Non-linear symmetry-preserving observers on lie groups

IEEE Transactions on Automatic Control

Volumn 54, Issue 7, 2009, Pages 1709-1713

  Bonnabel, Silvere ^a   Martin, Philippe ^a   Rouchon, Pierre ^a  

^a MINES ParisTech   (France)

Author keywords

Inertial navigation; Invariance; Lie group; Nonlinear asymptotic observer; Symmetry

Indexed keywords

ERROR EQUATION; ESTIMATED STATE; GLOBAL BEHAVIORS; INERTIAL NAVIGATION; INVARIANT SYSTEMS; LIE GROUP; NON-LINEAR; NONLINEAR ASYMPTOTIC OBSERVER; SYMMETRY; TECHNICAL NOTES;

ASYMPTOTIC ANALYSIS; INERTIAL NAVIGATION SYSTEMS; INVARIANCE; NAVIGATION;

OBSERVABILITY;

EID: 67949088083     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2009.2020646     Document Type: Article

References (18)

1. V. Arnold, Mathematical Methods of Classical Mechanics. Moscow, Russia: Mir, 1976.
2. S. Bonnabel, P. Martin, and P. Rouchon, "Symmetry-preserving observers," IEEE Trans. Automat. Control, vol. 53, no. 11, pp. 2514-2526, Dec. 2008.
3. S. Bonnabel, P. Martin, and P. Rouchon, "Groupe de lie et observateur non-linéaire," in Proc. CIFA 2006, Bordeaux, France, 2006.
4. S. Bonnabel, P. Martin, and P. Rouchon, Invariant Asymptotic Observers arXiv:mAth/0612193v1 math.OC, 2006.
5. S. Bonnabel, P. Martin, and P. Rouchon, "Non-linear observer on lie group for left-invariant dynamics with right-left equivariant output," in Proc. IFAC08, Seoul, Korea, 2008.
6. S. Bonnabel and P. Rouchon, "Invariant observers," in Control and Observer Design for Nonlinear Finite and Infinite Dimensional Systems New York: Springer, 2005, vol. 322, Lecture Notes in Control and Information Sciences, pp. 53-66.
7. F. Fagnani and J. Willems, "Representations of symmetric linear dynamical systems," SIAM J. Control and Optimiz., vol. 31, pp. 1267-1293, 1993.
8. J. W. Grizzle and S. I. Marcus, "The structure of nonlinear systems possessing symmetries," IEEE Trans. Automat. Control, vol. AC-30, no. 3, pp. 248-258, Mar. 1985.
9. T. Hamel and R. Mahony, "Attitude estimation on SO(3) based on direct inertial measurements," in Proc. Int. Conf. Robotics and Automation (ICRA), Orlando, FL, May 2006.
10. V. Jurdjevic and H. J. Sussmann, "Control systems on Lie groups," J. Differen. Equat., vol. 12, pp. 312-329, 1972.
11. W. S. Koon and J. E. Marsden, "Optimal control for holonomic and nonholonomic mechanical systems with symmetry and lagrangian reduction," SIAM J. Control and Optimiz., vol. 35, pp. 901-929, 1997.
12. R. Mahony, T. Hamel, and J.-M. Pflimlin, "Non-linear complementary filters on the special orthogonal group," IEEE Trans. Autom. Control vol. 53, no. 5, pp. 1203-1218, Jun. 2008.
13. R. Mahony, T. Hamel, and J.-M. Pflimlin, "Complementary filter design on the special orthogonal group SO(3)," in Proc. IEEE Conf. Decision and Control (CDC05), Seville, Spain, 2005.
14. P. Martin and E. Salaun, "Invariant observers for attitude and heading estimation from low-cost inertial and magnetic sensors," in Proc. 46th IEEE Conf. Decision and Control, pp. 1039-1045.
15. P. Martin and E. Salaun, "Design and implementation of a low-cost attitude and heading nonlinear estimator," in Proc. ICINCO 2008, Funchal, Portugal, May 2008, vol. 1, pp. 53-61.
16. P. Morin and C. Samson, "Practical stabilization of driftless systems on lie groups, the transverse function approach," IEEE Trans. Automat. Control, vol. 48, no. 9, pp. 1493-1508, Sep. 2003.
17. P. J. Olver, Classical Invariant Theory. Cambridge, U.K.: Cambridge Univ. Press, 1999.
18. W. Respondek and I. A. Tall, "Nonlinearizable single-input control systems do not admit stationary symmetries," Syst. Control Lett., vol. 46, pp. 1-16, 2002.