Formation Shape Control with Minimal Global Rigidity

Distance-based formation control over minimally rigid graphs suffer from so-called flip ambiguities. We here show how such controllers over 2D minimally globally rigid graphs can be proven stable, thus, avoiding the ambiguities. The approach is demonstrated on a 5-agent system, and involves embedding the 2D formation in 3D space and introducing virtual 3D body coordinate frames for the agents. By translating two of these frames along the z-axis, the rigidity matrix is full row rank and a Lyapunov stability analysis can be used to show exponential convergence to the desired formation shape for almost all initial conditions. Simulations are include to illustrate the benefit of utilizing distance-based formation control with minimally globally rigid graphs.