Intersection between natural and artificial swimmers: a scaling approach to underwater vehicle design.

Approximately 72% of the Earth’s surface is covered by water, yet only 20% has been mapped [1]. Autonomous Underwater Vehicles (AUVs) are one of the main tools for ocean exploration. The demand for AUVs is expected to increase rapidly in the coming years [2], so there is a need for faster and more energy efficient AUVs. A drawback to using this type of vehicle is the finite amount of energy that is stored onboard in the form of batteries. Science and roboticists have been studying nature for ways to move more efficiently. Phillips et al. [3] presents data that contradicts the idea that fish are better swimmers than conventional AUVs when comparing the energetic cost of swimming in the form of the Cost of Transport (COT). The data presented by Phillips et al. only applies to AUVs at higher length and naval displacement (mass) scales, so the question arises of whether an AUV built at different displacements and length scales is more efficient than biological animals and if current bio-inspired platforms are better than conventional AUVs. Besides power requirements, it is also useful to compare the kinematic parameters of natural and artificial swimmers. In this case, kinematic parameters indicate how fast the swimmer travels through the water. Also, they describe how fast the propulsion mechanism must act to reach a certain swimming speed. This research adopts the approach of Gazzola et al. [4] where the Reynolds number is associated with a dimensionless number, Swim number (Sw) in this case, that has all the kinematic information. A newly developed number that extends the swim number to conventional AUVs is the Propulsion number (Jw), which demonstrates excellent agreement with the kinematics of conventional AUVs. Despite being functionally similar, Sw and Jw do not have a one-to-one relationship. Sw, Jw, COT represent key performance metrics for an AUV, herein called performance criteria, which can be used to compare existing platforms with each other and estimate the performance of non-existent designs. The scaling laws are derived by evaluating the performance of 229 biological animals, 163 bioinspire platforms, and 109 conventional AUVs. AUVs and bio-inspired platforms have scarce data compared with biological swimmers. Only 5% of conventional and 38% of bio-inspired AUVs have kinematic data while 30% of conventional and 18% of bio-inspired AUVs have energetic data. The low amount of performance criteria data is due to the nature of most conventional AUVs as commercial products. Only recently has the COT metric been included in the performance criteria for bio-inspired AUVs. For this reason, the research here formulates everything in terms of allometric scaling laws. This type of formulation is used extensively when referring to biological systems and is defined by an exponential relationship f (x) = axb, where x is a physical parameter of the fish or vehicle, like length or displacement. Scaling laws have the added benefit of allowing comparisons with limited data, as is the case for AUVs. The length and displacement scale (physical scale) must be established before estimating the performance criteria. Scale is primarily determined by the payload needed for a particular application. For instance, surveying the water column in deep water will require different scientific tools than taking images of an oyster bed in an estuary. There is no way to identify the size of an AUV until it is designed for that application, since these scientific instruments each have their own volume, length, and weight. A methodology for estimating physical parameters using computer vision is presented to help determine the scale for the vehicle. It allows accurate scaling of physical parameters of biological and bio-inspired swimmers with only a side and top view of the platform. A physical scale can also be determined based on the vehicle’s overall volume, which is useful when determining how much payload is needed for a particular application. Further, this can be used in conjunction with 3D modeling software to scale nonexistent platforms. Following the establishment of a physical scale, which locomotion mode would be most appropriate? Unlike conventional AUVs that use propeller or glider locomotion, bio-inspired platforms use a variety of modes. Kinematics and energy expenditures are different for each of these modes. For bio-inspired vehicles, the focus will be on the body-caudal fin (BCF) locomotion, of which four types exist: anguilliform, carangiform, thunniform, and ostraciiform. There is ample research on anguilliform and carangiform locomotion modes, but little research on thunniform and ostraciiform modes. In order to determine which locomotion mode scales best for a bio-inspired AUV, this research examines the power output and kinematic parameters for all four BCF modes. In order to achieve this, computational fluid dynamics simulations are performed on a 2D swimmer for all four modes. Overset meshes are used in lieu of body-fitted meshes to increase stability and decrease computational time. These simulations were used to scale output power over several decades of Reynolds numbers for each locomotion mode. Carangiform locomotion was found to be the most energy efficient, followed by anguilliform, thunniform, and ostraciiform. In order to utilize the above scaling laws in designing a novel platform, or comparing an existing one, there must be a unifying framework. The framework for choosing a suitable platform is presented with a case study of two bio-inspired vehicles and a conventional one. The framework begins by determining how the platform can be physically scaled depending on the payload. Based on the physical scale and derived scaling laws, it then determines performance criteria. It also describes a method for relative cost scaling for each vehicle, which is not covered in the literature. The cost scaling is based on the assumption that all payloads and materials are the same. The case study shows that a conventional AUV performs better on all performance criteria and would cost less to build