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Abstract
The subject of this thesis is control of mechanical systems as they
evolve along the steady motions called relative equilibria. These
trajectories are of interest in theory and applications and have the
characterizing property that the system's bodyfixed velocity is
constant.
For example, constantspeed rotation about a principal axis is
a relative equilibrium of a rigid body in three dimensions.
We focus our study on simple mechanical control systems on Lie groups,
i.e., mechanical systems with the following properties: the configuration
manifold is a matrix Lie group, the total energy is equal to the kinetic
energy (i.e., no potential energy is present), and the kinetic energy and
control forces both satisfy an invariance condition.
The novel contributions of this thesis are twofold. First, we develop
sufficient conditions, algebraic in nature, that ensure that a simple
mechanical control system on a Lie group is locally controllable along a
relative equilibrium. These conditions subsume the wellknown local
controllability conditions for equilibrium points.
Second, for systems that have fewer controls than
degrees of freedom, we present a novel algorithm to control
simple mechanical control systems on Lie groups along relative
equilibria. Under some assumptions, we design iterative
smallamplitude control forces to accelerate along, decelerate along, and
stabilize relative equilibria. The technical approach is based upon
perturbation analysis and the design of inversion primitives and
composition methods. We finally apply the algorithms to a planar rigid body
and a satellite with two thrusters.
Original language  English 

Number of pages  80 

Publication status  Published  Jan 2008 
Keywords
 Geometric Control Theory
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Projects
 1 Finished

Simulering og kontrol af ikkeholonome mekaniske systemer
Nordkvist, N., Hjorth, P. G., Bullo, F., Ravn, O., Stramigioli, S. & Wisniewski, R.
01/09/2004 → 17/01/2008
Project: PhD