Semiglobal stability of saturated linear PID control for robot manipulators (Q1810565)

The authors of this paper consider the position regulation problem for robotic manipulators with constraints on their control inputs. They prove that the robot system under a saturated linear proportional-integral-derivative control is semi-globally asymptotically stable provided that the torque bounds exceed the gravitational torques, the proportional gain is large enough, and the integral gain is small enough. The authors' stability analysis uses the tools of singular perturbation theory. The analyses are supplemented by simulations of a two degree-of-freedom robot arm.