# Bio-Inspired Design of an Underwater Robot Exploiting Fin Undulation Propulsion
## 1 Introduction  
In nature, a large variety of strategies for underwater locomotion have evolved over millions of years and have achieved optimal performances. Therefore, the design of autonomous underwater vehicles (AUVs) is a promising field of application for bioinspired engineering. Bioinspired AUVs are underwater robots that can be employed for several different tasks that require high maneuverability and great endurance. These features are typical of fishes or other swimming animals, which move with high energy efficiency and, thanks to their flexible bodies, can perform maneuvres with great agility [1]. The cownose ray (_Rhinoptera Bonasus_) is a median size fish that combines these capabilities; therefore, it is taken as a source of inspiration for the development of a robot mimicking its locomotion. Thanks to their high efficiency and to their agility, batoid fish locomotion has inspired the development of several underwater robots [1], which are briefly described in the following paragraph. Many robots that take inspiration from a batoid fish use a single actuator to move each fin, and undulatory motion is obtained with the passive flexibility of the fin itself. One such robot is the Manta ray robot developed by [PERSON] et al. [5], which features a large central body and rigid leading edges with support for the flexible fin membrane. The Robo-Ray II is composed of a flexible rubber exterior shell containing a rigid central part and pneumatic artificial muscles actuating the fins [6; 7]. Robo-Ray III, made by [PERSON] et al. [8; 9], is characterized by a central body equipped with control flaps for stability and a flexible membrane of silicone rubber. The robot ray developed by [PERSON] et al. [10] features a rigid central body containing two servomotors that actuate the bionic fins, which are thin foils with a rigid leading edge. Other robots use a single mechanism to move the fin, but they actuate two degrees of freedom: the flapping motion and the twist angle of the fin, so that, with an appropriate combination of the two motions, they are able to recreate the oscillating motion of the fin of a batoid fish. One example of this kind is the robot developed by [PERSON] et al. [11], whose fins are made from some flexible ribs covered by an elastic skin. The manta ray robot developed by [PERSON] et al. [12] exploits a very similar principle and integrates a rigid structure with flexible metal cables. The robot realized by [PERSON] et al. [13] has fins composed of a flexible elastomer, and they are actuated by an electroactive polymer beam, which performs both flapping and twisting motions. The Aqua Ray robot, made by [PERSON] [14], is actuated by hydraulic bionic fin muscles, and three antagonistic muscles give the robot the ability to flap and twist its fins to recreate an oscillatory motion. Finally, other robots have several independent mechanisms actuating each fin. Although wave propagation along the fins of a cownose ray is similar to the motion of a heaving and pitching aerofoil such that it can be reproduced with a flapping and twisting fin, having more independent mechanisms on each fin gives the possibility to modulate the wave propagation, enhancing the maneuverability of the robot. The MantaBot robot created by [PERSON] et al. [15; 16] has fins composed of tensegrity structures actuated by tensioned cables and surrounded by a flexible elastomer. RoMan-III [17] and RoMan-IV [18] have multiple fin ribs that actuate a flexible membrane, and the body is rigid with actuation motors along the side of the body. The bionic fish developed by [PERSON] et al. [19], which has its flexible fins actuated by several motors, accurately reproduces the travelling wave present on a cownose ray and it is featured by high maneuvrability.