Similar Formation Maneuver Control of Multi-ASV Systems via Complex Laplacian and Global Orientation Estimation

This article studies the problem of similar formation maneuver control of multiple autonomous surface vehicles (ASVs) via complex Laplacian, where the ASVs can perform translation, rotation, and scaling transformations, and the follower's reliance on global orientation measurement is removed. Specifically, we provide a simple solution to the similar formation control problem of ASVs in 2-D space. The formation patterns including translation, rotation, and scaling can be characterized by the null space of complex Laplacian associated with the network topology. Different from existing results, considering a spanning 2-tree topological structure, the potential singularity of nongeneric nominal configuration is eliminated. It is worth noting that most existing formation maneuver schemes rely on the sensing of global orientation information. To remedy this, utilizing the ingenious equation relationship between orientation and local bearing angle, we propose an orientation estimation algorithm to recover the unmeasured global orientation information by using inter-node local bearing measured, such that follower ASVs not equipped with a compass can still perform formation maneuver tasks. Theoretical analysis and hardware in-loop experiments validate the effectiveness of the proposed control scheme.