A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon

Systems and Control Letters

Volumn 39, Issue 1, 2000, Pages 63-70

  Bhat, Sanjay P ^a   Bernstein, Dennis S ^b  

^a INDIAN INSTITUTE OF TECHNOLOGY BOMBAY   (India)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Attitude control; Dynamical systems; Global stability; Rotational motion; Unwinding

Indexed keywords

EID: 0346676588     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6911(99)00090-0     Document Type: Article

References (28)

1. J. Ahmed, D.S. Bernstein, Adaptive control of a dual-axis CMG with an unbalanced rotor, in: Proceedings of the 37th Conference on Decision and Control, IEEE, Tampa, FL, December 1998, pp. 4531-4536.
2. V.I. Arnold, Mathematical Methods of Classical Mechanics, 2nd ed., Springer, New York, 1989.
3. D.S. Bernstein (Ed.), Special issue on a nonlinear benchmark problem, Int. J. Robust Nonlinear Control 8(4/5) (1998).
4. N.P. Bhatia, O. Hajek, Local Semi-Dynamical Systems, Lecture Notes in Mathematics, vol. 90, Springer, Berlin, 1969.
5. N.P. Bhatia, G.P. Szegö, Stability Theory of Dynamical Systems, Springer, Berlin, 1970.
6. A.M. Bloch, P.S. Krishnaprasad, J.E. Marsden, G. Sanchez de Alvarez, Stabilization of rigid body dynamics by internal and external torques, Automatica 28 (4) (1992) 745-756.
7. A.E. Bryson Jr., Control of Spacecraft and Aircraft, Princeton University Press, Princeton, NJ, 1994.
8. R.T. Bupp, D.S. Bernstein, V.T. Coppola, A benchmark problem for nonlinear control design, Int. J. Robust Nonlinear Control 8 (1998) 307-310.
9. R.T. Bupp, D.S. Bernstein, V.T. Coppola, Experimental implementation of integrator backstepping and passive nonlinear controllers on the RTAC testbed, Int. J. Robust Nonlinear Control 8 (1998) 435-457.
10. M.L. Curtis, Matrix Groups, 2nd ed., Springer, New York, 1984.
11. B.A. Dubrovin, A.T. Fomenko, S.P. Novikov, Modern Geometry - Methods and Applications, Part II, Graduate Texts in Mathematics, Springer, New York, 1985.
12. V. Guillemin, A. Pollack, Differential Topology, Prentice-Hall, Englewood Cliffs, NJ, 1974.
13. J.K. Hale, Ordinary Differential Equations, 2nd ed., Pure and Applied Mathematics, vol. XXI, Krieger, Malabar, FL, 1980.
14. M. Jankovic, D. Fontaine, P.V. Kokotovic, Tora example: Cascade- and passivity-based control designs, IEEE Trans. Control Systems Technol. 4 (3) (1996) 292-297.
15. S.M. Joshi, A.G. Kelkar, J.T.-Y. Wen, Robust attitude stabilization of spacecraft using nonlinear quaternion feedback, IEEE Trans. Automat. Control 40 (10) (1995) 1800-1803.
16. T.R. Kane, P.W. Likins, D.A. Levinson, Spacecraft Dynamics, McGraw-Hill, New York, 1983.
17. D.E. Koditschek, Application of a new Lyapunov function to global adaptive tracking, in: Proceedings of the 27th Conference on Decision and Control, IEEE, Austin, Texas, December 1988, pp. 63-68.
18. K.-Y. Lum, D.S. Bernstein, V.T. Coppola, Global stabilization of the spinning top with mass imbalance, Dyn. Stability Systems 10 (4) (1995) 339-365.
19. J.E. Marsden, J. Scheurle, Lagrangian reduction and the double spherical pendulum, Z. Angew. Math. Phys. 44 (1) (1993) 17-43.
20. R.E. Mortenson, A globally stable linear attitude regulator, Int. J. Control 8 (3) (1968) 297-302.
21. S.V. Salehi, E.P. Ryan, A non-linear feedback attitude regulator, Int. J. Control 41 (1) (1985) 281-287.
22. N. Sreenath, Nonlinear control of planar multibody systems in shape space, Math. Control Signals Systems 5 (1992) 343-363.
23. C.-J. Wan, D.S. Bernstein, V.T. Coppola, Global stabilization of the oscillating eccentric rotor, Nonlinear Dyn. 10 (1996) 49-62.
24. C.-J. Wan, V.T. Coppola, D.S. Bernstein, Global asymptotic stabilization of the spinning top, Opt. Control Appl. Methods 16 (1995) 189-215.
25. C.-J. Wan, P. Tsiotras, V.T. Coppola, D.S. Bernstein, Global asymptotic stabilization of a spinning top with torque actuators using stereographic projection, Dyn. Control 7 (1997) 215-233.
26. J.T.-Y. Wen, K. Kreutz-Delgado, The attitude control problem, IEEE Trans. Automat. Control 36 (10) (1991) 1148-1162.
27. B. Wie, P.M. Barba, Quaternion feedback for spacecraft large angle maneuvers, J. Guidance Control Dyn. 8 (3) (1985) 360-365.
28. B. Wie, H. Weiss, A. Arapostathis, Quaternion feedback regulator for spacecraft eigenaxis rotations, J. Guidance Control 12 (3) (1989) 375-380.