Energy regulation of torque–driven robot manipulators in joint space

Abstract

The energy regulation of fully actuated torque–driven robot manipulators in joint space is addressed in this paper. The proposed controller is designed via an energy shaping plus damping injection approach. The contribution is the proposal of an energy regulator with partial damping injection capable of inducing oscillations in the undamped joints of robot manipulators, with an user specified desired frequency and amplitude, by adding only damping in the rest of the joints, which may require less control effort than a trajectory tracking controller with full damping injection. Although viscous friction is considered in all joints of robot manipulator, it has been compensated via the proposed energy regulator. Moreover, the controlled periodic motion oscillates around a desired joint position as reference, and this provides a nice feature in the robot, mainly when there is not interest in the undamped joint to follow an specified time-varying sinusoidal function, but generating an oscillatory motion of constant amplitude and frequency. Instrumental in stability analysis is the Lyapunov’s theory and LaSalle’s theorem, which allows concluding that the closed-loop trajectories approach an invariant set that could include a unique equilibrium or periodic orbits. Numerical simulations on a manipulator arm model of two degrees of freedom illustrate the main results.