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Research Papers

# Semiglobal Nonmemoryless Attitude Controls on the Special Orthogonal Group

[+] Author and Article Information
Taeyoung Lee

Mechanical and Aerospace Engineering,
George Washington University,
Washington, DC 20052
e-mail: tylee@gwu.edu

Dong Eui Chang

Electrical Engineering,
KAIST,
Daejeon 34141, Korea
e-mail: dechang@kaist.ac.kr

Yongsoon Eun

Information and Communication Engineering,
DGIST,
Daegu 42988, Korea
e-mail: yeun@dgist.ac.kr

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received April 14, 2018; final manuscript received September 5, 2018; published online October 5, 2018. Assoc. Editor: Mohammad A. Ayoubi.

J. Dyn. Sys., Meas., Control 141(2), 021005 (Oct 05, 2018) (10 pages) Paper No: DS-18-1189; doi: 10.1115/1.4041447 History: Received April 14, 2018; Revised September 05, 2018

## Abstract

This paper presents tracking strategies for the attitude dynamics of a rigid body that are global on the configuration space SO(3) and semiglobal over the phase space $SO(3)×ℝ3$. It is well known that global attractivity is prohibited for continuous attitude control systems on the special orthogonal group. Such topological restriction has been dealt with either by constructing smooth attitude control systems that exclude a set of zero measure in the region of attraction or by introducing discontinuities in the control input. This paper proposes nonmemoryless attitude control systems that are continuous in time, where the region of attraction guaranteeing exponential convergence completely covers the special orthogonal group. This provides a new framework to address the topological restriction in attitude controls. The efficacy of the proposed methods is illustrated by numerical simulations and an experiment.

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## References

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## Figures

Fig. 1

Simulation results for two attitude tracking controls presented in Sec. 3 and a hybrid attitude control [9] (AGTS: solid, SGTS: bold, and HYB: dashed; the switching time for HYB is denoted by vertical dotted lines): (a) tracking errors and (b) control inputs

Fig. 2

Simulation results for two adaptive attitude tracking controls presented in Sec. 4 and an adaptive hybrid control [9] (aAGTS: solid, aSGTS: bold, and aHYB: dashed; the switching time for aHYB is denoted by vertical dotted lines): (a) tracking errors and estimation error and (b) control inputs

Fig. 3

Hexrotor attitude control experiment: (a) initial attitude and (b) stabilizing the inverted equilibrium

Fig. 4

Experimental results for two adaptive attitude tracking controls presented in Sec. 4 (aAGTS: solid, aSGTS: bold): (a) tracking errors and estimated disturbance and (b) control inputs

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