Skip to main content
    • Aa
    • Aa

Is it worth learning differential geometric methods for modeling and control of mechanical systems?

  • Andrew D. Lewis (a1)

Evidence is presented to indicate that the answer is, “Yes, sometimes.”

Corresponding author
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1.H. Arai , K. Tanie and N. Shiroma , “Nonholonomic control of a three-DOF planar underactuated manipulator,” IEEE Trans. Robotics Autom. 14 (5), 681695 (1998).

2.D. R. Auckly and L. V. Kapitanski , “On the λ-equations for matching control laws,” SIAM J. Control Optim. 41 (5), 13721388 (2002).

3.S. P. Bhat and D. S. Bernstein , “A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon,” Syst. Control Lett. 39, 6370 (2000).

4.A. M. Bloch , Nonholonomic Mechanics and Control of Interdisciplinary Applied Mathematics 24 (Springer-Verlag, New York-Heidelberg-Berlin, 2003).

5.A. M. Bloch , N. E. Leonard and J. E. Marsden , “Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem,” IEEE Trans. Autom. Control 45 (12), 22532270 (2000).

6.A. M. Bloch , D. E. Chang , N. E. Leonard and J. E. Marsden , “Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping,” IEEE Trans. Autom. Control 46 (10), 15561571 (2001).

7.F. Bullo and A. D. Lewis , “Kinematic controllability and motion planning for the snakeboard,” IEEE Trans. Robot. Autom. 19 (3), 494498 (2003).

8.F. Bullo and A. D. Lewis , “Low-order controllability and kinematic reductions for affine connection control systems,” SIAM J. Control Optim. 44 (3), 885908 (2005).

10.F. Bullo and K. M. Lynch , “Kinematic controllability and decoupled trajectory planning for underactuated mechanical systems,” IEEE Trans. Robot. Autom. 17 (4), 402412 (2001).

11.F. Bullo and M. Žefran , “On mechanical systems with nonholonomic constraints and symmetries,” Syst. Control Lett. 45 (2), 133143 (2002).

12.M. Dalsmo and A. J. van der Schaft , “On representations and integrability of mathematical structures in energy-conserving physical systems,” SIAM J. Control Optim. 37 (1), 5491 (1998).

14.A. D. Lewis , “Simple mechanical control systems with constraints,” IEEE Trans. Autom. Control 45 (8), 14201436 (2000).

15.A. D. Lewis and R. M. Murray , “Controllability of simple mechanical control systems,” SIAM J. Control Optim. 35 (3), 766790 (1997).

18.K. M. Lynch , N. Shiroma , H. Arai and K. Tanie , “Collision-free trajectory planning for a 3-DOF robot with a passive joint,” Int. J. Robot Res. 19 (12), 11711184 (2000).

20.R. Ortega , M. W. Spong , F. Gómez-Estern and G. Blankenstein , “Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment,” IEEE Trans. Autom. Control 47 (8), 12181233 (2002).

22.H. J. Sussmann , “A general theorem on local controllability,” SIAM J. Control Optim. 25 (1), 158194 (1987).

23.H. J. Sussmann and V. Jurdjevic , “Controllability of nonlinear systems,” J. Differential Equations 12, 95116 (1972).

24.M. Takegaki and S. Arimoto , “A new feedback method for dynamic control of manipulators,” Trans. ASME Ser. G J. Dynam. Syst. Meas. Control 103 (2), 119125 (1981).

26.A. J. van der Schaft , “Stabilization of Hamiltonian systems,” Nonlinear Anal. TMA 10 (10), 10211035 (1986).

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

  • ISSN: 0263-5747
  • EISSN: 1469-8668
  • URL: /core/journals/robotica
Please enter your name
Please enter a valid email address
Who would you like to send this to? *