# American Institute of Mathematical Sciences

July  2022, 15(7): 1823-1837. doi: 10.3934/dcdss.2022010

## 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

Received  October 2021 Revised  December 2021 Published  July 2022 Early access  January 2022

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

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.

Citation: Yaobang Ye, Zongyu Zuo, Michael Basin. Robust adaptive sliding mode tracking control for a rigid body based on Lie subgroups of SO(3). Discrete and Continuous Dynamical Systems - S, 2022, 15 (7) : 1823-1837. doi: 10.3934/dcdss.2022010
##### References:

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##### References:
Adaptive attitude tracking responses without disturbances
Robust adaptive sliding mode attitude tracking responses with disturbances
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
 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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