Real-time trajectory generation for differentially flat systems

International Journal of Robust and Nonlinear Control

Volumn 8, Issue 11, 1998, Pages 995-1020

  Van Nieuwstadt, Michiel J ^a   Murray, Richard M ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Flatness; Flight control; Trajectory generation

Indexed keywords

ALGORITHMS; CONTROL SYSTEM ANALYSIS; DEGREES OF FREEDOM (MECHANICS); LINEARIZATION; MOTION CONTROL; STATE SPACE METHODS; SYSTEM STABILITY; TRACKING (POSITION); TRAJECTORIES;

DIFFERENTIALLY FLAT SYSTEMS; TRAJECTORY GENERATION;

NONLINEAR CONTROL SYSTEMS;

EID: 0032163450     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1239(199809)8:11<995::AID-RNC373>3.0.CO;2-W     Document Type: Article

References (48)

1. Shamma, J. S., 'Robust stability with time-varying structured uncertainty', IEEE Trans. Automat. Control, 39(4), 714-724 (1994).
2. Packard, A., 'Gain scheduling via linear fractional transformations', Systems Control Lett., 22(2), 79-92 (1994).
3. Hunt, L. R., R. Su and G. Meyer, 'Global transformations of nonlinear systems', IEEE Trans. Automat. Control, AC-28(1), 24-31 (1983).
4. Jakubczyk, B. and W. Respondek, 'On linearization of control systems', Bull. Acad. Polonaise des Sci. Sér. des Sci. Math., XXVIII, 517-522 (1980).
5. Isidori, A. and C. I. Byrnes, 'Output regulation of nonlinear systems', IEEE Trans. Automat. Control, 35(2), 131-140 (1990).
6. Chen, D. G. and B. Paden, 'Stable inversion of nonlinear nonminimum-phase systems', Int. J. Control, 64(1), 81-97 (1996).
7. Devasia, S. and B. Paden, 'Exact output tracking for nonlinear time-varying systems', Proc. IEEE Control and Decision Conf., 1994, pp. 2346-2355.
8. Meyer, G., L. R. Hunt and R. Su, 'Nonlinear system guidance', Proc. IEEE Control and Decision Conf., 1995, pp. 590-595.
9. Getz, N. H. and K. Hedrick, 'An internal equilibrium manifold method of tracking for nonlinear nonminimum phase systems', in Proc. IEEE Control and Decision Conf., 1995, pp. 2241-2245.
10. Getz, N. H., Dynamic inversion of nonlinear maps with applications to nonlinear control and robotics, Ph.D. thesis, UC Berkeley, Berkeley, California, 1995.
11. Fliess, M., J. Lévine, Ph. Martin and P. Rouchon, 'Sur les systèmes non linéaires différentiellement plats', C. R. Acad. Sci. Paris t. 315, Série I, 619-624 (1992).
12. Fliess, M., J. Lévine, Ph. Martin and P. Rouchon, 'Linéarisation par bouclage dynamique et transformations de Lie-Bäcklund', C. R. Acad. Sci. Paris t. 317, Série I, 981-986 (1993).
13. Fliess, M., J. Levine, P. Martin and P. Rouchon, 'Flatness and defect of non-linear systems: introductory theory and examples', Int. J. Control, 61(6), 1327-1361 (1995).
14. Fliess, M., J. Lévine and P. Rouchon, 'Generalized state variable representation for a simplified crane description', Int. J. Control, 58(2), 277-283 (1993).
15. Rouchon, P., M. Fleiss, J. Lévine and P. Martin, 'Flatness, motion planning and trailer systems', Proc. IEEE Control and Decision Conf., 1993, pp. 2700-2705.
16. Rouchon, P., M. Fliess, J. Lévine and P. Martin, 'Flatness and motion planning: the car with n trailers', Proc. European Control Conf., 1992, pp. 1518-1522.
17. Martin, P., 'Aircraft control using flatness', in Multiconference on Computational Engineering in Systems Applications, pp. 194-199 (1996).
18. Martin, P., S. Devasia and B. Paden, 'A different look at output tracking - Control of a VTOL aircraft', Automatica, 32(1), 101-107 (1994).
19. Chelouah, K., E. Delaleu, P. Martin and P. Rouchon, 'Differential flatness and control of induction motors', Multiconference on Computational Engineering in Systems Applications, 1996, pp. 80-85.
20. Martin, P. and P. Rouchon, 'Flatness and sampling control of induction motors', in Workshop IF AC Symp., 1996.
21. Lévine, J., J. Lottin and J. C. Ponsart, 'A nonlinear approach to the control of magnetic bearings', IEEE Trans. Control Systems Technol., 5, 524-544 (1996).
22. Rothfuss, R., J. Rudolph and M. Zeitz, 'Flatness based control of a nonlinear chemical reactor model', Automatica, 32(10), 1433-1439 (1996).
