## 2 Underwater Locomotion  
Marine environments can seem extraterrestrial for humans at times. Hence, the study of the locomotion techniques and the morphology of aquatic creatures is essential. These types of biological studies offer insights providing keys toward the successful mimicry of these marine creatures. The aquatic environment plays a large role in defining the types of underwater locomotion, as governed by the four main forces acting on bodies underwater [15]: vertical weight and buoyancy alongside hydrodynamic lift, and horizontal thrust and drag (Figure 1a). Fish are able to generate lift and thrust in order to swim. They can achieve swimming using their fins or swimming propulsors (Figure 1b). According to the motion of these fins, fish swimming methods can be classified into several categories.  
The two main categorizations of fish motion are based on which fins are performing the bending motion and the frequency at which the fins move. In terms of the first category, fish use their body and/or caudal fin to generate thrust (BCF). Examples include carangiform and anguilliform such as tuna and eel. Other types of fish use their median and/or paired fins (MPF). Examples include rajiform and labriform such as batoids. The frequency of movement of the fish's body and fins indicates whether the motion is undulatory or oscillatory. During undulatory motion, the fish's body performs a wave-shaped pattern, whereas oscillatory swimming uses only swivel-like motion.  
Additional underwater locomotion modes fall outside the previous categorizations [16]. One example is the jet propulsion performed by jellyfish, octopus, and squid. Drag-induced swimming is exhibited by turtles as they generate thrust by moving their flippers in the opposing direction of motion. Friction-based crawling is performed by crustaceans, and echinoderms such as starfish use adhesive-based crawling.  
In terms of assessing swimming performance, one of the most important metrics is the swimming speed of fish and, in particular, the critical swimming speed (\(U_{L}rit\)), which is commonly measured in centimeters per second (cm/s) or body lengths per second (BL/s) [17; 18]. One of the main factors that affects fish swimming speed is the tail beat frequency in Hertz (Hz). It relates to the fish's velocity through the stride length, which is the distance traveled by the fish per tail beat, expressed as ratio of the body length (L) [19; 20]. The Reynolds number (Re) and Strouhal number (St) are also important factors to assess the hydrodynamic performance of the fish's swimming. Several robotic fish platforms inspired from actual fish morphology and swimming, such as tuna, use the same metrics to assess their robots' performance [13; 21; 22; 23]. Another important factor is to analyze the efficiency of fish propulsion. However, it is hard to establish an accurate measure of propulsive efficiency for real biological fish. In general, efficiency is defined as the ratio of useful output to total input. For a self-propelled body, the measure of such work depends on the drag the body needs to overcome to move, which is hard to quantify as it differs with the shape of the body, as well as the body-propulsor hydrodynamics [24]. It is also challenging to determine input power in fish, which relates to muscle shaft power and the fish's metabolism and oxygen (fuel) consumption [25]. A common metric used to quantify the fitness of fish and their efficiency is the cost of transport (COT), defined as the energy expended per traveled distance. The COT is a good indication of the fish's swimming efficiency, and there have been several attempts to define and normalize COT for fish propulsive efficiency [24; 26; 27; 28].