Scalable Formation Control of Double Integrator Agents: A Distributed Observer Approach

This work studies formation control of double integrator agents where its formation size is scalable via a scaling factor (scalable formation). Previous works on scalable formation are limited to either fixed undirected graph or fixed directed graph with p-rooted graph condition. This work proposes a novel distributed algorithm for scalable formation based on a distributed observer to estimate agents' positions. The novel algorithm results in a new matrix, a Laplacian matrix with additional diagonal terms, where the desired formation pattern is embedded in this diagonal terms. With the proposed algorithm, only spanning tree condition is needed as the necessary and sufficient condition to achieve the scalable formation. Numerical examples are shown to illustrate the proposed method.