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.