Now showing items 10-29 of 33

    • Energy-preserving affine connections 

      Lewis, Andrew D. (1997)
      A Riemannian affine connection on a Riemannian manifold has the property that is preserves the ``kinetic energy'' associated with the metric. However, there are other affine connections which have this property, and ...
    • An example with interesting controllability and stabilisation properties 

      Hirschorn, Ron M.; Lewis, Andrew D. (2005)
      A simple three-state system with two inputs is considered. The system's controllability is determined using properties of vector-valued quadratic forms. The quadratic structure is then used as the basis for the design of ...
    • Geometric local controllability: second-order conditions 

      Hirschorn, Ron M.; Lewis, Andrew D. (2002)
      In a geometric point of view, a nonlinear control system, affine in the controls, is thought of as an affine subbundle of the tangent bundle of the state space. In deriving conditions for local controllability from ...
    • Geometric sliding mode control: The linear and linearised theory 

      Hirschorn, Ron M.; Lewis, Andrew D. (2002)
      The idea of sliding mode control for stabilisation is investigated to determine its geometric features. A geometric definition is provided for a sliding submanifold, and for various properties of a sliding submanifold. Sliding ...
    • The geometry of the Gibbs-Appell equations and Gauss's Principle of Least Constraint 

      Lewis, Andrew D. (1995)
      We present a generalisation of the Gibbs-Appell equations which is valid for general Lagrangians. The general form of the Gibbs-Appell equations is shown to be valid in the case when constraints and external forces ...
    • The geometry of the maximum principle for affine connection control systems 

      Lewis, Andrew D. (2000)
      The maximum principle of Pontryagin is applied to systems where the drift vector field is the geodesic spray corresponding to an affine connection. The result is a second-order differential equation whose right-hand side ...
    • Group structures in a class of control systems 

      Lewis, Andrew D. (1992)
      We investigate two classes of control systems, one of Brockett and one of Murray and Sastry. We are able to show that these two systems may be formulated in the language of principle fibre bundles. Controllability of ...
    • High-order variations for families of vector fields 

      Hirschorn, Ron M.; Lewis, Andrew D. (2002)
      Sufficient conditions involving Lie brackets of arbitrarily high-order are obtained for local controllability of families of vector fields. After providing a general framework for the generation of high-order ...
    • Jacobian linearisation in a geometric setting 

      Lewis, Andrew D.; Tyner, David R. (IEEE, 2003)
      Linearisation is a common technique in control applications, putting useful analysis and design methodologies at the disposal of the control engineer. In this paper, linearisation is studied from a differential ...
    • Kinematic controllability and motion planning for the snakeboard 

      Bullo, Francesco; Lewis, Andrew D. (IEEE, 2003)
      The snakeboard is shown to be kinematically controllable. Associated with the two decoupling vector fields for the problem, a constrained static nonlinear programming problem is posed whose solutions provide a solution to ...
    • Lagrangian submanifolds and an application to the reduced Schrödinger equation in central force problems 

      Lewis, Andrew D. (D. Reidel, 1992)
      In this Letter, a Lagrangian foliation of the zero energy level is constructed for a family of planar central force problems. The dynamics on the leaves are explicitly computed and these dynamics are given a simple ...
    • Lifting distributions to tangent and jet bundles 

      Lewis, Andrew D. (1998)
      We provide two natural ways to lift a distribution from a manifold to its tangent bundle, and show that they agree if and only if the original distribution is integrable. The case when the manifold is the total space ...
    • The linearisation of a simple mechanical control system 

      Bullo, Francesco; Lewis, Andrew D. (2002)
      A geometric interpretation is given for the linearisation of a mechanical control system with a kinetic minus potential energy Lagrangian.
    • Low-order controllability and kinematic reductions for affine connection control systems 

      Bullo, Francesco; Lewis, Andrew D. (2002)
      Controllability and kinematic modeling notions are investigated for a class of mechanical control systems. First, low-order controllability results are given for a class of mechanical control systems. Second, a ...
    • Nonholonomic mechanics and locomotion: the snakeboard example 

      Lewis, Andrew D.; Ostrowski, James P.; Burdick, Joel W.; Murray, Richard M. (IEEE, 1994)
      Analysis and simulations are performed for a simplified model of a commercially available variant on the skateboard, known as the Snakeboard.1 Although the model exhibits basic gait patterns seen in a large number of ...
    • On the homogeneity of the affine connection model for mechanical control systems 

      Bullo, Francesco; Lewis, Andrew D. (IEEE, 2000)
      This work presents a review of a number of control results for mechanical systems. The key technical results derive mainly from the homogeneity properties of affine connection models for a large class of mechanical systems. ...
    • Optimal control for a simplified hovercraft model 

      Coombs, A. Theo; Lewis, Andrew D. (2000)
      Time-optimal and force-optimal extremals are investigated for a planar rigid body with a single variable direction thruster. A complete and explicit characterisation of the singular extremals is possible for this problem.
    • Reduction, linearization, and stability of relative equilibria for mechanical systems on Riemannian manifolds 

      Bullo, Francesco; Lewis, Andrew D. (2004)
      Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability ...
    • Rigid body mechanics in Galilean spacetimes 

      bhand, Ajit; Lewis, Andrew D. (2004)
      An observer-independent formulation of rigid body dynamics is provided in the general setting of a Galilean spacetime. The equations governing the motion of a rigid body undergoing a rigid motion in a Galilean spacetime ...
    • Simple mechanical control systems with constraints 

      Lewis, Andrew D. (IEEE, 2000)
      We apply some recently developed control theoretic techniques to the analysis of a class of mechanical systems with constraints. Certain simple aspects of the theory of affine connections play an important part in our ...