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Global tracking for robot manipulators using a simple causal PD controller plus feedforward

Published online by Cambridge University Press:  09 April 2009

Eduardo V. L. Nunes  and
Liu Hsu
Eduardo V. L. Nunes*
Affiliation:
Department of Electrical Engineering/COPPE, Federal University of Rio de Janeiro, P.O. BOx 68504, Rio de Janeiro, 21941-972 RJ, Brazil.
Liu Hsu
Affiliation:
Department of Electrical Engineering/COPPE, Federal University of Rio de Janeiro, P.O. BOx 68504, Rio de Janeiro, 21941-972 RJ, Brazil.
*
*Corresponding author. E-mail: [email protected]
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Summary

This paper shows that a well-known causal PD controller plus feedforward solves the global output feedback tracking control problem of robot manipulators, by requiring only the existence of the robot natural damping, no matter how small. To this end, we first demonstrate that a robot controlled by a causal PD is globally input-to-state stable (ISS) with respect to a bounded input disturbance. Then, we prove that the addition of a feedforward compensation renders the error system uniformly globally asymptotically stable. Furthermore, we present a possible extension to more general nonlinear systems and also to uncertain systems.

Keywords

Robot manipulatorsOutput feedbackGlobal trackingInput-to-state stabilityPD control
Type
Article
Information
Robotica , Volume 28 , Issue 1 , January 2010 , pp. 23 - 34
Copyright
Copyright © Cambridge University Press 2009

