Exact structured singular value of robotic manipulators and quantitative analysis of passivity based control

This paper gives an exact and explicit expression of the structured singular value for robotic manipulators with a passivity based control in port-controlled Hamiltonian form, even though it is not possible to give the exact or explicit structured singular value for general systems. First, we focus on dynamics with endlink mass perturbation after the settling time. Second, we derive the exact and explicit structured singular value for manipulators by using structural properties of the dynamics. The derived structured singular value is nothing but the structured singular value of manipulators without control because the passivity based control preserves the Hamiltonian structure. Furthermore, based on the derived structured singular value, we quantitatively analyze the robust stability of robotic manipulators with the passivity based control