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Research Papers

Adaptive Control of Multiagent Systems for Finding Peaks of Uncertain Static Fields

[+] Author and Article Information
Mahdi Jadaliha

Department of Mechanical Engineering,  Michigan State University, East Lansing, MI 48824-1226jadaliha@msu.edu

Joonho Lee

Department of Mechanical Engineering,  Michigan State University, East Lansing, MI 48824-1226leejoon8@egr.msu.edu

Jongeun Choi1

Department of Mechanical Engineering,Department of Electrical and Computer Engineering,  Michigan State University, East Lansing, MI 48824-1226jchoi@egr.msu.edu

1

Corresponding author.

J. Dyn. Sys., Meas., Control 134(5), 051007 (Jul 12, 2012) (8 pages) doi:10.1115/1.4006369 History: Received March 11, 2010; Revised February 21, 2012; Published July 12, 2012; Online July 12, 2012

In this paper, we design and analyze a class of multiagent systems that locate peaks of uncertain static fields in a distributed and scalable manner. The scalar field of interest is assumed to be generated by a radial basis function network. Our distributed coordination algorithms for multiagent systems build on techniques from adaptive control. Each agent is driven by swarming and gradient ascent efforts based on its own recursively estimated field via locally collected measurements by itself and its neighboring agents. The convergence properties of the proposed multiagent systems are analyzed. We also propose a sampling scheme to facilitate the convergence. We provide simulation results by applying our proposed algorithms to nonholonomic differentially driven mobile robots. The extensive simulation results match well with the predicted behaviors from the convergence analysis and illustrate the usefulness of the proposed coordination and sampling algorithms.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 2

The position of the sensor and states of robot i

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Figure 3

The trajectories of agents in cases 1, 2, and 3 are shown in the first, second, and third columns, respectively. The first, second, third, and fourth rows correspond to initial pose 1 and field 1, initial pose 1 and field 2, initial pose 2 and field 1, and initial pose 2 and field 2, respectively. The locations of robots are marked by snapshots of poses at t = 0 s, t = 100 s, and t = 1000 s, by white, magenta, and black arrowheads, respectively, showing their positions and heading angles. Horizontal and vertical axes are x and y coordinates, respectively, and the background colors show the scalar fields.

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Figure 4

The norm of the parameter estimation error, i.e., ⋕θ̃i(t)⋕ by agent i for all i∈I in cases 1, 2, and 3 are shown in the first, second, and third columns, respectively. The first, second, third, and fourth rows correspond to initial pose 1 and field 1, initial pose 1 and field 2, initial pose 2 and field 1, and initial pose 2 and field 2, respectively. Vertical and horizontal axes are ⋕θ̃i(t)⋕ (in a logarithmic scale) and time, respectively.

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Figure 1

(a) Dead zone created by algal blooms in the Gulf of Mexico (NASA). (b) The oil slick as seen from space by NASA’s Terra satellite on May 24, 2010 (Photo courtesy of NASA).

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