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.

[1]  R. Kelly.  Global positioning of robot manipulators via PD control plus a class of nonlinear integral actions , 1998, IEEE Trans. Autom. Control..

[2]  Suguru Arimoto,et al.  PID control of robotic manipulator with uncertain Jacobian matrix , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[3]  Warren E. Dixon,et al.  Adaptive set-point control of robotic manipulators with amplitude-limited control inputs , 2000, Robotica.

[4]  F. Hoppensteadt.  Asymptotic stability in singular perturbation problems. II: Problems having matched asymptotic expansion solutions☆ , 1974 .

[5]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[6]  Nenad Kircanski,et al.  Resolved-rate and resolved-acceleration-based robot control in the presence of actuators' constraints , 1997, Proceedings of International Conference on Robotics and Automation.

[7]  Ernest Barany,et al.  Global regulation of uncertain manipulators using bounded controls , 1997, Proceedings of International Conference on Robotics and Automation.

[8]  Víctor Santibáñez,et al.  A Natural Saturating Extension of the PD-With-Desired-Gravity-Compensation Control Law for Robot Manipulators With Bounded Inputs , 2007, IEEE Transactions on Robotics.

[9]  Rafael Kelly,et al.  Semiglobal stability of saturated linear PID control for robot manipulators , 2003, Autom..

[10]  Warren E. Dixon,et al.  Tracking Control of Robot Manipulators with Bounded Torque Inputs , 1999, Robotica.

[11]  Suguru Arimoto,et al.  Control Theory of Nonlinear Mechanical Systems , 1996 .

[12]  W.E. Dixon.  Adaptive regulation of amplitude limited robot manipulators with uncertain kinematics and dynamics , 2004, Proceedings of the 2004 American Control Conference.

[13]  Suguru Arimoto,et al.  A New Feedback Method for Dynamic Control of Manipulators , 1981 .

[14]  Suguru Arimoto,et al.  Fundamental problems of robot control: Part I, Innovations in the realm of robot servo-loops , 1995, Robotica.

[15]  Suguru Arimoto.  Robustness of learning control for robot manipulators , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[16]  Mark W. Spong,et al.  Robot dynamics and control , 1989 .

[17]  Suguru Arimoto,et al.  Stability and robustness of PID feedback control for robot manipulators of sensory capability , 1984 .

[18]  Abdelhamid Laib.  Adaptive output regulation of robot manipulators under actuator constraints , 2000, IEEE Trans. Robotics Autom..

[19]  Rafael Kelly,et al.  A class of nonlinear PID global regulators for robot manipulators , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[20]  Fernando Reyes-Cortés,et al.  Experimental Evaluation of Identification Schemes on a Direct Drive Robot , 1997, Robotica.

[21]  Ramón Silva-Ortigoza,et al.  A New Tuning Procedure for PID Control of Rigid Robots , 2008, Adv. Robotics.

[22]  Ilya V. Burkov.  Stabilization of position or uniform motion of mechanical systems via bounded control and without velocity measurements , 2009, 2009 IEEE Control Applications, (CCA) & Intelligent Control, (ISIC).

[23]  Rafael Kelly,et al.  A new set-point controller with bounded torques for robot manipulators , 1998, IEEE Trans. Ind. Electron..

[24]  Rob Dekkers,et al.  Control of Robot Manipulators in Joint Space , 2005 .

[25]  Rafael Kelly,et al.  A tuning procedure for stable PID control of robot manipulators , 1995, Robotica.