23. Rouchon, P., 'Vibrational control and flatness of chemical reactors', in Multiconference on Computational Engineering in Systems Applications, 1996, pp. 211-212.
24. van Nieuwstadt, M., M. Rathinam and R. M. Murray, 'Differential flatness and absolute equivalence', Proc. IEEE Control and Decision Conf., 1994, pp. 326-333. Also available as Caltech Technical Report CIT/CDS 94-006.
25. van Nieuwstadt, M., M. Rathinam and R. M. Murray, 'Differential flatness and absolute equivalence', Proc. IEEE Control and Decision Conf., 1994, pp. 326-333. Also available as Caltech Technical Report CIT/CDS 94-006.
26. Isidori, A., Nonlinear Control Systems, 2nd edn, Springer, Berlin, 1989.
27. Nijmeijer, H. and A. van der Schaft, Nonlinear Dynamical Control Systems, Springer, Berlin, 1990.
28. Cartan, E., Sur l'equivalence absolue de certains systèmes d'équations différentielles et sur certaines familles de courbes'. Œuvres Complètes, Vol. II, Gauthier-Villars, 1953, pp. 1133-1168.
29. Cartan, E., 'Sur l'intégration de certains systèmes indéterminés d'équations différentielles', Œuvres Complètes, Vol. II, Gauthier-Villars, 1953, pp. 1169-1174.
30. Sluis, W. M., Absolute Equivalence and its Applications to Control Theory. Ph.D. thesis, University of Waterloo, Waterloo, Ontario, 1992.
31. Charlet, B., J. Lévine and R. Marino, 'On dynamic feedback linearization', Systems Control Lett., 13, 143-151 (1989).
32. Fliess, M., Lévine, J., P. Martin, F. Ollivier and P. Rouchen, 'Flatness dynamic feedback linearizability: two approaches', Proc. European Control Conf., 1995.
33. Martin, Ph., 'Endogenous feedbacks and equivalence", Mathematical Theory of Networks and Systems, Regensburg, Germany, 1993.
34. Bullo, F. and R. M. Murray, 'Experimental comparison of trajectory trackers for a car with trailers', IF AC World Conf., 1996, pp. 407-412.
35. van Nieuwstadt, M., Trajectory Generation for Nonlinear Control Systems. Ph.D. thesis, California Institute of Technology, 1996.
36. Martin, P. and P. Rouchon, 'Feedback linearization and driftless systems', Math. Control Signal Systems, 7, 235-254 (1994).
37. Martin, P. and P. Rouchon, 'Any (controllable) driftless system with 3 inputs and 5 states is flat', Systems Control Lett., 25, 167-173 (1995).
38. Murray, R. M., Trajectory generation for a towed cable system using differential flatness', IF AC World Conf., 1996, pp. 395-400.
39. Murray, R. M., M. Rathinam and W. Sluis, 'Differential flatness of mechanical control systems: a catalog of prototype systems', Asme IMECE, San Francisco, 1995.
40. M. Kantner, B. Bodenheimer, P. Bendotti and R. M. Murray, 'An experimental comparison of controllers for a vectored thrust, ducted fan engine', Proc. American Control Conf., 1995, pp. 1956.
41. van Nieuwstadt, M. and R. M. Murray, 'Approximate trajectory generation for differentially flat systems with zero dynamics', Proc. IEEE Control and Decision Conf., 1995, pp. 4224-4230.
42. Grizzle, J. W., M. D. Di Benedetto and F. Lamnabhi-Lagarrigue, 'Necessary conditions for asymptotic tracking in nonlinear systems', IEEE Trans. Automat. Control, 39(9), 1782-1795 (1994).
43. Khalil, H., Nonlinear Systems, Macmillan Publishing Company, New York, 1992.
44. Murray, R. M., E. L. Wemhorfand K. Kantner, Sparrow 2.1 Reference Manual. California Institute of Technology, 1995. Available electronically from http://avalon.caltech.edu/̃sparrow.
45. van Nieuwstadt, M. and R. M. Murray, 'Fast mode switching for a thrust vectored aircraft', Multiconf. on Computational Engineering in Systems Applications, Lille, France, 1996.
46. Rathinam, M. and R. Murray, 'Configuration flatness of lagrangian systems underactuated by one control', Proc. IEEE Control and Decision Conf., 1996, to appear.
47. Rathinam, M. and R. Murray, 'Flatness of nonlinear systems underactuated by two controls', Proc. European Control Conf., 1996, submitted.
48. Martin, Ph., Contribution à l'étude des systèmes differentiellement plats, Ph.D. thesis, L'Ecole Nationale Superieure des Mines de Paris, 1993.