Robust impedance control of robotic manipulators

A task space robust trajectory tracking control is developed for robotic manipulators. A second order linear model, which defines the desired impedance for the robot, is used to generate the reference position, velocity and acceleration trajectories under the influence of an external force. The control objective is to make the robotic manipulator's end effector to track the reference trajectories in the task space. A sliding mode based robust control is used to deal with system uncertainties and unmodeled dynamics. Thus, a sliding manifold is defined by a linear combination of the tracking errors of the system in the task space built from the difference between the real and the desired position, velocity and acceleration trajectories. Moreover, the ideal relay has been substituted by a relay with a dead-zone in order to fit in with the actual way in which a real computational device implements the sign function being typical in sliding mode control. Furthermore, a higher level supervision algorithm is proposed in order to reduce the amplitude of the high frequency components of the output associated to an overestimation of the system uncertainties bounds. Then, the robust control law is applied to the case of a robot with parametric uncertainties and unmodeled dynamics. The closed-loop system is proved to be stable while the control objective fulfilled is in practice. Finally, a simulation example which shows the usefulness of the proposed scheme is presented.