Robust adaptive sliding mode tracking control for a rigid body based on Lie subgroups of SO(3)

Yaobang Ye; Zongyu Zuo; Michael Basin

doi:10.3934/dcdss.2022010

Article Contents

2022, Volume 15, Issue 7: 1823-1837. Doi: 10.3934/dcdss.2022010

This issue Previous Article A brief survey on stability and stabilization of impulsive systems with delayed impulses Next Article Robust dynamic sliding mode control design for interval type-2 fuzzy systems

Robust adaptive sliding mode tracking control for a rigid body based on Lie subgroups of SO(3)

1.
Seventh Research Division, Beihang University, Beijing, 100191, China
2.
Department of Physical and Mathematical Sciences, Autonomous University of Nuevo Le$ \acute{o} $n, San Nicolas de los Garza, 66450, Mexico
3.
International Laboratory of Information and Navigation Systems, ITMO University, Saint Petersburg 197101, Russia

^*Corresponding author: Zongyu Zuo
^*Corresponding author: Zongyu Zuo

Received: September 30, 2021

Revised: November 30, 2021

Published: July 2022

This work was supported by the National Natural Science Foundation of China under Grant 62073019

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Abstract

This paper considers the attitude tracking control problem for a rigid body. In order to avoid the complexity and ambiguity associated with other attitude representations (such as Euler angles or quaternions), the attitude dynamics and the proposed control system are represented globally on special orthogonal groups. An adaptive controller based on a Lie subgroup of SO(3) is developed such that the rigid body can track any given attitude command asymptotically without requiring the exact knowledge of the inertia moment. In the presence of external disturbances, the adaptive controller is enhanced with an additional robust sliding mode term by following the same idea within the framework of SO(3). Finally, simulation results are presented to demonstrate efficiency of the proposed controllers.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. Adaptive attitude tracking responses without disturbances

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Figure 2. Robust adaptive sliding mode attitude tracking responses with disturbances

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Table 1. parameters in simulation

Parameters	Scenario (i)	Scenario (ii)
$ k $	10	50
$ k_{J} $	0.35	0.4
$ \varsigma $	$ \backslash $	0.002
$ \delta $	$ \backslash $	0.8
$ \varepsilon $	$ \backslash $	1

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