Geometric Collocation Method on SO(3) with Application to Optimal Attitude Control of a 3D Rotating Rigid Body
Joint Authors
Li, Jie
Xiang, Xiaojia
Wu, Lizhen
Shen, Lincheng
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-12-07
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
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 so(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.
American Psychological Association (APA)
Xiang, Xiaojia& Wu, Lizhen& Shen, Lincheng& Li, Jie. 2015. Geometric Collocation Method on SO(3) with Application to Optimal Attitude Control of a 3D Rotating Rigid Body. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-14.
https://search.emarefa.net/detail/BIM-1074705
Modern Language Association (MLA)
Xiang, Xiaojia…[et al.]. Geometric Collocation Method on SO(3) with Application to Optimal Attitude Control of a 3D Rotating Rigid Body. Mathematical Problems in Engineering No. 2015 (2015), pp.1-14.
https://search.emarefa.net/detail/BIM-1074705
American Medical Association (AMA)
Xiang, Xiaojia& Wu, Lizhen& Shen, Lincheng& Li, Jie. Geometric Collocation Method on SO(3) with Application to Optimal Attitude Control of a 3D Rotating Rigid Body. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-14.
https://search.emarefa.net/detail/BIM-1074705
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1074705