Multi-Agent Formation based on Self-loop Laplacian
Djati Wibowo (a*), Muhamad Rausyan Fikri (a),

a) Faculty of Engineering Technology, Sampoerna University
Jl. Raya Pasar Minggu No.Kav.16, Jakarta Selatan 12780, Indonesia
*djati.wibowo[at]sampoernauniversity.ac.id

Abstract

This work studies formation control of Multi-Agent Systems (MASs) where its formation size is scalable via a scaling factor (scalable formation). Literature on scalable formation where the design of communication weight is based on the formation pattern is limited to the case of k-rooted graph and generic configuration of formation pattern. Different from the literature, scalable formation in this work is achieved under a weak assumption on graph and the formulation allows for a more general formation pattern. In this work, scalable formation is achieved by designing a self-loop communication weight for each agent which results in a new matrix called self-loop Laplacian. The self-loop weight is a function of the desired formation pattern. The convergence of the proposed algorithm is shown by standard linear system theory by first deriving the spectral properties of the self-loop Laplacian. The effectiveness of the proposed method is illustrated by numerical example.

Keywords: scalable formation, self-loop weight, multi-agent

Topic: Electrical Engineering