Control Algorithms Along Relative Equilibria of Underactuated Lagrangian Systems on Lie Groups

Nikolaj Nordkvist; F. Bullo

doi:10.1109/TAC.2008.2007143

Control Algorithms Along Relative Equilibria of Underactuated Lagrangian Systems on Lie Groups

Nikolaj Nordkvist, F. Bullo

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

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.

Original language	English
Journal	IEEE Transactions on Automatic Control
Volume	53
Issue number	11
Pages (from-to)	2651-2658
ISSN	0018-9286
DOIs	https://doi.org/10.1109/TAC.2008.2007143
Publication status	Published - Dec 2008

Keywords

Mechanical systems
underactuated systems
relative equilibria
nonlinear control

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10.1109/TAC.2008.2007143

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title = "Control Algorithms Along Relative Equilibria of Underactuated Lagrangian Systems on Lie Groups",

abstract = "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.",

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AU - Nordkvist, Nikolaj

AU - Bullo, F.

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AB - 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.

KW - Mechanical systems

KW - underactuated systems

KW - relative equilibria

KW - nonlinear control

U2 - 10.1109/TAC.2008.2007143

DO - 10.1109/TAC.2008.2007143

M3 - Journal article

SN - 0018-9286

VL - 53

SP - 2651

EP - 2658

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 11

ER -

Control Algorithms Along Relative Equilibria of Underactuated Lagrangian Systems on Lie Groups

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