Growing optimally rigid formations

Daniel Zelazo, Frank Allgöwer

Abstract: This work extends the theory on rigid frameworks for formation keeping in multi-agent systems. We introduce the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> performance measure for relative sensing networks where the underlying sensing graph is rigid. The first contribution shows that the optimal H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> 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 H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> optimal vertex addition and edge splitting procedures. These results are then used to derive a centralized algorithm for generating an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> optimally rigid relative sensing network.