Abstract
It is shown for the first time that, even if there exist nonlinear unknown dynamics, aPD feedback control without higher-order nonlinear compensation can guarantee global stability for the trajectory following problem of a robot manipulator. ThePD control under investigation is a position and velocity feedback control with a time-varying gain, and does not contain any higher-order nonlinearity. The proposed control is in general continuous and does not require any knowledge of robotic systems except size bounding function on nonlinear dynamics. Asymptotic stability of velocity tracking error and arbitrarily small position tracking error are guaranteed. Another novel and interesting result shown in this paper is that a measure on protection against saturation of actuators has been incorporated into consideration of control design and robustness analysis.
Similar content being viewed by others
References
J.J. Craig,Adaptive Control of Mechanical Manipulators. Addison-Wesley Publishing Co.: New York, NY, 1988.
J.J. Craig,Introduction to Robotics. Addison Wesley: Boston, MA, 1986.
N.V. Dunskaya and E.S. Pyatnitskii, “Stabilization of mechanical and electromechanical systems,”Automation and Remote Control, pp. 1565–1574, 1989.
D.M. Dawson, Z. Qu, F.L. Lewis, and J.F. Dorsey, “Robust control for the tracking of robot motion,”Int. J. Control, vol. 52, pp. 581–595, 1990.
S.V. Gusev, “Linear stabilization of nonlinear systems program motion,”Systems Control Lett., vol. 11, pp. 409–412, 1988.
S. Kawamura, F. Miyazaki, and S. Arimoto, “Is a local linearPD feedback control law effective for trajectory tracking of robot motion?” inProc. of 1988 IEEE Conf. on Robotics and Automation, pp. 1345–1340.
V. I. Matyukhin, “Nominal stability of manipulator robots in a decomposition mode,”Automation and Remote Control, pp. 314–323, 1989.
E.S. Pyatnitskii, “Design of hierarchical control systems for mechanical and electromechanical plants with the aid of decomposition,”Automation and Remote Control, pp. 64–73, 1989.
Z. Qu and J. Dorsey, “Robust tracking control of robots by a linear feedback law,”IEEE Trans. Automat. Control, vol. 36, pp. 1081–1084, 1991.
Z. Qu and J. Dorsey, “RobustPID control of robots,”Int. J. of Robotics and Automation, vol. 6, pp. 228–235, 1991.
Z. Qu, J. Dorsey, Z. Zhang, and D. Dawson, “Robust control of robots by computed torque law,”Systems Control Lett. vol. 16, pp. 25–32, 1991.
Z. Qu, D. Dawson, and J. Dorsey, “Exponentially stable trajectory following of robotic manipulators under a class of adaptive control,”Automatica, vol. 28, pp. 579–586 1992.
C. Samson, “Robust nonlinear control of robotic manipulators,”Proceeding of 22nd IEEE CDC, pp. 1211–1216, 1983.
C. Samson, “Robust control of a class of nonlinear systems and applications to robotics,”Int. J. Adaptive Control and Signal Processing, vol. 1, pp. 49–68, 1987.
J.J. Slotine and W. Li,Applied Nonlinear Control, Prentice-Hall: Englewood Cliffs, NJ, 1991.
X. Wang and L.-K. Chen, “Proving the uniform boundedness of some commonly used control schemes for robots,”Proc. of 1989 IEEE Conf. on Robotics and Automation, pp. 1491–1496.
Author information
Authors and Affiliations
Additional information
This work is supported in part by U.S. National Science Foundation under grant MSS-9110034.
Rights and permissions
About this article
Cite this article
Qu, Z. Global stability of trajectory tracking of robot underPD control. Dynamics and Control 4, 59–71 (1994). https://doi.org/10.1007/BF02115739
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02115739