Model-free robot joint position regulation and tracking with prescribed performance guarantees

The problem of robot joint position control with prescribed performance guarantees is considered; the control objective is the error evolution within prescribed performance bounds in both problems of regulation and tracking. The proposed controllers do not utilize either the robot dynamic model or any approximation structures and are composed by simple PID or PD controllers enhanced by a proportional term of a transformed error through a transformation related gain. Under a sufficient condition for the damping gain, the proposed controllers are able to guarantee (i) predefined minimum speed of convergence, maximum steady state error and overshoot concerning the position error and (ii) uniformly ultimate boundedness (UUB) of the velocity error. The use of the integral term reduces residual errors allowing the proof of asymptotic convergence of both velocity and position errors to zero for the regulation problem under constant disturbances. Performance is a priori guaranteed irrespective of the selection of the control gain values. Simulation results of a three dof spatial robotic manipulator and experimental results of one dof manipulator are given to confirm the theoretical findings.