Adaptive control for a class of Hamiltonian systems

Abstract This paper presents an adaptive scheme for the motion control of an important class of Hamiltonian systems. The controller does not require knowledge of either the structure or the parameter values of the system dynamic model, is very simple and computationally efficient, and is shown to be globally stable. Furthermore, the control strategy is very general and is implementable for either position regulation or trajectory tracking with a wide variety of systems. Computer simulation results are given for an industrial robot, a biomechanical system and a satellite. These results demonstrate that accurate and robust motion control can be achieved by using the proposed scheme.

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

[2]  Rolf Johansson,et al.  Adaptive control of robot manipulator motion , 1990, IEEE Trans. Robotics Autom..

[3]  Homayoun Seraji,et al.  Direct adaptive impedance control of robot manipulators , 1993, J. Field Robotics.

[4]  Joel Franklin,et al.  Methods of Mathematical Economics , 1980 .

[5]  Eduardo D. Sontag,et al.  Remarks on the time-optimal control of a class of hamiltonian systems , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[6]  H.M. Schwartz,et al.  Issues in Robot Adaptive Control , 1990, 1990 American Control Conference.

[7]  Sahjendra N. Singh,et al.  Inverse Trajectory Control and Zero Dynamics Sensitivity of an Elastic Manipulator , 1991 .

[8]  Daniel E. Koditschek,et al.  Application of a new Lyapunov function to global adaptive attitude tracking , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[9]  P. Wolfe.  THE SIMPLEX METHOD FOR QUADRATIC PROGRAMMING , 1959 .

[10]  Kristin Glass,et al.  Adaptive control of a human wrist motion similator , 1991 .

[11]  Kristin Glass,et al.  Hierarchical control of human joint motion simulators , 1993 .

[12]  Suguru Arimoto,et al.  Learning control theory for robotic motion , 1990 .

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

[14]  F.E. Zajac,et al.  Paraplegic standing controlled by functional neuromuscular stimulation. I. Computer model and control-system design , 1989, IEEE Transactions on Biomedical Engineering.

[15]  Homayoun Seraji,et al.  Configuration control of redundant manipulators: theory and implementation , 1989, IEEE Trans. Robotics Autom..

[16]  R. Colbaugh,et al.  On Controlling Robots with Redundancy , 1991, 1991 American Control Conference.

[17]  Christopher I. Byrnes,et al.  On the attitude stabilization of rigid spacecraft , 1991, Autom..

[18]  William K. Durfee,et al.  Linear and Nonlinear Approaches to Control of Single Joint Motion by Functional Electrical Stimulation , 1990, 1990 American Control Conference.

[19]  R. Colbaugh,et al.  Improved configuration control for redundant robots , 1990, J. Field Robotics.

[20]  N. P. Bhatia,et al.  Dynamical Systems: Stability, Theory and Applications , 1967 .

[21]  Ann K. Stehney,et al.  Geometrical Methods of Mathematical Physics by Bernard F. Schutz , 1980 .

[22]  Romeo Ortega,et al.  Adaptive motion control of rigid robots: a tutorial , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[23]  Homayoun Seraji,et al.  Decentralized adaptive control of manipulators , 1994, J. Field Robotics.

[24]  Richard Colbaugh,et al.  Cartesian control of redundant robots , 1989, J. Field Robotics.

[25]  Jean-Jacques E. Slotine,et al.  Hamiltonian adaptive control of spacecraft , 1990 .

[26]  S. Shankar Sastry,et al.  Adaptive Control of Mechanical Manipulators , 1987 .

[27]  A. J. Schaft,et al.  Stabilization of Hamiltonian systems , 1986 .

[28]  P. Crouch,et al.  Spacecraft attitude control and stabilization: Applications of geometric control theory to rigid body models , 1984 .

[29]  J. Slotine,et al.  On the Adaptive Control of Robot Manipulators , 1987 .

[30]  Anuradha M. Annaswamy,et al.  Stable Adaptive Systems , 1989 .