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

Wassim M. Haddad

School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332

Tansel Yucelen

Department of Mechanical Engineering, University of South Florida, Tampa, FL 33620

Rafal Goebel

Department of Mathematics and Statistics, Loyola University Chicago, Chicago, IL 60626

1Corresponding author.

ASME 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.

Copyright (c) 2017 by ASME
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