Distance + Angle-Based Control of 2-D Rigid Formations

A well-known problem with distance-based formation control is the existence of multiple equilibrium points not associated with the desired formation. This problem can be potentially mitigated by introducing an additional controlled variable. In this article, we generalize the distance + angle-based scheme for 2-D formations of single-integrator agents by using directed graphs and triangulation of the n-agent formation. We show that under certain conditions on the control gains and desired formation shape, our controller ensures the asymptotic stability of the correct formation for almost all initial agent positions.