The goal of this document is to introduce a new method of constructing automatic vehicle formations, called the subdivision method, which uses the idea that vehicles in a formation are connected by ‘virtual springs,’ but breaks the global structure into several overlapping subdivisions. This method has benefits like reduced connectivity and capability for task hierarchy. In this document, we describe the method and investigate its advantages and demerits, through both theoretical and empirical lenses, under the specific condition of branchless chaining of subdivisions. We find that subdivided networks, compared to undivided ones, on the whole demonstrate poorer convergence and robustness to deformation under noise, but better noise absorption in a string stability sense. We also find that it is possible to adjust subdivision parameters to get performance close to that of undivided systems.
The structure of this document is as follows. In the first chapter, we motivate the problem of vehicle formation and highlight that of using virtual spring systems to establish interdependent artificial potentials. In the second chapter, we concretely define the concept of using subdivisions within the virtual spring system framework. In the third chapter, we explore the subdivision dynamics from the standpoints of equilibrium characteristics and local Lyapunov stability. In the fourth chapter, we perform parametric numerical tests of convergence performance and robustness to perturbation. In the fifth chapter, we bring together all results from previous chapters and evaluate the characteristics of the subdivided system as a whole. In the final chapter, we contemplate the usefulness of the subdivision method, and highlight some future work.