Singularity computation for iterative control of nonlinear affine systems

Asian Journal of Control

Volumn 2, Issue 2, 2000, Pages 57-75

  Popa, Dan O ^a   Wen, John T ^a  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

Author keywords

Affine system; Gradient algorithm; Nonholonomic system; Nonlinear control; Path planning; Singular control

Indexed keywords

EID: 0010108131     PISSN: 15618625     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1934-6093.2000.tb00146.x     Document Type: Article

References (37)

1. Bloch, A.M, et. al., "Control and Stabilization of Nonholonomic Dynamic Systems," in IEEE/RSJ Int. Workshop Intell. Rob. Syst., Osaka, Japank, pp. 1248-1253(1991).
2. Bröckelt, R.W., "Asymptotic Stability and Feedback Stabilization," in Differential Geometric Control Theory, Birkhauser, Boston, pp. 181-208 (1983).
3. Chelouach, A. and M. Petitot, "Finitely Discretizable Systems: Concepts and Definitions," in Proc. 34th IEEE Conf. Decis. Contr., New Orleans, LA, pp. 19-24, (1995).
4. Chitour, Y., "Applied and Theoretical Aspects of the Controllability of Nonholonomic Systems," Ph.D. Thesis, Rutgers University (1996).
5. Chow, W.L, Über Systeme von Linearen Partiellen Differentialgleichungen Ester Ordnung, in Math. Ann., pp. 117,98-105(1939).
6. D'Angelo, H., Linear Time-Varying Systems, Allyn and Bacon, Boston (1970).
7. Divelbiss, A. and J.T. Wen, Nonholonomic Path Planning with Inequality Constraints, in Proc. 32nd IEEE Conf. Decis. Contr., San Antonio, TX, pp. 2712-2717 (1993).
8. Divelbiss, A. and J. Wen, "A Global Approach to nonholonomic Motion planning," in Proc. IEEE Conf. Decis. Co/r.,Tucson, Arizona, pp. 1597-1602(1992).
9. Divelbiss, A. and J. Wen, "Nonholonomic Motion Planning with Inequality Constraints," in Proc. IEEE Int. Conf. Rob. Aiitom., San Diego, CA (1994).
10. Divelbiss, A., "Nonholonomic Motion Planning in the Presence of Obstacles," Ph.D. Thesis, Rensselaer Polytechnic Institute (1993).
11. Rouchon, P. and M. Fliess et. al., "Flatness, Motion Planning and the Trailer System," in Proc. 32nd IEEE Conf. Decis. Contr., San Antonio, Texas, pp. 2700-2705 (1993).
12. Goldstein, H., Classical mechanics, 2nd/Ed.,Addison-Wesley, Reading, MA (1980)
13. Lafferriere, G. and H.J. Sussmann, "Motion Planning for Controllable Systems Without Drift," in IEEE R&A Workshop Nonholonomic Motion Planning, Sacramento, CA ( 1991).
14. Isidori, A., Nonlinear Control Systems, Springer-Verlag (1989).
15. Jean, F., "The Singular Locus for the TV-trailers Car Control System," in Proc. 34th Conf. Decis. Contr.., New Orleans, LA, pp. 3869-3870 (1995).
16. Kawski, M., "High-Order Small-Time Local Controllability," in Nonlinear Controllability and Optimal Control, Ed. H.J. Sussmann and Marcel Dekker(1990).
17. Lizarralde, F., J.T. Wen and D.O. Popa, "Feedback Stabilization of Nonholonomic Systems," in Proc. Conf. Inform. Sei. Syst., Princeton, New Jersey (1996).
18. Neimark, J.I. and N.A. Fufaev, Dynamics of Nonholonomic Systems, American Mathematical Society (1972).
19. Popa, D. and J. Wen, "Nonholonomic Path-Planning with Obstacle Avoidance: A Path-Space Approach," Proc. Int. Conf. Adv. Rob. Conf., Minneapolis, MN, pp. 2262-2267 (1995).
20. Popa, D., and J. Wen, "Characterization of Singular Controls for Nonholonomic Path Planning," Proc. IFAC World Congr., San Francisco, CA, Vol. F, pp. 61-67(1996).
21. Popa, D., "Path Planning and Feedback Stabilization of Nonholonomic Control Systems," Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, Ny (1998).
22. Murray, R., "Nilpotent Bases for a Class of NonIntegrable Distributions with Applications to Trajectory Generation of Nonholonomic Systems," Mathematics of Control, Signals and Systems : MCSS (1994).
23. Tibury, D.M., "Exterior Differential Systems and Nonholonomic Motion Planning," Memo. No. UCB/ ERL M94/90, U.C. Berkeley (1994).
24. M'Closkey, R.T. and R. Murray, "Convergence Rates for Nonholonomic Systems in Power Form," in Proc. Amer. Contr. Conf., San Francisco, CA (1993).
25. Murray, R.M. and S., Sastry, "Steering Nonholonomic Systems Using Sinusoids," in Proc. IEEE Conf. Decis. Contr., Honolulu, Hi, pp. 2097-2101 (1990).
26. Murray, R., Z. Li and S. Sastry, A mathematical Introduction to Robotic manipulation, CRC press (1993).
27. Sontag, E.D., "Control of Systems Without Drift via Generic Loops," in IEEE Trans. Automat. Contr., Vol. 40, No. 7, pp. 1210-1219 (1995).
28. Sontag, E.D., "Integrability of Certain Distributions associated to Actions on Manifolds and an Introduction to Lie-Algebraic Control," in Nonlinear Controllability and Optimal Control, Eds. H.J. Sussmann and Marcel Dekker (1990).
29. Sontag, E.D., Mathematical Control Theory: Deter-ministic Finite Dimensional Systems, Springer, New York (1990).
30. Spong, M.V.,-"Energy Based Control of a Class of Underactuated Mechanical Systems," in Proc. 13th IFAC World Congr., San Francisco, 1996, pp. 531-435.
31. Spong, M.V. and M. Vidyasagar, Robot Dynamics and Control, John Wiley & Sons, New York (1989).
32. Liu, \V. and H.J. Sussmann, "Abnormal sub-Riemannian Minimizers," (1992).
33. Sussmann, H.J., "A Continuation Method for Nonholonomic Path-Finding Problem," in Proc. 32nd IEEE Conf. Decis. Contr., San Antonio, TX, pp. 2718-2723 (1993).
34. Sussmann, H.J. and Y. Chitour, "A Continuation method for Nonholonomic Path Finding problem," Proc. IM A Workshop Rob. (1993).
35. Sussmann, H.J. and Y. Chitour, "Motion Planning for a Model of a Front-Wheel Driven car Using a Continuation method," Rutgers University Report (1995).
36. Varsan, C., "On Decomposition and Integral Representation of Solutions for Affine Control Systems," in Syst. & Contr. Lett., Vol. 22, pp. 53-59 (1994).
37. Canudas de Wit, C. and O. Sordalen, "Exponential Stabilization of Mobile robots with Nonholonomic Constraints," in IEEE Trans. Automat. Contr., Vol. 37, No. 11, pp. 1791-1797 (1992).