## 3 Collaborative AUVs
### Collaborative Navigation  
Groups of AUVs can work together under different navigation schemes, which are generally parallel or leader-follower [110]. On a parallel formation (shown in Figure 15), all AUVs are equipped with the same systems and sensors, to locate and navigate themselves precisely and to communicate with its neighbor AUVs. In a leader-follower scheme (shown in Figure 16), leader AUV is equipped with high-precision instruments meanwhile follower AUVs are equipped with low-precision equipment [128]. Communication is only required between the vehicle leader and its followers, there is no need for the followers to communicate with each other. Figure 16: Leader-follower navigation of AUVs with AUV 1 as a leader of the formation. Figure 15: Parallel navigation of AUVs. The lower cost and the reduced communications needs make the leader-follower scheme the main navigation control method of AUVs. Its basic principles and algorithms are relatively mature [110]. However, unstable communications and communication delays are still challenging problems and need to be addressed. Since there are problems with signals when multiple systems emit at the same time, co-localization of AUVs is mostly based on time synchronization. However, time synchronization methods have some shortcomings such as the need for AUVs to go to surface to receive the synchronization signal. As an alternative, [PERSON] et al. [129] studied multi-AUVs collaborative navigation and positioning without time synchronization. Authors established a collaborative navigation positioning model for multi-AUVs and designed an EKF for collaborative navigation. This design only needs the time delay of the AUV itself and does not need to consider whether the AUV has synchronized with others. In simulated experiments, they compared the precision of their algorithm with a prediction model and results showed that, even when error increases over time, the precision of co-localization without time synchronization was higher. [PERSON] et al. [130] addressed the problems of leader-follower AUV formation control with model uncertainties, current disturbances, and unstable communication. The effectiveness of the method is simulated by tracking a spiral helix curve path with one leader AUV and four follower AUVs. Considering model uncertainties and current disturbances, a second-order integral AUV model with a nonlinear function and current disturbances was established. The simulation results showed that leader-follower AUV formation controllers are feasible and effective. After an adjustment period, all follower AUVs can converge to the desired formation structure, and the formation can keep tracking the desired path. [PERSON] et al. [131] focused on the problem of tracking control for multi-AUV systems and proposed an adaptive fuzzy-finite time control method. In this algorithm, algebraic graph theory is combined with a leader-follower architecture for describing the communication of the system. Then, the error compensation mechanism is introduced. Finally, the application of finite time and fuzzy logic system improves the convergence rate and the robustness of multi-AUV system. The effectiveness of the proposed algorithm was illustrated by simulation. Choosing the architecture of 4 AUVs including 1 leader and 3 followers. In order to avoid the unknown internal and external interferences, the algebraic graph theory and a fuzzy logic system technique are integrated into the distributed controllers. The simulation results demonstrate the effectiveness of the proposed algorithm and robustness of the multi-AUV system with a faster convergence speed compared with others algorithms. When AUVs navigate in closed formations, the delay between the transmission and reception of the acoustic signals represents a high risk. Therefore, a solution with a response time significantly faster must be explored. [PERSON] et al.