Bearing-only formation stabilization for three agents using elevation angles and area constraints

Recently, elevation angle-based formation control, which uses elevation angle constraints to define the desired formation shape, was proposed in the literature. The control laws in this approach only use bearing measurements in agents’ local frames and are thus coordinate-free. However, local stability was established for this approach. Also, using elevation angle constraints alone can lead to ordering ambiguity in the formation shape. In this paper, we propose the use of elevation angle constraints and area constraints to define the desired formation shape for three agent systems and present a bearing-only formation control law for the system. We establish almost global stability results for the three-agent system by introducing a gain parameter κ for the area error. We analyze the effect of this gain parameter and show that by choosing a sufficiently large κ, almost global stability result can be ensured for the three-agent system. Appropriate lower bound for κ is also derived for establishing almost global stability. Agents modeled as single and double integrators are considered in our analysis, and simulations are provided to validate the proposed algorithms.