Stability of Robot Manipulators Under Saturated PID Compensation

The joint position regulation problem for robot manipulators under a standard saturated proportional-integral differential (PID) compensator is studied in this brief. The main result states the existence of PID control gains yielding semiglobal asymptotic stability if the control torque bounds are larger than gravitational torques. Energy shaping plus damping injection methods, as well as singular perturbation analysis, are used to establish stability conditions to achieve regulation at any desired position. Some experiments are carried out to illustrate the stability results.