Bearing-based Multi-Agent Formation Control: A Survey and Taxonomy

Formation control of multi-agent systems (MASs) using bearing measurements has attracted considerable attention in recent years. Compared to positions and displacements, bearing measurements contain the least information, which cost-effective sensors in many practical applications can easily measure. However, a critical challenge arises from the conflict between the achieved formation maneuvers and the incomplete observability of bearings, which lack distance information. Past surveys have primarily focused on methods based on static formation shapes, such as bearing rigidity, but lack a systematic overview of approaches through persistence of excitation (PE) variations in bearings over time. Thus, in this paper, we present a comprehensive survey and introduce a two-level taxonomy for bearing-based formation control methods of MASs. The taxonomy reveals that to achieve shape-invariant maneuvers or both shape-invariant and shape-varying maneuvers, the control methods need to steer the formation frameworks to satisfy rigidity (including bearing rigidity and angle rigidity) and PE (including agent-to-center PE, neighboring-pair PE, and entire-MAS PE) conditions, respectively. This guarantees the observability of the agents’ positions and hence the convergence of the formation tracking errors. We also review approaches that combine bearings with other measurements, organized by increasing flexibility of the achieved maneuvers. The survey also includes an overview of experimental platforms for bearing observation and discusses future challenges and directions in this field.