## 1 Introduction  
With the increasing demand to discover, study, utilize, and explore the underwater world, underwater IoT technology has become necessary to satisfy these human goals [1]. To satisfy these purposes, the autonomous underwater vehicle (AUV) was developed to operate and navigate in underwater environments without the need for human control [2]. AUVs are used for many purposes, such as exploring underwater depths, research, rescue, underwater safety, and underwater equipment maintenance and repair [3]. While AUVs perform their tasks, they may have to navigate close to the seabed. In this case, AUVs can be affected by undesirable and rapidly changing hydrodynamic forces and moments due to the bottom effect. For this reason, AUVs should have good hydrodynamic performance. Therefore, these UAVs, in order to be able to position themselves in a very short time and follow the determined trajectory, should perform these maneuvers quickly and with the lowest tracking error [4]. AUVs are supplied with different sensors, like sonar, cameras, pH sensors, fluorometers, magnetometers, and so on. Whether the data collected by UAVs are on the sea surface or deep in the ocean, the data can be either stored within the UAV or transmitted to other station vehicles on the sea surface [2]. One traditional technique to transfer data between UAVs and sea-surface stations is to use cables as a communication link. However, this technique is limited in range and degree of motion freedom. Therefore, the remote transmission of data is required. In underwater environments, radio signals are not suitable due to the limited range of radio frequencies. Instead, acoustic waves are leveraged in underwater communications since they can travel for longer distances [5]. However, compared with radio waves, acoustic waves have more latency and lower speed. Therefore, unique innovations and techniques have appeared in the operation and design of underwater IoT systems due to this essential difference in the communication medium. Energy efficiency is one of the critical issues and challenging problems, especially for the application used in this study, where the UAV works to navigate deep in the ocean to collect data from the nodes and transmit them to the station on the sea surface due to the fact that underwater nodes are battery-operated and difficult to recharge. Moreover, acoustic transceivers consume significantly more power than radio transceivers [5]. However, the energy consumption resulting from the navigation of UAVs is significant and dominant. Therefore, the optimization of trajectory planning is the key to minimizing the energy consumption of AUVs during their navigation and tour deep in the ocean based on data collection approaches. This study has addressed the problem of data collection by an underwater cruiser (AUV) and returning the data to a station ship on the sea surface. The scenario can be described as follows:  
* The UAV starts its tour from the ship station, and it sinks deep into the ocean to visit many nodes distributed randomly in the volumetric space of the ocean. * The nodes represent sensors devoted to recording real data in the ocean. These node sensors communicate the data to the underwater cruiser when the cruiser arrives within the prescribed or suitable distance from the node. * The UAV tries to visit all the nodes and return to the surface ship station along the shortest (optimal) path. * The power consumption due to the AUV's tour is of course directly related to the length of the navigation path. Accordingly, to minimize power consumption, an optimization technique can be considered to generate the optimal path based on the configuration space of the node position. This optimal path has to be followed by an underwater cruiser such that it has to visit and collect data from all nodes and then go back to the station.