Cross-dimensional formation control of second-order heterogeneous multi-agent systems

Lang Ma; Yu-Long Wang; Min-Rui Fei; Quan-Ke Pan

doi:10.1016/j.isatra.2022.02.036

Cross-dimensional formation control of second-order heterogeneous multi-agent systems

ISA Trans. 2022 Aug:127:188-196. doi: 10.1016/j.isatra.2022.02.036. Epub 2022 Feb 25.

Authors

Lang Ma¹, Yu-Long Wang², Min-Rui Fei³, Quan-Ke Pan⁴

Affiliations

¹ Shanghai Key Laboratory of Power Station Automation Technology, Shanghai University, Shanghai, 200444, China; School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, 200444, China. Electronic address: larryma@shu.edu.cn.
² Shanghai Key Laboratory of Power Station Automation Technology, Shanghai University, Shanghai, 200444, China; School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, 200444, China. Electronic address: yulongwang@shu.edu.cn.
³ Shanghai Key Laboratory of Power Station Automation Technology, Shanghai University, Shanghai, 200444, China; School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, 200444, China. Electronic address: mrfei@staff.shu.edu.cn.
⁴ School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, 200444, China. Electronic address: panquanke@shu.edu.cn.

PMID: 35277265
DOI: 10.1016/j.isatra.2022.02.036

Abstract

This paper is concerned with the cross-dimensional formation control of a second-order multi-dimensional heterogeneous multi-agent system. Agents are first separated into several groups according to their position/velocity vector dimensions. Then the cross-dimensional formation control problem is formulated such that agents in the same group form a time-varying formation in their own dimension and agents in different groups cooperatively move in multiple dimensions. This can make follower agents in different dimensions cooperatively track a leader. Moreover, a cross-dimensional formation protocol is designed based on full or partial information of neighboring agents. For higher-dimensional agents, full information of lower-dimensional neighbors is adopted. For lower-dimensional ones, only partial information of higher-dimensional neighbors is used. Furthermore, a necessary and sufficient condition for the second-order heterogeneous multi-agent system to achieve cross-dimensional formation is provided. Accordingly, a criterion for designing cross-dimensional formation protocol is further derived. Finally, under an undirected graph, a lower-dimensional protocol design criterion is obtained if there is no data exchange between lower- and higher-dimensional followers. The effectiveness of the obtained results is demonstrated through cross-dimensional target enclosing performance analysis for multiple robots and quadrotors.

Keywords: Cross-dimensional formation; Formation control; Multi-agent systems.