Global Trajectory Tracking Through Static Feedback for Robot Manipulators With Bounded Inputs

In this work, two globally stabilizing bounded control schemes for the tracking control of robot manipulators with saturating inputs are proposed. They may be seen as extensions of the so-called PD+ algorithm to the bounded input case. With respect to previous works on the topic, the proposed approaches give a global solution to the problem through static feedback. Moreover, they are not defined using a specific sigmoidal function, but any one on a set of saturation functions. Consequently, each of the proposed schemes actually constitutes a family of globally stabilizing bounded controllers. Furthermore, the bound of such saturation functions is explicitly considered in their definition. Hence, the control gains are not tied to satisfy any saturation-avoidance inequality and may consequently take any positive value, which may be considered beneficial for performance-adjustment/improvement purposes. Further, a class of desired trajectories that may be globally tracked avoiding input saturation is completely characterized. For both proposed control laws, global uniform asymptotic stabilization of the closed-loop system solutions towards the prespecified desired trajectory is proved through a strict Lyapunov function. The efficiency of the proposed schemes is corroborated through experimental results.