A GES joint position trajectory tracking smooth controller of torque-driven robot manipulators affected by disturbances

This paper presents a controller for joint position tracking of torque-driven robot manipulators affected by torque disturbances. In particular, the proposed approach allows concluding global exponential stability (GES) of the state-space origin of the closed-loop system when constant disturbances affect the robot dynamics. Besides, when time-varying disturbances are presented, the trajectories of the closed-loop system are proven to be bounded as result of the input-to-state stability. The main contribution is the design of the control law and a nonlinear observer based on an alternative energy shaping approach. The nonlinear observer is designed to compute and compensate for unknown disturbances, whether they are constant or time-varying. Furthermore, a detailed stability analysis of the closed-loop system based on Lyapunov theory and input-to-state stability is presented. As far as the authors know, this is the first energy-shaping controller for trajectory tracking control of robot manipulators affected by constant disturbances that achieves global exponential stability. Real-time experiments on a manipulator arm of two degrees-of-freedom illustrate the performance of the proposed controller.