Free Access
Issue
ESAIM: COCV
Volume 10, Number 4, October 2004
Page(s) 526 - 548
DOI https://doi.org/10.1051/cocv:2004018
Published online 15 October 2004
  1. C. Altafini, Geometric motion control for a kinematically redundant robotic chain: Application to a holonomic mobile manipulator. J. Rob. Syst. 20 (2003) 211-227. [CrossRef] [Google Scholar]
  2. V.I. Arnold, Math. methods of Classical Mechanics. 2nd ed., Grad. Texts Math. 60 (1989). [Google Scholar]
  3. L. Berard-Bergery, Sur la courbure des métriques Riemanniennes invariantes des groupes de Lie et des espaces homogènes. Ann. Sci. Ecole National Superior 11 (1978) 543. [Google Scholar]
  4. F. Bullo, N. Leonard and A. Lewis, Controllability and motion algorithms for underactuates Lagrangian systems on Lie groups. IEEE Trans. Autom. Control 45 (2000) 1437-1454. [CrossRef] [Google Scholar]
  5. F. Bullo and R. Murray, Tracking for fully actuated mechanical systems: a geometric framework. Automatica 35 (1999) 17-34. [CrossRef] [MathSciNet] [Google Scholar]
  6. M. Camarinha, F. Silva Leite and P. Crouch, Second order optimality conditions for an higher order variational problem on a Riemannian manifold, in Proc. 35th Conf. on Decision and Control. Kobe, Japan, December (1996) 1636-1641. [Google Scholar]
  7. E. Cartan, La géométrie des groupes de transformations, in Œuvres complètes 2, part I. Gauthier-Villars, Paris, France (1953) 673-792. [Google Scholar]
  8. H. Cendra, D. Holm, J. Marsden and T. Ratiu, Lagrangian reduction, the Euler-Poincaré equations and semidirect products. Amer. Math. Soc. Transl. 186 (1998) 1-25. [Google Scholar]
  9. M. Crampin and F. Pirani, Applicable differential geometry. London Mathematical Society Lecture notes. Cambridge University Press, Cambridge, UK (1986). [Google Scholar]
  10. P.E. Crouch and F. Silva Leite, The dynamic interpolation problem on Riemannian manifolds, Lie groups and symmetric spaces. J. Dynam. Control Syst. 1 (1995) 177-202. [CrossRef] [MathSciNet] [Google Scholar]
  11. M. do Carmo, Riemannian geometry. Birkhäuser, Boston (1992). [Google Scholar]
  12. L. Eisenhart, Riemannian geometry. Princeton University Press, Princeton (1966). [Google Scholar]
  13. V. Jurdjevic, Geometric Control Theory. Cambridge Stud. Adv. Math. Cambridge University Press, Cambridge, UK (1996). [Google Scholar]
  14. S. Kobayashi and K. Nomizu, Foundations of differential geometry I and II. Interscience Publisher, New York (1963) and (1969). [Google Scholar]
  15. J. Lee, Riemannian manifolds. An introduction to curvature. Springer, New York, NY (1997). [Google Scholar]
  16. A. Lewis and R. Murray, Configuration controllability of simple mechanical control systems. SIAM J. Control Optim. 35 (1997) 766-790. [CrossRef] [MathSciNet] [Google Scholar]
  17. A. Lewis and R. Murray, Decompositions for control systems on manifolds with an affine connection. Syst. Control Lett. 31 (1997) 199-205. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  18. J. Marsden, Lectures on Mechanics. Cambridge University Press, Cambridge (1992). [Google Scholar]
  19. J. Marsden and T. Ratiu, Introduction to mechanics and symmetry, Springer-Verlag, 2nd ed., Texts Appl. Math. 17 (1999). [Google Scholar]
  20. J. Milnor, Curvature of left invariant metrics on Lie groups. Adv. Math. 21 (1976) 293-329. [CrossRef] [Google Scholar]
  21. R. Murray, Z. Li and S. Sastry, A Mathematical Introduction to Robotic Manipulation. CRC Press (1994). [Google Scholar]
  22. L. Noakes, G. Heinzinger and B. Paden, Cubic splines on curved spaces. IMA J. Math. Control Inform. 12 (1989) 465-473. [CrossRef] [MathSciNet] [Google Scholar]
  23. K. Nomizu, Invariant affine connections on homogeneous spaces. Amer. J. Math. 76 (1954) 33-65. [CrossRef] [MathSciNet] [Google Scholar]
  24. F. Park and B. Ravani, Bézier curves on Riemannian manifolds and Lie groups with kinematic applications. ASME J. Mech. design 117 (1995) 36-40. [CrossRef] [Google Scholar]
  25. J. M. Selig, Geometrical methods in Robotics. Springer, New York, NY (1996). [Google Scholar]
  26. M. Zefran, V. Kumar and C. Croke, On the generation of smooth three-dimensional rigid body motions. IEEE Trans. Robot. Automat. 14 (1998) 576-589. [CrossRef] [Google Scholar]

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