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References

1.Ailon, A. and Ortega, R., “An observer-based controller for robot manipulators with flexible joints,” Syst. Control Lett. 21, 329–335 (1993).CrossRefGoogle Scholar
2.Berghuis, H. and Nijmeijer, H., “Global regulation of robots using only position measurements,” Syst. Control Lett. 21, 289–293 (1993).CrossRefGoogle Scholar
3.Kelly, R., “A Simple Set-Point Robot Controller by Using only Position Measurements,” Preprint 12th IFAC World Congress, Sydney, vol. 6 (1993) pp. 173–176.Google Scholar
4.Ortega, R., Loria, A., Nicklasson, P. J. and Sira-Ramirez, H., Passivity-Based Control of Euler–Lagrange Systems: Mechanical, Electrical and Electromechanical Applications (Springer-Verlag, London, UK, 1998).CrossRefGoogle Scholar
5.Burkov, I., “Mechanical System Stabilization via Differential Observer,” Proceedings of IFAC Conference System Structure Control, Nantes, France (1995) pp. 532–535.Google Scholar
6.Loria, A., “Global tracking control of one degree of freedom Euler–Lagrange systems without velocity measurements,” Eur. J. Control 2, 144–151 (Jun. 1996).CrossRefGoogle Scholar
7.Zhang, F., Dawson, D. M., de Queiroz, M. S. and Dixon, W. E., “Global adaptive output feedback tracking control of robot manipulators,” IEEE Trans. Automat. Control 45 (6), 1203–1208 (2000).CrossRefGoogle Scholar
8.Sadegh, N. and Horowitz, R., “Stability and robustness analysis of a class of adaptive controllers for robotic manipulators,” Int. J. Rob. Res. 9 (3), 74–92 (1990).CrossRefGoogle Scholar
9.Loria, A. and Melhem, K., “Position feedback global tracking control of EL systems: A state transformation approach,” IEEE Trans. Automat. Control 47 (5), 841–847 (2002).CrossRefGoogle Scholar
10.Besançon, G., Battilotti, S. and Lanari, L., “A new separation result for a class of quadratic-like systems with application to Euler–Lagrange models,” Automatica 39, 1085–1093 (2003).CrossRefGoogle Scholar
11.Dixon, W. E., Zergeroglu, E. and Dawson, D. M., “Global robust output feedback tracking control of robot manipulators,” Robotica 22, 351–357 (2004).CrossRefGoogle Scholar
12.Santibañez, V. and Kelly, R., “Global Asymptotic Stability of Bounded Output Feedback Tracking Control for Robot Manipulators,” Proceedings of IEEE Conference of Decision and Control, Orlando, FL (2001) pp. 1378–1379.Google Scholar
13.Moreno, J. and Gonzalez, S., “An Adaptive Output Feedback Tracking Controller for Manipulators Subject to Constrained Torques,” Proceedings of IEEE Conference of Decision and Control, San Diego, CA (2006) pp. 2026–2031.Google Scholar
14.Sontag, E., “Smooth stabilization implies coprime factorization,” IEEE Trans. Automat. Control 34 (4), 435–443 (1989).CrossRefGoogle Scholar
15.Jiang, Z. P. and Mareels, M. Y., “A small-gain control method for nonlinear cascade systems with dynamic uncertainties,” IEEE Trans. Automat. Control 42 (3), 292–308 (1997).CrossRefGoogle Scholar
16.Khalil, H., Nonlinear Systems, 3rd ed. (Prentice Hall, New Jersey, USA, 2002).Google Scholar
17.Jiang, Z. P., Mareels, M. Y. and Wang, Y., “A lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems,” Automatica 32 (8), 1211–1215 (1996).CrossRefGoogle Scholar
18.Sontag, E. and Wang, Y., “On characterizations of the input-to-state stability property,” Syst. Control Lett. 24 (5), 351–359 (1995).CrossRefGoogle Scholar
19.Sciavicco, L. and Siciliano, B., Modeling and Control of Robot Manipulator (Springer-Verlag, London, UK, 2000).CrossRefGoogle Scholar
20.Santibañez, V. and Kelly, R., “PD control with feedforward compensation for robot manipulators: analysis and experimentation,” Robotica 19, 11–19 (2001).CrossRefGoogle Scholar
21.Angeli, D., “Input-output-to-state stability of pd-controlled robotic systems,” Automatica 35, 1285–1290 (1999).CrossRefGoogle Scholar
22.Koditscheck, D., “Application of a New Lyapunov Function to Global Adaptive Attitude Tracking,” Proceedings of IEEE Conference on Decision and Control, Austin, TX (1988).Google Scholar
23.Tomei, P., “Adaptive PD controller for robot manipulators,” IEEE Trans. Rob. Automat. 7 (4), 565–570 (1991).CrossRefGoogle Scholar
24.Kelly, R., “Comments on ‘adaptive PD controller for robot maqipulators’,” IEEE Trans. Rob. Automat. 9 (1), 117–119 (1993).CrossRefGoogle Scholar
25.Arimoto, S., “Fundamental problems of robot control. Part I. Innovations in the realm of robot servo-loops,” Robotica 13, 19–27 (1995).CrossRefGoogle Scholar
26.Arimoto, S., “Fundamental problems of robot control. Part II. A nonlinear circuit theory towards an understanding of dexterous motions,” Robotica 13, 111–122 (1995).CrossRefGoogle Scholar
27.Jiang, Z. P., Teel, A. R. and Praly, L., “Small-gain theorem for ISS systems and applications,” Math. Control Signals Syst. 7, 95–120 (1994).CrossRefGoogle Scholar
28.Reyes, F. and Kelly, R., “Experimental evaluation of identification schemes on a direct drive robot,” Robotica 15, 563–571 (1997).CrossRefGoogle Scholar
29.Fossen, T. I., Guidance and Control of Ocean Vehicles (John Wiley, Chichester, UK, 1994).Google Scholar
30.Aamo, O., Arcak, M., Fossen, T.-I. and Kokotović, P., “Global output tracking control of a class of Euler–Lagrange systems with monotonic nonlinearities in the velocities,” Int. J. Control 74 (7), 649–658 (2001).CrossRefGoogle Scholar
31.Nunes, E. V. L., Hsu, L. and Lizarralde, F., “Output-Feedback Sliding Mode Control for Global Asymptotic Tracking of Uncertain Systems Using Locally Exact Differentiators,” Proceedings of American Control Conference, Minneapolis, MN (2006) pp. 5407–5412.Google Scholar
32.Oliveira, T. R., Peixoto, A. J., Nunes, E. V. L. and Hsu, L., “Control of uncertain nonlinear systems with arbitrary relative degree and unknown control direction using sliding modes,” Int. J. Adaptive Control Signal Processing 21 (8/9), 692–707 (2007).CrossRefGoogle Scholar
33.Nunes, E. V. L., Hsu, L. and Lizarralde, F., “Global Output Feedback Tracking Controller Based on Hybrid Estimation for a Class of Uncertain Nonlinear Systems,” Proceedings of 10th International Workshop on Variable Structure Systems, Antalya, Turkey (2008) pp. 141–146.Google Scholar
34.Abraham, R., Marsden, J. E. and Ratiu, T., Manifolds, Tensor Analysis, and Applications, 2nd ed., Applied Mathematical Sciences, vol. 75 (Springer-Verlag, New York, USA, 1988).CrossRefGoogle Scholar