Trajectory tracking for fully actuated mechanical systems

ECC 1997 - European Control Conference

Volumn , Issue , 1997, Pages 2780-2785

  Bullo, Francesco ^a   Murray, Richard M ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Lie groups; Mechanical systems; Nonlinear control; Riemannian geometry

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); GEOMETRY; LIE GROUPS;

FEED-FORWARD CONTROLLERS; FULLY ACTUATED MECHANICAL SYSTEM; LAGRANGIAN SYSTEM; MECHANICAL SYSTEMS; NON LINEAR CONTROL; PROPORTIONAL DERIVATIVES; RIEMANNIAN GEOMETRY; TRAJECTORY TRACKING;

MACHINE DESIGN;

EID: 84949090582     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.23919/ecc.1997.7082530     Document Type: Conference Paper

References (18)

1. A. M. Bloch and P. E. Crouch. Nonholonomic control systems on Riemannian manifolds. SIAM Journal of Control and Optimization, 33(1):126-148, January 1995.
2. W. M. Boothby. An Introduction to Differentiable Manifolds and Riemannian Geometry. Academic Press, New York, second edition, 1986.
3. F. Bullo and R. M. Murray. Tracking for fully actuated mechanical systems: a geometric framework. Technical Report Caltech/CDS 97-001, California Institute of Technology, January 1997. Modified version submitted to Automatica. Available electronically via http://www.cds.caltech.edu.
4. M. P. Do Carmo. Riemannian Geometry. Birkhauser, Boston, 1992.
5. T. I. Fossen. Guidance and Control of Ocean Vehicles. John Wiley and Sons, New York, NY, 1994.
6. D. E. Koditschek. The application of total energy as a Lyapunov function for mechanical control systems. In J. E. Marsden, P. S. Krishnaprasad, and J. C. Simo, editors, Dynamics and Control of Multibody Systems, volume 97, pages 131-157. AMS, 1989.
7. A. D. Lewis and R. M. Murray. Controllability of simple mechanical control systems. SIAM Journal of Control and Optimization, 35(3), May 1997.
8. J. E. Marsden and T. S. Ratiu. Introduction to Mechanics and Symmetry. Springer Verlag, New York, NY, 1994.
9. G. Meyer. Design and global analysis of spacecraft attitude control systems. Technical report, NASA, March 1971. Tech. Report R-361.
10. R. M. Murray. Nonlinear control of mechanical systems: a Lagrangian perspective. In IFAC Symposium on Nonlinear Control Systems (NOLCOS), pages 378-389, Lake Tahoe, CA, June 1995.
11. R. M. Murray, Z. X. Li, and S. S. Sastry. A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton, Florida, 1994.
12. H. Nijmeijer and A. Van Der Schaft. Nonlinear Dynamical Control Systems. Springer Verlag, New York, NY, 1990.
13. B. Paden and R. Panja. Globally asymptotically stable 'PD+' controller for robot manipulators. International Journal of Control, 47(6):1697-1712, 1988.
14. M. Rathinam and R. M. Murray. Configuration flatness of Lagrangian systems underactuated by one control. SIAM Journal of Control and Optimization, 1996. To appear.
15. J. C. Simo, D. R. Lewis, and J. E. Marsden. Stability of relative equilibria I: The reduced energy momentum method. Archive for Rational Mechanics and Analysis, 115:15-59, 1991.
16. M. Takegaki and S. Arimoto. A new feedback method for dynamic control of manipulators. Journal of Dynamic Systems, Measurement, and Control, 102:119-125, June 1981.
17. J. T.-Y. Wen and D. S. Bayard. A new class of control laws for robotic manipulators. Part I: Non-adaptive case. International Journal of Control, 47(5):1361-1385, 1988.
18. J. T.-Y. Wen and K. Kreutz-Delgado. The attitude control problem. IEEE Transactions on Automatic Control, AC-36:1148-1162, October 1991.