Department of Mathematics and Statistics: Dr. Andrew D. Lewis
These are the preprint versions of the papers, and will differ somewhat from what you will see published. I do not accept responsibility for those items which have not been reviewed.
Recent Submissions

An example with interesting controllability and stabilisation properties
(2005)A simple threestate system with two inputs is considered. The system's controllability is determined using properties of vectorvalued quadratic forms. The quadratic structure is then used as the basis for the design of ... 
Reduction, linearization, and stability of relative equilibria for mechanical systems on Riemannian manifolds
(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 ... 
Discussion on: ``Dynamic Sliding Mode Control for a Class of Systems with Mismatched Uncertainty''
(Lavoisier, 2005)This is an invited discussion paper on the paper ``Dynamic Sliding Mode Control for a Class of Systems with Mismatched Uncertainty'' by XingGang Yan, Sarah K. Spurgeon, and Christopher Edwards, that will appear in the ... 
Rigid body mechanics in Galilean spacetimes
(2004)An observerindependent 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 ... 
Kinematic controllability and motion planning for the snakeboard
(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 ... 
On the homogeneity of the affine connection model for mechanical control systems
(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. ... 
Controllability and motion algorithms for underactuated Lagrangian systems on Lie groups
(IEEE, 2000)In this paper, we provide controllability tests and motion control algorithms for underactuated mechanical control systems on Lie groups with Lagrangian equal to kinetic energy. Examples include satellite and underwater ... 
Simple mechanical control systems with constraints
(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 ... 
Decompositions of control systems on manifolds with an affine connection
(NorthHolland, 1997)In this letter we present a decomposition for control systems whose drift vector field is the geodesic spray associated with an affine connection. With the geometric insight gained with this decomposition, we are able to ... 
Nonholonomic mechanics and locomotion: the snakeboard example
(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 ... 
Lagrangian submanifolds and an application to the reduced Schrödinger equation in central force problems
(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 ... 
Controllability of a hovercraft model (and two general results)
(2003)Modelling and controllability studies of a hovercraft system are undertaken. The system studied is a little more complicated than some in the literature in that the inertial dynamics of the thrust fan are taken into ... 
Loworder controllability and kinematic reductions for affine connection control systems
(2002)Controllability and kinematic modeling notions are investigated for a class of mechanical control systems. First, loworder controllability results are given for a class of mechanical control systems. Second, a ... 
Geometric sliding mode control: The linear and linearised theory
(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 linearisation of a simple mechanical control system
(2002)A geometric interpretation is given for the linearisation of a mechanical control system with a kinetic minus potential energy Lagrangian. 
Geometric local controllability: secondorder conditions
(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 ... 
Highorder variations for families of vector fields
(2002)Sufficient conditions involving Lie brackets of arbitrarily highorder are obtained for local controllability of families of vector fields. After providing a general framework for the generation of highorder ... 
Controllable kinematic reductions for mechanical systems: concepts, computational tools, and examples
(2001)This paper introduces the novel notion of kinematic reductions for mechanical systems and studies their controllability properties. We focus on the class of simple mechanical control systems with constraints and model ...