Geometric control of mechanical systems : modeling, analysis, and design for simple mechanical control systems

Part I: Modeling of mechanical systems Introductory examples and problems Linear and multilinear algebra Differential geometry Simple mechanical control systems Lie groups, systems on groups, and symmetries.- Part II: Analysis of mechanical control systems Stability Controllability Low-order controllability and kinematic reduction Perturbation analysis.- Part III: A sampling of design methodologies Linear and nonlinear potential shaping for stabilization Stabilization and tracking for fully actuated systems Stabilization and tracking using oscillatory controls Motion planning for underactuated systems Appendices Time-dependent vector fields Some proofs.

[1]  P J Fox,et al.  THE FOUNDATIONS OF MECHANICS. , 1918, Science.

[2]  A. Krener.  A Generalization of Chow’s Theorem and the Bang-Bang Theorem to Nonlinear Control Problems , 1974 .

[3]  Suguru Arimoto,et al.  A New Feedback Method for Dynamic Control of Manipulators , 1981 .

[4]  Peter E. Crouch,et al.  Geometric structures in systems theory , 1981 .

[5]  A. Schaft.  Controllability and observability for affine nonlinear Hamiltonian systems , 1982 .

[6]  A. J. van der Schaft,et al.  Symmetries, conservation laws, and time reversibility for Hamiltonian systems with external forces , 1983 .

[7]  Bernard Bonnard.  Controlabilite de Systemes Mecaniques Sur Les Groupes de Lie , 1984 .

[8]  A. J. Schaft,et al.  Stabilization of Hamiltonian systems , 1986 .

[9]  Arjan van der Schaft,et al.  Non-linear dynamical control systems , 1990 .

[10]  A. Bloch,et al.  Control and stabilization of nonholonomic dynamic systems , 1992 .

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

[12]  van der Arjan Schaft,et al.  On the Hamiltonian Formulation of Nonholonomic Mechanical Systems , 1994 .

[13]  Clementina D. Mladenova,et al.  Robotic problems over a configurational manifold of vector parameters and dual vector parameters , 1994, J. Intell. Robotic Syst..

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

[15]  Control theory of non-linear mechanical systems : a passivity-based and circuit-theoretic approach , 1996 .

[16]  P. Krishnaprasad,et al.  Nonholonomic mechanical systems with symmetry , 1996 .

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

[18]  Naomi Ehrich Leonard,et al.  Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem , 2000, IEEE Trans. Autom. Control..

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

[20]  Naomi Ehrich Leonard,et al.  Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping , 2001, IEEE Trans. Autom. Control..

[21]  Kevin M. Lynch,et al.  Kinematic controllability and decoupled trajectory planning for underactuated mechanical systems , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[22]  Romeo Ortega,et al.  Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment , 2002, IEEE Trans. Autom. Control..

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

[24]  Sonia Martínez,et al.  Analysis and design of oscillatory control systems , 2003, IEEE Trans. Autom. Control..

[25]  A. Agrachev,et al.  Control Theory from the Geometric Viewpoint , 2004 .

[26]  Francesco Bullo,et al.  Low-Order Controllability and Kinematic Reductions for Affine Connection Control Systems , 2005, SIAM J. Control. Optim..

[27]  Arjan van der Schaft,et al.  Hamiltonian dynamics with external forces and observations , 1981, Mathematical systems theory.

[28]  Arjan van der Schaft,et al.  Controlled invariance for hamiltonian systems , 1985, Mathematical systems theory.

[29]  S. Bhat.  Controllability of Nonlinear Systems , 2022 .