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

• Published in: Journal of robotics and mechatronics Vol. 32; no. 2; pp. 422 - 436
• Main Authors: Ikemoto, Yusuke, Nishimura, Kenichiro, Mizutama, Yuichiro, Sasaki, Tohru, Jindai, Mitsuru
• Format: Journal Article
• Language: English
• Published: Tokyo Fuji Technology Press Co. Ltd 20.04.2020
• Subjects: Algorithms; Connectivity; Distributed sensor systems; Graph theory; Iterative methods; Kernels; Mathematical analysis; Matrix algebra; Matrix methods; Mobile computing; Position sensing; Reaction-diffusion equations; Robot control; Robots; Wireless networks
• ISSN: 0915-3942; 1883-8049
• DOI: 10.20965/jrm.2020.p0422

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.