Coordinate-free formation stabilization based on relative position measurements

This paper presents a method to stabilize a group of agents moving in a two-dimensional space to a desired rigid geometric configuration. A common approach is to use information of relative interagent position vectors to carry out this specific control task. However, existing works in this vein either require the agents to express their measurements in a global coordinate reference, or generally fail to provide global stability guarantees. Our contribution is a globally convergent method that uses relative position information expressed in each agent’s local reference frame, and can be implemented in a distributed networked fashion. The proposed control strategy, which is shown to have exponential convergence properties, makes each agent move so as to minimize a cost function that encompasses all the agents in the team and captures the collective control objective. The coordinate-free nature of the method emerges through the introduction of a rotation matrix, computed by each agent, in the cost function. We consider that the agents form a nearest-neighbor communications network, and they obtain the required relative position information via multi-hop propagation, which is inherently affected by time-delays. We support the feasibility of such distributed networked implementation by obtaining global stability guarantees for the formation controller when these time-delays are incorporated in the analysis. The performance of our approach is illustrated with simulations.