Configuration flatness of lagrangian systems underactuated by one control

SIAM Journal on Control and Optimization

Volumn 36, Issue 1, 1998, Pages 164-179

  Rathinam, Muruhan ^a   Murray, Richard M ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Differential flatness; Lagrangian mechanics; Nonlinear control

Indexed keywords

COMPUTATIONAL GEOMETRY; DEGREES OF FREEDOM (MECHANICS); LAGRANGE MULTIPLIERS; NONLINEAR CONTROL SYSTEMS;

DIFFERENTIAL FLATNESS; LAGRANGIAN CONTROL SYSTEMS; RIEMANNIAN GEOMETRY;

CONTROL SYSTEM ANALYSIS;

EID: 0031646784     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012996300987     Document Type: Article

References (21)

1. R. ABRAHAM AND J. MARSDEN, Foundations of Mechanics, 2nd ed., Addison-Wesley, Reading, MA, 1985.
2. B. CHARLET, J. LÉVINE, AND R. MARINO, On dynamic feedback linearization, Systems Control Lett., 13 (1989), pp. 143-151.
3. M. FLIESS, J. LÉVINE, P. MARTIN, AND P. ROUCHON, Flatness and defect of nonlinear systems: Introductory theory and examples, Internat. J. Control, 61 (1995), pp. 1327-1361.
4. M. FLIESS, J. LEVINE, P. MARTIN, AND P. ROUCHON, Linéarisation par bouclage dynamique et transformations de Lie-Bäcklund, C. R. Acad. Sci. Paris Sèr. I Math., 317 (1993), pp. 981-986.
5. S. KOBAYASHI AND K. NOMIZU, Foundations of Differential Geometry, Vol. 1, Interscience Publishers, New York, 1963.
6. H. LAMB, Hydrodynamics, Dover Publications, New York, 1945.
7. N. LEONARD, Compensation for actuator failures: Dynamics and control of underactuated underwater vehicles, in Proceedings of the 9th International Symposium on Unmanned Untethered Submersible Technology, Durham, NH, 1995; Autonomous Undersea Systems Institute, Lee, NH.
8. A. D. LEWIS AND R. M. MURRAY, Configuration controllability of simple mechanical control systems, SIAM J. Control Optim., 35 (1997), pp. 766-790.
9. P. MARTIN, Contribution à l'étude des systèmes differentiellement plats, Ph.D. thesis, École des Mines de Paris, 1992.
10. P. MARTIN, S. DEVASIA, AND B. PADEN, A different look at output tracking: Control of a vtol aircraft, Automatica, 32 (1996), pp. 101-107.
11. R. MURRAY, M. RATHINAM, AND W. SLUIS, Differential flatness of mechanical control systems, in Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, San Francisco, 1995.
12. J.-B. POMET, A differential geometric setting for dynamic equivalence and dynamic linearization, in Geometry in Nonlinear Control and Differential Inclusions, B. Jakubczyk, W. Respondek, and T. Rzeżuchowski, eds., Warsaw, Banach Center Publications, 1995, pp. 319-339.
13. M. RATHINAM AND W. SLUIS, A test for differential flatness by reduction to single input systems, in Proceedings of IFAC 96, Vol. E, 1996, pp. 257-262; Technical Memorandum CIT-CDS 95-018, California Institute of Technology, Pasadena, CA 91125, 1995.
14. P. ROUCHON, M. FLIESS, J. LEVINE, AND P. MARTIN, Flatness, motion planning and trailer systems, in Proceedings of the IEEE Conference on Decision and Control, San Antonio, 1993.
15. D. SAUNDERS, The Geometry of Jet Bundles, Cambridge University Press, London, 1989.
16. W. SHADWICK, Absolute equivalence and dynamic feedback linearization, Systems Control Lett., 15 (1990), pp. 35-39.
17. W. SLUIS, Absolute Equivalence and Its Applications to Control Theory, Ph.D. thesis, University of Waterloo, Waterloo, Canada, 1993.
18. W. M. SLUIS AND D. TILBURY, A Bound on the Number of Integrators Needed to Linearize a Control System, Systems Control Lett., 29 (1996), pp. 43-50.
19. D. TILBURY, R. M. MURRAY, AND S. S. SASTRY, Trajectory generation for the N-trailer problem using Goursat normal form, IEEE Trans. Automat. Control, 40 (1995), pp. 802-819.
20. M. VAN NIEUWSTADT AND R. MURRAY, Approximate trajectory generation for differentially flat systems with zero dynamics, in Proceedings of the 34th IEEE Conference on Control and Decision, New Orleans, LA, December 1995, pp. 4224-4230.
21. M. VAN NIEUWSTADT, M. RATHINAM, AND R. MURRAY, Differential flatness and absolute equivalence, in Proceedings IEEE Conference on Control and Decision, Lake Buena Vista, FL, 1994, pp. 326-332.