Distributed tracking of a non-minimally rigid formation for multi-agent systems

ABSTRACT

The objective of this paper is to design distributed control algorithms for a multi-agent system such that a rigid formation can be achieved asymptotically and the agents can finally move with a desired velocity. In particular, it is assumed that the formation is not necessarily minimally rigid, and the desired velocity is available to only a subset of the agents. Estimators are constructed for the agents to estimate the desired velocity, which are further used to design the control inputs of the agents. The proposed control algorithms consist of a formation acquisition term which depends on a potential function and the rigidity matrix, and a velocity estimation term. To deal with non-minimal rigidity, the centre manifold theorem is exploited to prove the stability of the resulting system. Simulation results are also provided to show the effectiveness of the proposed control algorithms.

KEYWORDS:

• Multi-agent system
• formation tracking control
• graph rigidity
• distributed estimator

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the National Science Foundation of China [grant number 61473240] Fundamental Research Funds for the Central Universities [grant number 20720150177].

Notes on contributors

Lu Bai

Lu Bai received her BS and MS degrees from Xiamen University, Xiamen, P. R. China, in 2012 and 2015, respectively. She is currently pursuing her Ph.D. degree at Nanyang Technological University, Singapore. Her research interests include multi-agent systems, formation control and distributed optimisation.

Fei Chen

Fei Chen received his Ph.D. degree in control theory and control engineering from Nankai University, Tianjin, China, in 2009. He was a postdoctoral researcher in the Department of Computer and Electrical Engineering, Utah State University, Logan, UT. Since November 2010, he has been with the Department of Automation, Xiamen University, Xiamen, China, where he is currently an associate professor. He was selected as 2014 outstanding reviewer for IEEE Transactions on Control of Network Systems, and awarded New Century Excellent Talents in Fujian Province University in 2015. He is a senior member of the IEEE (2015).

Weiyao Lan

Weiyao Lan received his BS degree in precision instrument from Chongqing University, China, in 1995; MS degree in control theory and control engineering from Xiamen University, China, in 1998; and Ph.D. degree in automation and computer-aided engineering in 2004 from the Chinese University of Hong Kong, Hong Kong, China. From 1998 to 2000, he was a tutor at the Department of Automation, Xiamen University, Fujian, China. During 2004–2006, he had been a research fellow at the Department of Electrical and Computer Engineering, National University of Singapore, Singapore. Since 2007, he has been with the Department of Automation, Xiamen University, where he is currently a professor. Dr Lan is a member of the 10th Technical Committee on Control Theory of Chinese Association of Automation, and is serving as an associate editor for the Transactions of the Institute of Measurement and Control. His research interests include nonlinear control theory and applications, intelligent control technology, and robust and optimal control.