Abstract
This article addresses the formation control of under-actuated multiple autonomous surface vehicles (MASVs) with input quantization under communication delay conditions, which is influenced by external marine disturbances and internal model uncertainties. A two-level distributed guidance and quantization control architecture based on the Nussbaum function is proposed. At the communication level, a time-delay distributed event-triggered extended state observer (ESO) is introduced to estimate the state of the single virtual leader, thereby further conserving communication resources. At the control level, the distributed formation guidance laws based on ESO are proposed in the kinematic subsystem, enabling effective tracking of the ideal trajectory while estimating the states of neighboring agents and unknown ocean disturbances. In the dynamics subsystem, a fuzzy logic system is used to estimate the uncertain terms within the model, and a linear model is introduced to handle the input quantization process. Additionally, the fuzzy adaptive quantization tracking control laws based on the Nussbaum function are proposed to achieve accurate tracking of the guidance signals and reduce actuator execution frequency, which makes the proposed scheme more applicable to practical marine engineering scenarios. The stability of the designed control structure is proven based on stability theory, and all signals within the closed-loop control system are uniformly ultimately bounded. Simulation experiments validate the rationality and effectiveness of the proposed method.