## 1 Introduction  
A significant part of the Earth is made of water provenience of lakes, rivers, and oceans, most of them still unexplored [1; 2; 3; 4]. Underwater robots have begun to revolutionize seabed exploration, generally providing better information at a lower cost. The propulsion system of an underwater robot ultimately defines the types of movements and maneuvers it can perform. In the design of propulsion systems, aspects such as energy consumption, robot hardware, and the effects on the marine environment should be considered [3]. Autonomous underwater vehicles (AUVs) are robots that navigate based on algorithms and surrounding information. They are equipped with multiple advanced sensors to carry out exploration, operations of intelligence, and reconnaissance, as well as maritime research and development [1; 2]. AUVs are important for oceanography for exploration and collecting data. There are a variety of vehicles with different sizes, shapes, working depth limits, energy sources, and methods of propulsion; about 155 unique configurations exist which are in different stages of development and are being used for scientific, commercial, oceanographic, and military applications [3; 4]. The main components of underwater vehicles [1; 4] are the cabin or hull, sensor systems, energy source, and the propulsion system. Communications systems are challenging for AUVs due to constraints not found in other environments; autonomous systems are based on acoustic sensors. [PERSON] et al. [5] described a review of different technologies used for underwater localization,communications, and navigation for these types of vehicles. The propulsion system allows movement in the aquatic environment. The more conventional propulsion systems mentioned in recent work are propellers, water gliders, injections, magnetohydrodynamic impellers, traction with the seabed, and bio-inspired systems. According to [PERSON] et al. [3], submarine robots can be classified by their level of autonomy, the type of mission to be performed, and their propulsion system. The mission for which a submarine robot is designed will define the type of sensors, actuators, and structure that it must possess. In underwater robotics, bio-inspired design is expected to improve energy efficiency, maneuverability, and stability [6]. Researchers have found propellers to be significant sources of pollution of underwater environments, increasing the mortality of marine creatures and ecosystem disturbances. On the other side, biomimetic robots harmonize with the environment and are expected to be quieter, more maneuverable, and provoke fewer accidents [7]. Natural selection ensures that the biological systems in fish evolve in their habitat and with their way of life. Their skills can inspire innovative designs to improve how man-made systems operate and interact with the aquatic environment [8]. Underwater living species have improved the ability to swim over millions of years of evolution to adapt to the environment [9]. Biomimetic AUVs (BAUVs) are based on fish physiology, having fins with a degree of freedom placed vertically or horizontally on the back of the underwater vehicle. In all designs published so far, the thrust is applied in only one direction. There are previous studies on BAUVs mimicking diverse types of fishes and locomotion systems. [PERSON] et al. [10] implemented a 3R-link mechanism to imitate the undulatory tail motion of a fish. An undulatory robot proposed by [PERSON] et al. [6] at project Fish Locomotion and Sensing (FILOSE), mimics a rainbow trout that adapts to the current flow due to its flexible body. [PERSON] et al. [11] developed a 2-link structure which presents an adaptive swimming behavior through the control of the tail beat frequency (TBF) and caudal amplitude (CA). A 4-bar mechanism was proposed by [PERSON] et al. [12], consisting of four links and two actuators, provoking the caudal fin movement. [PERSON] et al.