PID type robot joint position regulation with prescribed performance guaranties

This paper proposes a PID type regulator that achieves not only the global asymptotic convergence of the robot joint velocities and position errors to zero but it also guarantees a prescribed performance for the position error transient that is independent of system constants and control parameters. The proportional term of the control input uses a transformed error (TP) which incorporates the desired performance function; given sufficiently high proportional and damping gains, the proposed TPID controller ensures the position error's prescribed performance irrespective of constant disturbances and choice of control gains. Control parameter selection is merely confined in achieving admissible input torques. Simulation results for a three dof spatial robot confirm the theoretical analysis and illustrate the robustness of the prescribed performance regulator in case of time-variant bounded disturbances.