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Research Papers

Control of Directed Formations Using Interconnected Systems Stability

[+] Author and Article Information
Pengpeng Zhang, Milad Khaledyan, Tairan Liu

Department of Mechanical and
Industrial Engineering,
Louisiana State University,
Baton Rouge, LA 70803

Marcio de Queiroz

Department of Mechanical and
Industrial Engineering,
Louisiana State University,
Baton Rouge, LA 70803
e-mail: mdeque1@lsu.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received July 24, 2017; final manuscript received October 4, 2018; published online December 6, 2018. Assoc. Editor: Suman Chakravorty.

J. Dyn. Sys., Meas., Control 141(4), 041003 (Dec 06, 2018) (11 pages) Paper No: DS-17-1381; doi: 10.1115/1.4041703 History: Received July 24, 2017; Revised October 04, 2018

This paper deals with the problem of rigid formation control using directed graphs in both two-dimensional (2D) and three-dimensional (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 interagent 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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Figures

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Fig. 1

Directed framework example

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Fig. 2

Basis step for the 3D formation case

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Fig. 3

Simulation: desired framework F* in ℝ3

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Fig. 4

Simulation: Agent trajectories qi(t), i=1,…8

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Fig. 5

Simulation: interagent distance errors eij(t), (i,j)∈Ed∗

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Fig. 6

Simulation: control inputs ui(t), i=1,…,8 along each direction

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Fig. 7

Experiment: desired framework F∗ in ℝ2

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Fig. 8

Experiment: robot trajectories qi(t), i=1,…5

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Fig. 9

Experiment: interagent distance errors, eij(t), (i,j)∈Ed∗

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Fig. 10

Experiment: control inputs, ui(t), i=1,…,5 along each direction

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Fig. 11

Tetrahedron for the nth step of the 3D formation case

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