On stability of a nonlinear PID-like controller with gravity compensation for input-saturated robot manipulators^∗

In this note, the regulation problem of an n-link robot manipulator that is subject to input saturation is addressed. Our control strategy is based on a control law that uses gravity compensation together with a PID-like controller with bounded actions. The design is based on the usage of symmetrical hard saturation functions whose saturation levels are free to be selected by the user. As the resulting closed- loop equation is autonomous, we propose a Lyapunov function and apply an invariance principle known in the literature to prove asymptotic stability. Numerical simulations on a three degrees-of-freedom robot manipulator are presented, where the performance of our controller with respect to others reported in the literature is compared.