Lie algebra application to mobile robot control: A tutorial

Robotica

Volumn 21, Issue 5, 2003, Pages 483-493

  Coelho, Paulo ^a   Nunes, Urbano ^a  

^a UNIVERSITY OF COIMBRA   (Portugal)

Author keywords

Input output linearization; Lie algebra; Mobile robots; Nonlinear systems

Indexed keywords

CONTROL SYSTEM ANALYSIS; FEEDBACK CONTROL; LINEARIZATION; MATHEMATICAL MODELS; NONLINEAR CONTROL SYSTEMS;

INPUT OUTPUT LINEARIZATION; LIE ALGEBRA;

MOBILE ROBOTS;

EID: 0142211181     PISSN: 02635747     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0263574703005149     Document Type: Article

References (18)

1. R. Murray and S. Sastry, "Nonholonomic motion planning: steering using sinusoids," IEEE Trans. on Automatic Control, 38(5), 700-716 (May, 1993).
2. F. Lamiraux and J. P. Laumond, "Smooth motion planning for car-like vehicles," IEEE Trans. on Robotics and Automation, 17(4), 498-502 (August, 2001).
3. A. De Luca and G. Oriola, "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).
4. J. Hauser, S. Sastry and P. Kokotovic, "Nonlinear control via approximate input-output linearization: The ball and beam example," IEEE Trans. on Automatic Control, 37(3), 392-398 (March, 1992).
5. N. Jo and J. Seo, "Input output linearization approach to state observer design for nonlinear system," IEEE Trans. on Automatic Control, 45(12), 2388-2393 (December, 2000).
6. F. Doyle, F. Allgower and M. Morari, "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).
7. N. Sarkar, X. Yun and V. Kumar, "Control of mechanical systems with rolling constraints: Application to dynamic control of mobile robots," Int. J. Rob. Res., 13(1), 55-69 (1994).
8. F. Doyle and Hobgood, "Input-output linearization using approximate process models," Report (School of Chemical Engineering, Purdue University, February, 1995).
9. M. Hall, The Theory of Groups (New York: Macmillan, 1959).
10. V. S. Varadarajan, Lie Groups, Lie Adgebra, and their Representations (Springer-Verlag, New York, 1984).
11. A. Isidori, Nonlinear Control Systems, 2nd ed. (Springer-Verlag, Berlin, 1989).
12. H. Nijmeijer and A. Schaft, Nonlinear Dynamic Control Systems (Springer-Verlag, New York, 1990).
13. H. Khalill, Nonlinear Systems, 3rd ed. (Prentice-Hall, 2002).
14. X. Yun, V. Kumar, N. Sarkar and E. Paljug, "Control of multiple arms with rolling constraints," Proc. of Int. Conf. on Robotics and Automation, pp. 2193-2198 (Nice, France, May, 1992).
15. G. Campion, B. d'Andrea-Novel and G. Bastin, "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).
16. A. de Luca and G. Oriola, "Modelling and control of nonholonomic mechanical systems." In: Kinematic and Dynamics of Multi-Body Systems pp. 277-342 (J. Angeles & A. Kecskemethy, Eds.), (Springer-Verlag, Wien, 1995).
17. J. J. Slotine and W. Li, Applied Nonlinear Control (Prentice Hall, Inc. Englewood Cliffs, New Jersey, 1991).
18. P. Coelho, "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)).