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research-article

Control of Directed Formations Using Interconnected Systems Stability

[+] Author and Article Information
Pengpeng Zhang

Department of Mechanical and Industrial Engineering, Louisiana State University, Baton Rouge, LA 70803 USA
pzhan16@lsu.edu

Marcio de Queiroz

Department of Mechanical and Industrial Engineering, Louisiana State University, Baton Rouge, LA 70803 USA
mdeque1@lsu.edu

Milad Khaledyan

Department of Mechanical and Industrial Engineering, Louisiana State University, Baton Rouge, LA 70803 USA
mkhale2@lsu.edu

Tairan Liu

Department of Mechanical and Industrial Engineering, Louisiana State University, Baton Rouge, LA 70803 USA
tliu7@lsu.edu

1Corresponding author.

ASME doi:10.1115/1.4041703 History: Received July 24, 2017; Revised October 04, 2018

Abstract

This paper deals with the problem of rigid formation control using directed graphs in both 2D and 3D spaces. Directed graphs reduce the number of communication, sensing, and/or control channels of the multi-agent system. We show that the directed version of the gradient descent control law asymptotically stabilizes the inter-agent distance error dynamics of minimally persistent formation graphs. The control analysis begins with a (possibly cyclic) primitive formation that is grown consecutively by Henneberg-type insertions, resulting at each step in two interconnected nonlinear systems which are recursively analyzed using the stability of interconnected systems. Simulation and experimental results are presented for the directed formation controller in comparison to the standard undirected controller.

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