Abstract
This paper considers a control problem that requires the design of an observed-based compensator in order to guarantee the asymptotic convergence of the output (namely, the joint generalized coordinates of ann-degree of freedom robot) to a corresponding output produced by a linear reference model. It is shown that, for a model having a relative degree vector {r 1, ...,r n}, withr i ≥2, it is possible to determine a controller-observer yielding a robot output that converges exponentially to the desired model output. Moreover, the combined system comprising the plant and the controller is internally stable in the semiglobal sense. The solution to the standard trajectory-following problem in robotics is obtained as a simplified case of the underlying model matching problem. While the controller-observer is nonlinear, its dynamic part is linear time-varying; in addition, the construction does not assume a priori the knowledge or even the existence of an upper bound to the model state vector.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Canudas de Wit, C., Astrom, K. J., andFixot, N.,Computed Torque Control via a Nonlinear Observer, International Journal of Adaptive Control and Signal Processing, Vol. 4, pp. 443–452, 1990.
Nicosia, S., andTomei, P.,Robot Control by Using Only Joint Position Measurements, IEEE Transactions on Automatic Control, Vol. 35, pp. 1058–1061, 1990.
Berghuis, H., andNijmeijer, H.,A Passivity Approach to Controller-Observer Design Robot, Memorandum No. 1050, Faculty of Applied Mathematics, University of Twente, 1992.
Ailon, A., andOrtega, R.,An Observed-Based Set-Point Controller for Robot Manipulators with Flexible Joints, Systems and Control Letters, Vol. 21, pp. 329–335, 1993.
Kelly, R., Ortega, R., Ailon, A., andLoria, A.,Global Regulation of Flexible Joint Robot Using Approximate Differentiation, IEEE Transactions on Automatic Control, Vol. 39, pp. 1222–1224, 1994.
Berghuis, H., andNijmeijer, H.,Global Regulation of Robots Using Only Position Measurements, Systems and Control Letters, Vol. 21, pp. 289–293, 1993.
Wonham, W. M.,Linear Multivariable Control: A Geometric Approach, 2nd Edition, Springer, New York, New York, 1979.
Isidori, A.,Nonlinear Control Systems, 2nd Edition, Springer, Berlin, Germany 1989.
Spong, M. W., andVidyasagar, M.,Robot Dynamics and Control, John Wiley and Sons, New York, New York, 1989.
Asada, H., andSlotine, J. J. E.,Robot Analysis and Control, John Wiley and Sons, New York, New York, 1986.
Spong, M. W., Thorp, J. S., andKleinwaks, J. M.,The Control of Robot Manipulators with Bounded Input, IEEE Transactions on Automatic Control, Vol. 31, pp. 483–490, 1986.
Kheradpir, S., andThorp, J. S.,Real-Time Control of Robot Manipulators in the Presence of Obstacles, IEEE Journal of Robotics and Automation, Vol. 4, pp. 687–698, 1988.
Kankaanranta, R. K., andKoivo, H. N.,Dynamics and Simulation of Compliant Motion of a Manipulator, IEEE Journal of Robotics and Automation, Vol. 4, pp. 163–173, 1988.
Carignan, C. R., andAkin, D. L.,Cooperative Control of Two Arms in the Transport of an Inertia Load in Zero Gravity, IEEE Journal of Robotics and Automation, Vol. 4, pp. 414–419, 1988.
Bacciotti, A.,Potentially Global Stabilizability, IEEE Transactions on Automatic Control, Vol. 31, pp. 974–976, 1986.
Sussmann, H. J., andKokotovic, P. V.,The Peaking Phenomenon and the Global Stabilization of Nonlinear Systems, IEEE Transactions on Automatic Control, Vol. 36, pp. 424–439, 1991.
Lin, Z., andSaberi, A.,Semiglobal Exponential Stabilization of Linear Systems Subject to Input Saturation via Linear Feedbacks, Systems and Control Letters, Vol. 21, pp. 225–239, 1993.
Ailon, A., andLangholz, G.,On the Existence of Time-Optimal Control of Mechanical Manipulators, Journal of Optimization Theory and Applications, Vol. 46, pp. 1–21, 1985.
Sontag, E. D., andSussmann, H. J.,Time-Optimal Control of Manipulators, Proceeding of the 1986 IEEE International Conference on Robotics and Automation, San Francisco, California, pp. 1692–1697, 1986.
Chen, Y. C.,On the Structure of the Time Optimal Controls of Robotic Manipulators, IEEE Transactions on Automatic Control, Vol. 34, pp. 115–116, 1989.
Author information
Authors and Affiliations
Additional information
Communicated by T. L. Vincent
This research was supported in part by the Paul Ivanier Center for Robotics Research and Production Management, Ben Gurion University of the Negev, Beer Sheva, Israel.
The authors wish to thank Evgany Landau from the Department of Electrical and Computer Engineering, Ben Gurion Univeersity of the Negev, for designing and performing the computer simulation.
Rights and permissions
About this article
Cite this article
Ailon, A., Segev, R. Stable observer-based trajectory controller for asymptotic model matching of a rigid robot. J Optim Theory Appl 87, 517–538 (1995). https://doi.org/10.1007/BF02192131
Issue Date:
DOI: https://doi.org/10.1007/BF02192131