Multi-Agent Formation with Size Scaling via Self-Position Feedback

This work studies formation control of Multi-Agent Systems (MASs) where its formation size is scalable via a scaling factor (scalable formation). Past works on scalable formation are limited to either fixed undirected graph or fixed directed graph with k-rooted graph condition. This work proposes a new distributed algorithm for scalable formation based on self-position feedback. When agent is assumed to be able to measure its own position, the proposed algorithm is shown to work under directed switching graph. Under directed fixed graph setting, a distributed observer is designed such that only relative position is needed in the algorithm. Spanning tree condition on directed fixed graph setting is shown to be the necessary and sufficient condition to achieve the scalable formation.