## 3 Collaborative AUVs
### Communication  
The rapid attenuation of higher frequency signals and the unstructured nature of the undersea environment make difficult to establish a radio communication system for AUVs. For those reasons, wireless transmission of signals underwater--especially for distances longer than 100 m--relies almost only on acoustic waves [14; 100]. Underwater acoustic communication using acoustic modems consists of transforming a digital message into sound that can be transmitted under water. The performance of these systems changes dramatically depending on the application and the range of operation [101]. The main factors to choose an underwater acoustic modem are:  
* Application: Consider the type and length of message (Command and control messages, voice messages, image streaming, etc.) frequency of operation and operating depth. * Cost: Depending on the complexity and performance, from some hundreds up to $50,000 (USD). * Size: Usually cylindrical, with lengths from 10 cm to 50 cm. * Bandwidth: Acoustic modems can perform underwater communication at up to some kb/s. Length of the message and time limitations must be considered
* Range: Range of operation for the vehicle's communication has impact on the cost of the system. Acoustic modems are suitable from short distances up to tens of km. Considerer than a longer range will increase the latency and power consumption of the system. * Power consumption: Depending on the range and modulation, the power consumption is in the range of 0.1 W to 1 W in receiving mode and 10 W to 100 W in transmission mode. Table 5 contains a few options of acoustic modems commercially available. The working principles of underwater acoustic communication can be described as follows [110]: First, information is converted into an electrical signal by an electrical transmitter. Second, after digital processing by an encoder, the transducer converts the electrical signal into an acoustic signal. Third, the acoustic signal propagates through the medium of water and propagates the information to the receiving transducer. In this case, the acoustic signal is converted into an electrical signal. Finally, after the digital signal is deciphered by the decoder, the information is converted to an audio, text or picture by the electrical receiver. Acoustic communications face many challenges, such as, small bandwidth, low data rate, high latency, and ambient noise [111]. These shortcomings might provoke that a cycle of communication in a collaborative mission take several seconds, or even more than a minute. Considering these, [PERSON] et al. [112] analyzed formation control protocols for multiple underwater vehicles in the presence of communication flaws and uncertainties. The error Port-Hamiltonian model about the desired trajectory was introduced and then, with the existence of relative information constraints or uncertainties, the formation control law was achieved by solving specific limitations of the linear matrix inequality problem. [PERSON] et al. [113] introduced a communication scheme between the AUVs and a unique representation of the overall vehicle state that limits message size. To limit data sent, every reported \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Max Bit Rate (bps)** & **Range (m)** & **Frequency Band (kHz)** \\ \hline Teledyne Benthos ATM-925 [102] & 360 & 2000–6000 & 9–27 \\ WHOI Micromodem [103] & 5400 & 3000 & 16–21 \\ Linkquest UWM 1000 [104] & 7000 & 350 & 27–45 \\ Evologics S2C R 48/78 [105] & 31,200 & 1000 & 48–78 \\ Sercel MATS 3G 34 kHz [106] & 24,600 & 5000 & 30–39 \\ L3 Oceania GPM-300 [107] & 1200 & 45,000 & Not specified \\ Tritech Micron Data Modem [108] & 40 & 500 & 20–28 \\ Bluerobotics Water Linked M64 & 64 & 200 & 100–200 \\ Acoustic Modem [109] & 64 & 200 & 100–200 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Commercial acoustic modems. position and path plan is encoded using a grid encoding scheme.