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This study proposes a new distributed control method based on an adaptivefuzzy control for multiple collaborative autonomous underwater vehicles (AUVs)to track a desired formation shape within a fixed time. First, a formationcontrol protocol based on a fixed-time backstepping sliding mode control isdesigned, in which the consensus cooperative tracking errors for each AUV willbe formulated. Then, to compensate for the saturated control torques, anadaptive auxiliary variable is introduced. Finally, a fixed-time adaptive fuzzylogic control (FLC) is derived to approximate the unknown dynamics, in whichthe adaptive laws of the FLC is derived such that the adaptive signals anderrors can be convergent within a fixed time. The fixed time convergence isdesired in practice because it provides an exciting property that the globalconvergence of the whole system is independent with the initial states of theAUVs. The computer simulation results for a consensus formation control of fourAUVs show that the proposed formation control can provide high trackingperformance with lower and smoother control efforts

Distributed Fixed-Time Consensus Control for Multiple AUV Systems with Input Saturations