM by means of the Hamilton's principle. Second, when applying the symmetric bilateral control to the FMSM, we prove the passivity in the positioning operation by introducing a Lyapunov function related to the total energy. Finally, we also prove the passivity in the neighborhood of the desired state in the pushing operation to an environment.