Paper:

# Network Connectivity Control of Mobile Robots by Fast Position Estimations and Laplacian Kernel

## Yusuke Ikemoto^{*}, Kenichiro Nishimura^{**}, Yuichiro Mizutama^{**}, Tohru Sasaki^{***}, and Mitsuru Jindai^{***}

^{*}Department of Mechanical Engineering, Faculty of Science and Technology, Meijo University

1-501 Shiogamaguchi, Tempaku-ku, Nagoya 468-8502, Japan

^{**}Department of Mechanical and Intellectual Systems Engineering, Faculty of Engineering, University of Toyama

3190 Gofuku, Toyama-shi, Toyama 930-8555, Japan

^{***}Graduate School of Science and Engineering for Research, University of Toyama

3190 Gofuku, Toyama-shi, Toyama 930-8555, Japan

Together with wireless distributed sensor technologies, the connectivity control of mobile robot networks has widely expanded in recent years. Network connectivity has been greatly improved by theoretical frameworks based on graph theory. Most network connectivity studies have focused on algebraic connectivity and the Fiedler vector, which constitutes a network structure matrix eigenpair. Theoretical graph frameworks have popularly been adopted in robot deployment studies; however, the eigenpairs’ computation requires quite a lot of iterative calculations and is extremely time-intensive. In the present study, we propose a robot deployment algorithm that only requires a finite iterative calculation. The proposed algorithm rapidly estimates the robot positions by solving reaction-diffusion equations on the graph, and gradient methods using a Laplacian kernel. The effectiveness of the algorithm is evaluated in computer simulations of mobile robot networks. Furthermore, we implement the algorithm in the actual hardware of a two-wheeled robot.

*J. Robot. Mechatron.*, Vol.32, No.2, pp. 422-436, 2020.

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