On the homogeneity of the affine connection model for mechanical control systems

This work presents a review of a number of control results for mechanical systems. The key technical advances derive from the homogeneity properties of affine connections models for a large class of mechanical systems. Recent results on nonlinear controllability and on series expansions are presented in a unified fashion.

[1]  James P. Ostrowski.  Steering for a class of dynamic nonholonomic systems , 2000, IEEE Trans. Autom. Control..

[2]  A. D. Lewis,et al.  When is a mechanical control system kinematic? , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[3]  R. Gamkrelidze,et al.  THE EXPONENTIAL REPRESENTATION OF FLOWS AND THE CHRONOLOGICAL CALCULUS , 1979 .

[4]  Naomi Ehrich Leonard,et al.  Controllability and motion algorithms for underactuated Lagrangian systems on Lie groups , 2000, IEEE Trans. Autom. Control..

[5]  Richard M. Murray,et al.  Controllability of simple mechanical control systems , 1997 .

[6]  N. Woodhouse,et al.  SYMPLECTIC GEOMETRY AND ANALYTICAL MECHANICS (Mathematics and Its Applications) , 1988 .

[7]  A. Bloch,et al.  Nonholonomic and Vakonomic Control Systems on Riemannian Manifolds , 1993 .

[8]  Andrew D. Lewis.  The geometry of the maximum principle for ane connection control systems , 2000 .

[9]  Francesco Bullo,et al.  Averaging and Vibrational Control of Mechanical Systems , 2002, SIAM J. Control. Optim..

[10]  A. D. Lewis,et al.  Configuration Controllability of Simple Mechanical Control Systems , 1997 .

[11]  K. Nomizu,et al.  Foundations of Differential Geometry , 1963 .

[12]  James P. Ostrowski,et al.  Control Algorithms Using Affine Connections on Principal Fiber Bundles , 2000 .

[13]  Francesco Bullo,et al.  Series Expansions for the Evolution of Mechanical Control Systems , 2001, SIAM J. Control. Optim..

[14]  R. Ortega.  Passivity-based control of Euler-Lagrange systems : mechanical, electrical and electromechanical applications , 1998 .

[15]  Andrew D. Lewis,et al.  Simple mechanical control systems with constraints , 2000, IEEE Trans. Autom. Control..

[16]  Richard M. Murray,et al.  Decompositions for control systems on manifolds with an affine connection , 1997 .

[17]  S. Lang.  Differential and Riemannian Manifolds , 1996 .

[18]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[19]  Francesco Bullo,et al.  A series describing the evolution of mechanical control systems , 1999 .

[20]  Suguru Arimoto,et al.  Control Theory of Nonlinear Mechanical Systems , 1996 .

[21]  John Baillieul,et al.  Stable average motions of mechanical systems subject to periodic forcing , 1993 .

[22]  I. Holopainen.  Riemannian Geometry , 1927, Nature.

[23]  Eduardo D. Sontag,et al.  Time-optimal control of manipulators , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[24]  Romeo Ortega,et al.  Passivity-based Control of Euler-Lagrange Systems , 1998 .

[25]  A. Bloch,et al.  Nonholonomic Control Systems on Riemannian Manifolds , 1995 .

[26]  Charles-Michel Marle,et al.  Symplectic geometry and analytical mechanics , 1987 .

[27]  J. Marsden,et al.  Introduction to mechanics and symmetry , 1994 .