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Research Papers

Three-Dimensional Dynamic Formation Control of Multi-Agent Systems Using Rigid Graphs

[+] Author and Article Information
Pengpeng Zhang

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

Xiaoyu Cai

R&D Laser Tracker,
FARO Technologies,
Exton, PA 19341

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 21, 2015; final manuscript received June 5, 2015; published online August 13, 2015. Assoc. Editor: Sergey Nersesov.

J. Dyn. Sys., Meas., Control 137(11), 111006 (Aug 13, 2015) (7 pages) Paper No: DS-15-1034; doi: 10.1115/1.4030973 History: Received January 21, 2015

In this paper, we consider the problem of formation control of multi-agent systems in three-dimensional (3D) space, where the desired formation is dynamic. This is motivated by applications where the formation size and/or geometric shape needs to vary in time. Using a single-integrator model and rigid graph theory, we propose a new control law that exponentially stabilizes the origin of the nonlinear, interagent distance error dynamics and ensures tracking of the desired, 3D time-varying formation. Extensions to the formation maneuvering problem and double-integrator model are also discussed. The formation control is illustrated with a simulation of eight agents forming a dynamic cube.

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Figures

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Fig. 1

Desired formation F*(t) at t = 0

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Fig. 2

Single-integrator: agent trajectories from an arbitrary initial formation

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Fig. 3

Single-integrator: interagent distance errors for i,j ∈ V*

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Fig. 4

Single-integrator: control inputs along x (top plot), y (middle plot), and z (bottom plot) directions for i = 1,…,8 during the transient phase (left plots) and steady-state phase (right plots)

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Fig. 5

Double-integrator: agent trajectories from an arbitrary initial formation

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Fig. 6

Double-integrator: interagent distance error for i,j ∈ V*

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Fig. 7

Double-integrator: variable s along x (top plot), y (middle plot), and z (bottom plot) directions for i = 1,…,8

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Fig. 8

Double-integrator: control inputs along x (top plots), y (middle plots), and z (bottom plots) directions for i = 1,…,8 during the transient phase (left plots) and steady-state phase (right plots)

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