Servo-Constraint Based Computed Torque Control of Underactuated Mechanical Systems

Abstract

This paper aims to generalize the computed torque control method for underactuated systems which are modeled by a non-minimum set of generalized coordinates subjected to geometric constraints. The control task of the underactuated robot is defined in the form of servo constraint equations that have the same number as the number of independent control inputs. A PD controller is synthesized based on projecting the equations of motion into the nullspace of the distribution matrix of the actuator forces/torques. The results are demonstrated by numerical simulation and experiments conducted on a two degrees-of-freedom device.