An alternative proof to the asymptotic stability of PID controllers for regulation of robot manipulators

The control of robot manipulators has been extensively studied for many decades. Although there exists a wide variety of sophisticated techniques, when it comes to position regulation a classical PD control law can be employed only by gravitational compensation, while the stability proof is rather trivial. If the gravity term is unknown and thus it cannot be compensated, exact regulation can be achieved by using a PID control law. However, for this case the stability analysis is by far more complex and gain tuning less intuitive. In this note, we show that a common change of variables may make the stability analysis easier. Simulation results are provided to show that stability conditions are correct and up to some point similar to those obtained with previous approaches.