Geometric collocation method on SO(3) with application to optimal attitude control of a 3D rotating rigid body
type: Item
instance of: scholarly article
title: Geometric collocation method on SO(3) with application to optimal attitude control of a 3D rotating rigid body
zbMATH Open document ID: 1394.70065
DOI: 10.1155/2015/790409
author: Xiaojia Xiang
author: Lizhen Wu
author: Lincheng Shen
author: Jie Li
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: The collocation method is extended to the special orthogonal group SO(3) with application to optimal attitude control (OAC) of a rigid body. A left-invariant rigid-body attitude dynamical model on SO(3) is established. For the left invariance of the attitude configuration equation in body-fixed frame, a geometrically exact numerical method on SO(3), referred to as the geometric collocation method, is proposed by deriving the equivalent Lie algebra equation in \(\mathfrak{s} \mathfrak{o}(3)\) of the left-invariant configuration equation. When compared with the general Gauss pseudo-spectral method, the explicit RKMK, and Lie group variational integrator having the same order and stepsize in numerical tests for evolving a free-floating rigid-body attitude dynamics, the proposed method is higher in accuracy, time performance, and structural conservativeness. In addition, the numerical method is applied to solve a constrained OAC problem on SO(3). The optimal control problem is transcribed into a nonlinear programming problem, in which the equivalent Lie algebra equation is being considered as the defect constraints instead of the configuration equation. The transcription method is coordinate-free and does not need chart switching or special handling of singularities. More importantly, with the numerical advantage of the geometric collocation method, the proposed OAC method may generate satisfying convergence rate.
Mathematics Subject Classification ID: 70Q05
Mathematics Subject Classification ID: 65L60
zbMATH DE Number: 6927220
Wikidata QID: Q59119882
describes a project that uses: Matlab
describes a project that uses: GPOPS
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/790409
OpenAlex ID: W2195718189
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description: scientific article; zbMATH DE number 6927220