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Control algorithms along relative equilibria of underactuated Lagrangian systems on Lie groups

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2 Author(s)
Nikolaj Nordkvist ; Department of Mathematics, Technical University of Denmark, Matematiktorvet, Building 303 S, DK-2800 Kgs, Lyngby, Denmark ; Francesco Bullo

We present novel algorithms to control underactuated mechanical systems. For a class of invariant systems on Lie groups, we design iterative small-amplitude control forces to accelerate along, decelerate along, and stabilize relative equilibria. The technical approach is based upon a perturbation analysis and the design of inversion primitives and composition methods. We illustrate the algorithms on an underactuated planar rigid body and on a satellite with two thrusters.

Published in:

Decision and Control, 2007 46th IEEE Conference on

Date of Conference:

12-14 Dec. 2007