Formation Control and Network Localization via Orientation Alignment

We propose a formation control strategy based on inter-agent displacements for single-integrator modeled agents in the plane. Since the orientations of the local reference frames of the agents are not aligned with each other due to the absence of a common sense of orientation, the proposed strategy consists of an orientation alignment law and a formation control law. Under the proposed strategy, if the interaction graph is uniformly connected and all the initial orientation angles belong to an interval with length less than π, the orientations are exponentially aligned and the formation exponentially converges to the desired formation. We also show that the proposed strategy can be utilized for network localization as a dual problem.