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Jacobian linearisation in a geometric setting
(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 ... 
Group structures in a class of control systems
(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 ... 
Variational principles for constrained systems: theory and experiment
(1994)In this paper we present two methods, the nonholonomic method and the vakonomic method, for deriving equations of motion for a mechanical system with constraints. The resulting equations are compared. Results are also ... 
Configuration controllability of simple mechanical control systems
(Society for Industrial and Applied Mathematics, 1995)In this paper we present a definition of "configuration controllability" for mechanical systems whose Lagrangian is kinetic energy with respect to a Riemannian metric minus potential energy. A computable test for this ... 
The geometry of the GibbsAppell equations and Gauss's Principle of Least Constraint
(1995)We present a generalisation of the GibbsAppell equations which is valid for general Lagrangians. The general form of the GibbsAppell equations is shown to be valid in the case when constraints and external forces ... 
Aspects of Geometric Mechanics and Control of Mechanical Systems
(1995)Many interesting control systems are mechanical control systems. In spite of this, there has not been much effort to develop methods which use the special structure of mechanical systems to obtain analysis tools which ... 
Affine connections and distributions
(1996)We investigate various aspects of the interplay of an affine connection with a distribution. When the affine connection restricts to the distribution, we discuss torsion, curvature, and holonomy of the affine connection. ... 
Energypreserving affine connections
(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 ... 
Towards F=ma in a general setting for Lagrangian mechanics
(1998)By using a suitably general definition of a force, one may geometrically cast the EulerLagrange equations in a ``force balance'' form. The key ingredient in such a construction is the EulerLagrange 2force which is a ... 
Lifting distributions to tangent and jet bundles
(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 ... 
Affine connection control systems
(1999)The affine connection formalism provides a useful framework for the investigation of a large class of mechanical systems. Mechanical systems with kinetic energy Lagrangians and possibly with nonholonomic constraints are ... 
The geometry of the maximum principle for affine connection control systems
(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 secondorder differential equation whose righthand side ... 
Optimal control for a simplified hovercraft model
(2000)Timeoptimal and forceoptimal 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. 
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 ... 
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 ... 
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 ... 
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. 
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 ...