A force regulation guaranteeing input‐to‐state stability for a robot manipulator in a potential field

Abstract

This paper is concerned with the compliant force regulation for a robot manipulator interacting with a deformable environment described as a potential field. We extend the conventional result of the asymptotic force regulation based on the energy shaping method for a port-Hamiltonian system. Additionally, we add an extra compensator and equip a modified integrator dynamics to the proposed controller in order to introduce sufficient degrees of freedom. Those degrees of freedom enable dealing with a wider class of disturbances, which are possibly time-varying and appear in the dynamics of all the variables of the closedloop system. Moreover, first, we prove that the proposed controller achieves asymptotic force regulation at the desired position without disturbances. Second, we prove that the closed-loop system with the proposed controller becomes input-to-state stable with respect to any bounded disturbances and guarantees that both the solution of the system and resultant interaction force remain bounded.