FSG-based divinable time-varying formation tracking of multiple Lagrangian agents with unknown disturbances and directed graphs

Teng-Fei Ding; Ming-Feng Ge; Caihua Xiong; Zhi-Wei Liu; Guang Ling

doi:10.1016/j.isatra.2022.06.017

FSG-based divinable time-varying formation tracking of multiple Lagrangian agents with unknown disturbances and directed graphs

ISA Trans. 2023 Jan:132:278-291. doi: 10.1016/j.isatra.2022.06.017. Epub 2022 Jun 16.

Authors

Teng-Fei Ding¹, Ming-Feng Ge², Caihua Xiong³, Zhi-Wei Liu⁴, Guang Ling⁵

Affiliations

¹ School of Mechanical Engineering and Electronic Information, China University of Geosciences, Wuhan 430074, China; Key Laboratory of Image Processing and Intelligent Control (Huazhong University of Science and Technology), Ministry of Education, Wuhan 430074, China. Electronic address: dingtf@cug.edu.cn.
² School of Mechanical Engineering and Electronic Information, China University of Geosciences, Wuhan 430074, China. Electronic address: gemf@cug.edu.cn.
³ State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China. Electronic address: chxiong@hust.edu.cn.
⁴ School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China. Electronic address: zwliu@hust.edu.cn.
⁵ School of Science, Wuhan University of Technology, Wuhan 430070, China. Electronic address: guangling@whut.edu.cn.

PMID: 35760655
DOI: 10.1016/j.isatra.2022.06.017

Abstract

In this paper, a flexible shape generator (FSG) is designed to achieve the divinable transformation process of the time-varying formation, and consider the FSG-based time-varying formation tracking (TVFT) problem of multiple Lagrangian agents with unknown disturbances and directed graphs. A hierarchical control algorithm is newly designed to achieve the control goal without using the prior information of the system model and bounded disturbances, and the specific implementation of the proposed hierarchical algorithms is also provided. By using the Hurwitz criterion and adaptive system theory, the sufficient conditions are derived and the stability analysis show that the formation tracking errors of the considered system are uniform ultimate bounded. Several simulation examples are performed on five two-degree-of-freedom mechanical arms to show the effectiveness of theoretical results.

Keywords: Directed graphs; Divinable time-varying formation tracking (TVFT); Flexible shape generator (FSG); Multiple Lagrangian agents; Unknown disturbances.