Growing optimally rigid formations

This work extends the theory on rigid frameworks for formation keeping in multi-agent systems. We introduce the H₂ performance measure for relative sensing networks where the underlying sensing graph is rigid. The first contribution shows that the optimal H₂ sensing graph must be a minimally rigid graph. We then describe a variation of the Herrenberg construction for generating rigid graphs in the plane by adding performance requirements and sensing constraints, leading to the H₂ optimal vertex addition and edge splitting procedures. These results are then used to derive a centralized algorithm for generating an H₂ optimally rigid relative sensing network.