Dynamic affine formation control of networked under-actuated quad-rotor UAVs with three-dimensional patterns

doi:10.23919/JSEE.2022.000147

Journal of Systems Engineering and Electronics ›› 2022, Vol. 33 ›› Issue (6): 1269-1285.doi: 10.23919/JSEE.2022.000147

• CONTROL THEORY AND APPLICATION • Previous Articles

Dynamic affine formation control of networked under-actuated quad-rotor UAVs with three-dimensional patterns

Yang XU¹^,²(), Weiming ZHENG³(), Delin LUO³^,*(), Haibin DUAN⁴()

¹ School of Civil Aviation, Northwestern Polytechnical University, Xi’an 710072, China
² Yangtze River Delta Research Institute, Northwestern Polytechnical University, Taicang 215400, China
³ School of Aerospace Engineering, Xiamen University, Xiamen 361102, China
⁴ School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China

Received:2021-10-28 Online:2022-12-18 Published:2022-12-24
Contact: Delin LUO E-mail:yang.xu@nwpu.edu.cn;zwming@stu.xmu.edu.cn;luodelin1204@xmu.edu.cn;hbduan@buaa.edu.cn
About author:
XU Yang was born in 1987. He received his Ph.D. degree from Xiamen University, Xiamen, China, in 2019. He has been a visiting Ph.D. student at National University of Singapore from 2016 to 2018, and a research fellow at Westlake University from 2019 to 2020. Now, he is an associate professor in School of Civil Aviation, Northwestern Polytechnical University. His research interests include control theory and application of multiple robotic systems. E-mail: yang.xu@nwpu.edu.cn

ZHENG Weiming was born in 1997. He received his B.S. degree from Fuzhou University, Fuzhou, China, in 2019. He is currently pursuing his M.S. degree in Xiamen University, Xiamen, China. His research interests include cooperative control of multiple UAVs and sliding mode control. E-mail: zwming@stu.xmu.edu.cn

LUO Delin was born in 1968. He received his B.S. degree in control engineering from Harbin Institute of Technology, China, in 1991, and M.S. and Ph.D. degrees in navigation, guidance, and control from Nanjing University of Aeronautics and Astronautics, China, in 2002 and 2006, respectively. He is a full professor in Department of Automation, School of Aerospace Engineering, Xiamen University. His research interests include guidance and control, cooperative control of multiple unmanned aerial vehicles, and computational intelligence. E-mail: luodelin1204@xmu.edu.cn

DUAN Haibin was born in 1976. He received his Ph.D. degree from Nanjing University of Aeronautics and Astronautics (NUAA) in 2005. He was an academic visitor of National University of Singapore in 2007, a senior visiting scholar of The University of Suwon of South Korea in 2011. He is currently a full professor of School of Automation Science and Electrical Engineering, Beihang University, Beijing, China. He is currently an IEEE Senior Member and IFAC TC7.5 Technical Committee Member. His current research interests include bio-inspired computation, advanced flight control, and biological computer vision. E-mail: hbduan@buaa.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (61673327), the Industrial Development and Foster Project of Yangtze River Delta Research Institute of NPU, Taicang (CY20210202), the Fundamental Research Funds for the Central Universities (G2021KY05116;G2022WD01026), and the Basic Research Programs of Taicang (TC2021JC28)

Abstract

Abstract:

This paper focuses on the solution to the dynamic affine formation control problem for multiple networked under-actuated quad-rotor unmanned aerial vehicles (UAVs) to achieve a configuration that preserves collinearity and ratios of distances for a target configuration. In particular, it is investigated that the quad-rotor UAVs are steered to track a reference linear velocity while maintaining a desired three-dimensional target formation. Firstly, by integrating the properties of the affine transformation and the stress matrix, the design of the target formation is convenient and applicable for various three-dimensional geometric patterns. Secondly, a distributed control method is proposed under a hierarchical framework. By introducing an intermediary control input for each quad-rotor UAV in the position loop, the necessary thrust input and the desired attitude are extracted. In the attitude loop, the desired attitude represented by the unit quaternion is tracked by the designed torque input. Both conditions of linear velocity unavailability and mutual collision avoidance are also tackled. In terms of Lyapunov theory, it is prooved that the overall closed-loop error system is asymptotically stable. Finally, two illustrative examples are simulated to validate the effectiveness of the proposed theoretical results.

Key words: formation control, quad-rotor unmanned aerial vehicle (UAV), hierarchical control

Yang XU, Weiming ZHENG, Delin LUO, Haibin DUAN. Dynamic affine formation control of networked under-actuated quad-rotor UAVs with three-dimensional patterns[J]. Journal of Systems Engineering and Electronics, 2022, 33(6): 1269-1285.

Figures/Tables 20

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Symbol	Description
$i$	The $i$ th quad-rotor UAV
$\mathcal{G} = (\mathcal{V},\mathcal{E})$	Undirected graph
${\boldsymbol{L}}$	Stress matrix
${\mathcal{F}_I},{\mathcal{F}_B}$	Inertia frame, body frame
${m_i},g,{{\boldsymbol{J}}_i}$	Mass, gravitational acceleration, inertial matrix
${{\boldsymbol{p}}_i},{{\boldsymbol{v}}_i}$	Position, linear velocity
${{\boldsymbol{Q}}_i} = {[{\boldsymbol{q}}_i^{\rm{T}},{\eta _i}]^{\rm{T}}},{{\boldsymbol{\omega}} _i}$	Unit quaternion, angular velocity
${\boldsymbol{R}}({{\boldsymbol{Q}}_i})$	Rotation matrix
${ {{T} }_i},{ {\boldsymbol{\tau} } _i}$	Thrust input, torque input
${{\boldsymbol{p}}_d},{{\boldsymbol{v}}_d}$	Target configuration, desired reference linear velocity
${\tilde {\boldsymbol{v}}_i}$	Linear velocity tracking error
${{\boldsymbol{\alpha}} _i}$	Intermediary control input
${{\boldsymbol{\gamma}} _i},{{\boldsymbol{\chi}} _i}$	Auxiliary variables
${{\boldsymbol{\xi}} _i},{{\boldsymbol{\zeta}} _i},{\hat {\boldsymbol{\xi}} _i},{\hat {\boldsymbol{\zeta}} _i}$	Auxiliary error variables
${{\boldsymbol{u}}_i}$	Auxiliary control input
${{\boldsymbol{Q}}_{i,d} },{\tilde {\boldsymbol{Q}}_i}$	Desired attitude, attitude tracking error
${{\boldsymbol{\omega}} _{i,d} },{\tilde {\boldsymbol{\omega}} _i}$	Desired angular velocity, angular velocity tracking error
${k_\gamma },{k_\xi },{k_\zeta }$	Positive scalar gains
${k_q},{k_\omega },{k_\beta }$	Positive scalar gains
${k_\chi },{\bar k_\xi },{\bar k_\zeta }$	Positive scalar gains

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Dynamic affine formation control of networked under-actuated quad-rotor UAVs with three-dimensional patterns

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