Maneuvering and Robustness Issues in Undirected Displacement-Consensus-Based Formation Control

In this article, we first propose a novel maneuvering technique compatible with displacement-consensus-based formation controllers. We show that the formation can be translated with an arbitrary velocity by modifying the weights in the consensus Laplacian matrix. In fact, we demonstrate that the displacement-consensus-based formation control is a particular case of our more general method. We then uncover robustness issues with undesired steady-state motions and resultant distorted shapes in undirected displacement-consensus-based formation control. In particular, these issues are triggered when neighboring agents mismeasure their relative positions, e.g., their onboard sensors are misaligned and have different scale factors. We will show that if all the sensing is close to perfect but different among the agents, then the stability of the system is compromised. Explicit expressions for the eventual nondesired velocity and shape's distortion are given as functions of the scale factors and misalignments for formations based on tree graphs.