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Lie algebra application to mobile robot control: a tutorial

Published online by Cambridge University Press:  02 March 2021

Paulo Coelho  and
Urbano Nunes
Paulo Coelho*
Affiliation:
Institute of Systems and Robotics (ISR), Department of Electrical and Computer Engineering, University of Coimbra, Polo II, 3030-290Coimbra (Portugal)
Urbano Nunes*
Affiliation:
Institute of Systems and Robotics (ISR), Department of Electrical and Computer Engineering, University of Coimbra, Polo II, 3030-290Coimbra (Portugal)
*
Email: [email protected]
Email: [email protected]
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Summary

Lie algebra is an area of mathematics that is largely used by electrical engineer students, mainly at post-graduation level in the control area. The purpose of this paper is to illustrate the use of Lie algebra to control nonlinear systems, essentially in the framework of mobile robot control. The study of path following control of a mobile robot using an input-output feedback linearization controller is performed. The effectiveness of the nonlinear controller is illustrated with simulation examples.

Keywords

Lie algebraInput-output linearizationNonlinear systemsMobile robots
Type
Research Article
Information
Robotica , Volume 21 , Issue 5 , October 2003 , pp. 483 - 493
Copyright
Copyright © Cambridge University Press 2003

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References

1. Murray, R. and Sastry, S., “Nonholonomic motion planning: steering using sinusoids,” IEEE Trans. on Automatic Control, 38(5), 700–716 (May, 1993).CrossRefGoogle Scholar
2. Lamiraux, F. and Laumond, J.P., “Smooth motion planning for car-like vehicles,” IEEE Trans. on Robotics and Automation, 17(4), 498–502 (August, 2001).CrossRefGoogle Scholar
3. De Luca, A. and Oriolo, G., “Feedback control of a nonholonomic car-like robot.” In: Robot Motion Planning and Control J.-P. Laumond, Ed.), pp. 171–253 (Springer-Verlag, London, 1998).CrossRefGoogle Scholar
4. Hauser, J., Sastry, S. and Kokotovic, P., “Nonlinear control via approximate input-output linearization: The ball and beam example,” IEEE Trans. on Automatic Control, 37(3), 392–398 (March, 1992).CrossRefGoogle Scholar
5. Jo, N. and Seo, J., “Input output linearization approach to state observer design for nonlinear system,” IEEE Trans. on Automatic Control, 45(12), 2388–2393 (December, 2000).CrossRefGoogle Scholar
6. Doyle, F., Allgower, F. and Morari, M., “A normal form approach to approximate input-output linearization for maximum phase nonlinear SISO systems,” IEEE Trans. on Automatic Control, 41(2), 305–309 (February, 1996).CrossRefGoogle Scholar
7. Sarkar, N., Yun, X. and Kumar, V., “Control of mechanical systems with rolling constraints: Application to dynamic control of mobile robots,” Int. J. Rob. Res., 13(1), 55–69 (1994).CrossRefGoogle Scholar
8. Doyle, F. and Hobgood, “Input-output linearization using approximate process models,” Report (School of Chemical Engineering, Purdue University, February, 1995).CrossRefGoogle Scholar
9. Hall, M., The Theory of Groups (New York: Macmillan, 1959).Google Scholar
10. Varadarajan, V.S., Lie Groups, Lie Adgebra, and their Representations (Springer-Verlag, New York, 1984).CrossRefGoogle Scholar
11. Isidori, A., Nonlinear Control Systems, 2nd ed. (Springer-Verlag, Berlin, 1989).CrossRefGoogle Scholar
12. Nijmeijer, H. and Schaft, A., Nonlinear Dynamic Control Systems (Springer-Verlag, New York, 1990).CrossRefGoogle Scholar
13. Khalill, H., Nonlinear Systems, 3rd ed. (Prentice-Hall, 2002).Google Scholar
14. Yun, X., Kumar, V., Sarkar, N. and Paljug, E., “Control of multiple arms with rolling constraints,” Proc. of Int. Conf. on Robotics and Automation, pp. 2193–2198 (Nice, France, May, 1992).Google Scholar
15. Campion, G., d’Andrea-Novel, B. and Bastin, G., “Controllability and state feedback stabilization of nonholonomic mechanical systems.” In: Lecture Notes in Control and Information Science (C. Canudas de Wit, Ed.), 162, pp. 106–124 (Springer-Verlag, 1991).CrossRefGoogle Scholar
16. de Luca, A. and Oriolo, G., “Modelling and control of nonholonomic mechanical systems.” In: Kinematic and Dynamics of Multi-Body Systems (J. Angeles & A. Kecskemethy, Eds.), pp. 277–342 (Springer-Verlag, Wien, 1995).CrossRefGoogle Scholar
17. Slotine, J.J. and Li, W., Applied Nonlinear Control (Prentice Hall, Inc., Englewood Cliffs, New Jersey, 1991).Google Scholar
18. Coelho, P., “Lagrangians application in dynamic of wheeled mobile robots,” Tech. Report, No. ISR-LCIR-2001/01 (Institute of Systems and Robotics, University of Coimbra, Portugal, 2001 (in Portuguese)).Google Scholar