Surrounding formation of star frameworks using bearing-only measurements

In this paper, the novel surrounding formation protocol around a beacon is proposed using bearing-only formation. In the surrounding formation problem, all agents surround the beacon such that all the relative angles between some pairs of agents and the beacon satisfy predefined relative angles. Moreover, each agent senses and controls only its direction to the beacon in its local coordinate frame without knowledge of common global coordinate system. We propose an orientation estimator by adding an auxiliary variable which is assumed to be communicated by agents. A bearing-only based control law is proposed using the auxiliary variables. We show that the desired surrounding formation is almost globally asymptotically stable based on input-to-state stability theory. Further, under the proposed control law, the surrounding formation is collision-free under an assumption of initial positions. Numerical simulations are provided to support the proposed control method.