Distance-Based Planar Formation Control using Orthogonal Variables

In this paper, we propose a novel approach to the problem of augmenting distance-based formation controllers with a secondary feedback variable for the purpose of preventing formation ambiguities. We introduce two variables that form an orthogonal space and uniquely characterize a triangular formation in two dimensions. We show that the resulting controller ensures the almost-global asymptotic stability of the desired formation for an $n$-agent system without conditions on the triangulations of the desired formation or control gains.