Skip to main content Accessibility help
×
Home
Hostname: page-component-684bc48f8b-kl86h Total loading time: 3.192 Render date: 2021-04-11T09:44:39.008Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

Article contents

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
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
E-mail address:

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.

Type
Article
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below.

References

1.Ailon, A. and Ortega, R., “An observer-based controller for robot manipulators with flexible joints,” Syst. Control Lett. 21, 329335 (1993).CrossRefGoogle Scholar
2.Berghuis, H. and Nijmeijer, H., “Global regulation of robots using only position measurements,” Syst. Control Lett. 21, 289293 (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, 144151 (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), 12031208 (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), 7492 (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), 841847 (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, 10851093 (2003).CrossRefGoogle Scholar
11.Dixon, W. E., Zergeroglu, E. and Dawson, D. M., “Global robust output feedback tracking control of robot manipulators,” Robotica 22, 351357 (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), 435443 (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), 292308 (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), 12111215 (1996).CrossRefGoogle Scholar
18.Sontag, E. and Wang, Y., “On characterizations of the input-to-state stability property,” Syst. Control Lett. 24 (5), 351359 (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, 1119 (2001).CrossRefGoogle Scholar
21.Angeli, D., “Input-output-to-state stability of pd-controlled robotic systems,” Automatica 35, 12851290 (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), 565570 (1991).CrossRefGoogle Scholar
24.Kelly, R., “Comments on ‘adaptive PD controller for robot maqipulators’,” IEEE Trans. Rob. Automat. 9 (1), 117119 (1993).CrossRefGoogle Scholar
25.Arimoto, S., “Fundamental problems of robot control. Part I. Innovations in the realm of robot servo-loops,” Robotica 13, 1927 (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, 111122 (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, 95120 (1994).CrossRefGoogle Scholar
28.Reyes, F. and Kelly, R., “Experimental evaluation of identification schemes on a direct drive robot,” Robotica 15, 563571 (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), 649658 (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), 692707 (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

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 103 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 11th April 2021. This data will be updated every 24 hours.

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

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

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

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

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

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

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *