Force and position hybrid control by combining PD control and kinetic potential energy shaping

This paper proposes a force and position hybrid control method for robot manipulators, which makes some of the workspace variables controlled by PD and the other by Kinetic Potential Energy Shaping (KPES). The conventional energy shaping method allows one to design a stabilizing controller with a Lyapunov function candidate consisting of an artificial potential function that plays the role of a design parameter. The potential function depends only on position, and this framework is a natural generalization of the well-known PD control for linear systems. KPES generalizes the conventional method such that it allows one to select an artificial potential function depending on both position and velocity variables. One of the benefits of the conventional method is to preserve the passivity of the original plant system, which enhances the safety of the control system. However, KPES does not preserve passivity in general. This paper proposes a hybrid control method for robot manipulators, which makes some of the configuration variables controlled by PD and the other by KPES. The realized system enables position control of subsystems by KPES and preserves the passivity of the entire system when an external force acts on subsystems controlled by PD. This hybrid control system will be useful from a safety perspective for control problems in which the feedback system still has physical interaction with its environment. This paper presents a method to design a feedback system that guarantees asymptotic stability of the entire system, preserves passivity, and discusses application to a force and position hybrid control with respect to workspace variables of a robot manipulator. Furthermore, numerical examples are presented for a robot manipulator.