## 2 Fundamental Models and Literature Search
### Planning Model
#### 2.2.1 Objectives  
1. **Travel length**[21; 22; 23; 24]: The consideration of travel length holds paramount significance in path planning for oceanic data collection. By strategically planning routes that minimize travel distance, various operational advantages are attainable. Firstly,  
Figure 5: Clustering network. reduced travel distances result in lower energy consumption for vehicles or sensor nodes, thereby prolonging their operational lifespan. Moreover, shorter travel distances enable faster data collection and response times, crucial for real-time monitoring and decision-making in applications such as environmental monitoring or disaster response. 2. **Energy consumption of nodes**[25; 26; 27]: Energy consumption of the network consists of three parts, the transmission energy \(E_{t}\), the receiving energy \(E_{r}\), and the idle energy \(E_{idle}\). \(E_{t}\) refers to the energy expended when nodes send data packets to each other. The amount of transmission energy used is influenced by factors such as the frequency at which data are transmitted and the distance between the devices. \(E_{r}\) refers to the energy used by nodes when they receive data packets from other nodes. The energy consumption for receiving depends on factors like the data rate, modulation schemes, and processing complexity. \(E_{idle}\) represents the energy consumed by nodes when they are not actively transmitting or receiving data packets. Even when nodes are not actively sending or receiving, they still use a certain amount of energy to maintain their operational state, listen for incoming messages, and stay connected to the network. This idle energy consumption is often referred to as \"quiescent\" or \"standby\" energy. For a more detailed model explanation, readers may refer to [28; 29]. Moreover, some scholars have expanded the energy consumption to network lifetime [30; 31]. This refers to the duration until the first node becomes non-operational. Consequently, the node exhibiting the most substantial energy consumption emerges as the pivotal factor influencing this lifespan. 3. **Energy consumption utility**[32]: The energy consumption utility parameter, denoted as \(\beta\), encapsulates the balance between energy consumption (\(E\)) and the cumulative network throughput (\(I\)). The quantification of \(E\) denotes the energy consumption of the sensor network, while the network throughput hinges on the magnitude of data packet transmission during the operational sequence. Fundamentally, \(\beta\) is calculated as the ratio of network throughput \(I\) to energy consumption \(E\). By encapsulating this trade-off, \(\beta\) provides a comprehensive measure of the network's efficiency in converting energy inputs into valuable data outputs. Rather than solely focusing on minimizing energy usage, optimizing the energy consumption utility leads to a greater proportion of energy being allocated to data transmission, ultimately enhancing overall efficiency. 4. **Data collection time/Collection delay**[26; 33; 34]: Collection delay is one of the most important optimization terms. In contrast to electromagnetic waves, the conveyance of underwater signals predominantly relies upon acoustic waves. However, the velocity of sound waves in an underwater environment is constrained to 1500 m/s. In order to ensure the quality of online data, the AMV needs to complete data collection tasks within a shorter timeframe. Evidently, the most straightforward approach involves increasing the AMV's velocity. Nevertheless, this method is hindered by the limitations imposed by water flow resistance and hardware capacities, and achieving such improvement could be challenging. Therefore, the most effective way to reduce data collection time is by optimizing the path length. Generally, data collection time comprises two components.