Spatial barycentric coordinates based distributed formation control for multi-agent systems

Many applications of multi-agent systems have to execute some tasks in certain formations, while not all nodes have access to localization technologies such as GPS. This paper investigates the problem of formation control for multi-agent systems in three-dimensional space relying on distances between nodes and positions of anchor nodes. The position information of all nodes is represented using generalized spatial barycentric coordinates, and the condition that the formation shape can be uniquely represented by the barycentric coordinates is given. Then, based on this representation method, a distributed spatial formation algorithm is proposed to guide all agents from their initial positions towards the desired ones. Finally, simulation studies have been presented to validate the effectiveness and correctness of the proposed algorithm and design conditions.