Now showing items 1-10 of 33
Affine connection control systems
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 ...
Controllability and motion algorithms for underactuated Lagrangian systems on Lie groups
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
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 ...
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 results derive mainly from the homogeneity properties of affine connection models for a large class of mechanical systems. ...
Towards F=ma in a general setting for Lagrangian mechanics
By using a suitably general definition of a force, one may geometrically cast the Euler-Lagrange equations in a ``force balance'' form. The key ingredient in such a construction is the Euler-Lagrange 2-force which is a ...
Variational principles for constrained systems: theory and experiment
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 ...
Lifting distributions to tangent and jet bundles
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
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
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 ...
High-order variations for families of vector fields
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 ...