The multi-AUV time-varying formation reconfiguration control based on rigid-graph theory and affine transformation

Abstract

This paper studies the time-varying formation reconfiguration control for multiple underactuated autonomous underwater vehicles (AUVs) with an Euler–Lagrange-like model. The goal is to control a fleet of AUVs to achieve any desired formation shape using a distance-based graph rigidity and affine transformation (GR-AT) algorithm. Firstly, the distance-based graph rigidity with backstepping technology is utilized to solve the formation controlproblem, and we acquire the initial nominal formation. In the sequel, we transform the nominal formation into any desired formation shape using the properties of the affine transformation (including translation, scaling, rotation, shearing, or a combination of them). Even the geometric shapes formed can be constantly changed. The Lyapunov stability theory can ensure the uniform ultimate boundedness of whole distance errors. Finally, several simulation examples with formation reconfiguration are given to validate the efficacy of the designed control methods. Moreover, some experimental results are presented to confirm the validity and applicability of the scheme with four real bionic robot fish.