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Research Papers

Approximate Consensus of Multiagent Systems With Inaccurate Sensor Measurements

[+] Author and Article Information
Teymur Sadikhov

Mercedes-Benz Research and
Development North America, Inc.,
Sunnyvale, CA 94085
e-mail: teymursadikhov@gmail.com

Wassim M. Haddad

School of Aerospace Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: wm.haddad@aerospace.gatech.edu

Tansel Yucelen

Department of Mechanical Engineering,
University of South Florida,
Tampa, FL 33620
e-mail: yucelen@usf.edu

Rafal Goebel

Department of Mathematics and Statistics,
Loyola University Chicago,
Chicago, IL 60626
e-mail: rgoebel1@luc.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 19, 2016; final manuscript received February 1, 2017; published online June 5, 2017. Assoc. Editor: Sergey Nersesov.

J. Dyn. Sys., Meas., Control 139(9), 091003 (Jun 05, 2017) (10 pages) Paper No: DS-16-1039; doi: 10.1115/1.4036031 History: Received January 19, 2016; Revised February 01, 2017

One of the main challenges in robotics applications is dealing with inaccurate sensor data. Specifically, for a group of mobile robots, the measurement of the exact location of the other robots relative to a particular robot is often inaccurate due to sensor measurement uncertainty or detrimental environmental conditions. In this paper, we address the consensus problem for a group of agent robots with a connected, undirected, and time-invariant communication graph topology in the face of uncertain interagent measurement data. Using agent location uncertainty characterized by norm bounds centered at the neighboring agent's exact locations, we show that the agents reach an approximate consensus state and converge to a set centered at the centroid of the agents' initial locations. The diameter of the set is shown to be dependent on the graph Laplacian and the magnitude of the uncertainty norm bound. Furthermore, we show that if the network is all-to-all connected and the measurement uncertainty is characterized by a ball of radius r, then the diameter of the set to which the agents converge is 2r. Finally, we also formulate our problem using set-valued analysis and develop a set-valued invariance principle to obtain set-valued consensus protocols. Two illustrative numerical examples are provided to demonstrate the efficacy of the proposed approximate consensus protocol framework.

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Figures

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Fig. 1

Visualization of sets X2−x1 and X3−x1 used in agent's 1 update map

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Fig. 11

Network configuration of ten agents with sensor accuracy of radius r = 0.5 at t = 3.5 s

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Fig. 12

Network configuration of ten agents with sensor accuracy of radius r = 0.5 at t = 7.5 s

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Fig. 2

Initial network configuration of ten agents with sensor accuracy of radius r = 1

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Fig. 3

Network configuration of ten agents with sensor accuracy of radius r = 1 at t = 3.5 s

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Fig. 4

Network configuration of ten agents with sensor accuracy of radius r = 1 at t = 7.5 s

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Fig. 5

Plot of ‖x(t)−eNx¯‖2 versus time

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Fig. 6

Initial network configuration of ten agents with sensor accuracy of radius r = 1

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Fig. 7

Network configuration of ten agents with sensor accuracy of radius r = 1 at t = 3.5 s

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Fig. 8

Network configuration of ten agents with sensor accuracy of radius r = 1 at t = 7.5 s

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Fig. 9

Plot of ‖x(t)−eNx¯‖2 versus time

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Fig. 10

Initial network configuration of ten agents with sensor accuracy of radius r = 0.5

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Fig. 13

Agent guidance state (xi(t), t ≥ 0), ‖x(t)−eNx¯‖2, pitch rate (qi(t), t ≥ 0), guidance input (ui(t), t ≥ 0), and elevator control (νi(t), t ≥ 0) responses for the three airplanes on a line graph in the presence of inaccurate sensor measurements (solid, dashed, and dotted lines denote the responses for the first, second, and third airplanes, respectively)

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Fig. 14

Agent guidance state (xi(t), t ≥ 0), ‖x(t)−eNx¯‖2, pitch rate (qi(t), t ≥ 0), guidance input (ui(t), t ≥ 0), and elevator control (νi(t), t ≥ 0) responses for the three airplanes on an all-to-all graph in the presence of inaccurate sensor measurements (solid, dashed, and dotted lines denote the responses for the first, second, and third airplanes, respectively)

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