## 1 Introduction
In [25], the researchers designed a method of formation control that combines CNN-LSTM (Convolutional Neural Networks-Long Short-Term Memory) prediction and backsteps sliding mode control to overcome hydroacoustic communication constraints in the multi-AUV leader-follower formation. In [26], the researchers transformed the nonlinear AUV model into a second-order integral model via feedback linearization. They designed finite-time sliding-mode disturbance observers for unknown disturbances in the ocean and then estimated the unknown disturbances in finite time. In [27], a fixed-time terminal sliding mode control method was designed for a class of second-order nonlinear systems with unknown dynamics and perturbations. The results of this study were subsequently applied in [28] to achieve consistency control. To enhance convergence speed, [PERSON] et al. [29] improved the fixed-time stable system proposed in [27] by deriving a smaller upper bound for convergence time. They then applied the result to the second-order system discussed in [30], considering the input delay problem, and designed a fixed-time control strategy by using the leader-following mechanism. Building upon the abovementioned work, ref. [31] further improved the convergence speed and investigated a solution for handling the singularity problem of the sliding mode surface. References [30; 32; 33] transform the delay error system into a second-order system without delay for double integral and first-order linear multi-agent systems with determined input delay, and they use the fixed-time reaching law to achieve fixed-time consistency. In [34], the focus shifts to predicting the future time states of time-varying input delay single integral systems while carefully considering the uncertainties inherent in the transformed systems. Here, nonlinear fixed-time formation protocols for multi-robot systems in both directed and undirected topologies are proposed. In addition, in [33], drawing inspiration from the integral predictor in [35], a predictor was designed to predict the future state for a first-order nonlinear multi-agent system characterized by uniformly fixed input delay and uncertainties. Ref. [36] investigated the cooperative trajectory tracking (CTT) control problem of multiple autonomous underwater vehicles (AUVs), and designed a neural network-based data-driven control algorithm and used the radial basis function neural network to estimate the primary pseudo parameters. Ref. [37] developed a new MRMP (Multi-Robot Motion Planning) algorithm. The fitness for these variants was also measured for simulations where different target motion models were used when calculating the fitness function, highlighting the improved performance when using actual target motion models. Ref. [38] studied a novel reference filter for the Formation Keeping (FK) of multiple AUVs; the FK objectives were treated as servo-constraints. The reference values for the motion control can be directly computed using the Udwadia-Kalaba equation. A low-level Model Predictive Control (MPC) is assumed to be embedded to each agent. The existing limitations in their communication are also considered. Results verified the trajectory tracking and disturbance rejection, with low constraint violations. Ref. [39] studied a group of heterogeneous AUV systems with intermittent communication links being considered, as well as a finite-time trajectory-tracking control strategy; a distributed trajectory-tracking controller was designed using the states estimated by the intermittent communication network, even without velocity measurements. A homogeneous technique was utilized to prove that all followers can track the leader in a finite time. Finally, the effectiveness of the developed finite-time tracking control strategy is illustrated by numerical simulations. Ref. [40] addresses significant control challenges, including external disturbances, noise, model uncertainties, actuator faults, stochastic switching topologies, time-varying communication delays, and positional information between agents.