Session A13: Biological Fluid Dynamics: Locomotion I

Robotic Implementation of Online Deep Reinforcement Learning for Autonomous Underwater Navigation

In many robotic applications such as ocean surveying, robots must navigate autonomously in the presence of background flow fields using onboard sensors. Here, we investigate the application of deep reinforcement learning (RL) to discover efficient navigation policies in both simulated and physical environments. Inspired by the wide variety of flow-based navigation techniques found in nature, we compare flow sensing strategies for navigating in a 2D, unsteady simulated flow field, and find that velocity sensors yield highly successful and robust navigation policies. To investigate the real-world feasibility of this deep RL approach, we developed a palm-sized robotic swimmer that can learn online and autonomously. The deep neural network that controls the robot's actions is trained onboard using a high-speed microcontroller. Equipped with sensors, the robot is tasked with learning how to navigate in a 6'x6'x18' water tank.   

Marine copepod behavior responses in and near internal waves

The objective of this study is to provide insight to the bio-physical interaction and the role of biological versus physical forcing in mediating organism distributions in and near internal waves. A laboratory-scale configuration is presented with a density jump of 1 σ_t. Theoretical analysis of the two-layer system provided guidance to the target forcing frequency needed to generate a standing internal wave with a single dominant frequency of oscillation.  The results show a close match to the target wave parameters.  Marine copepod (mixed population of Acartia tonsa, Temora longicornis, and Eurytemora affinis) behavior assays were conducted for three different physical arrangements: (1) no density stratification (i.e. control), (2) stagnant two-layer density stratification, and (3) two-layer density stratification with internal wave motion.  Digitized trajectories of copepod swimming behavior indicate that in the control (case 1) the animals showed no preferential aggregation.  In the stagnant density jump treatment (case 2) copepods preferentially moved horizontally, parallel to the density interface.  In the internal wave treatment (case 3) copepods demonstrated loopy, orbital trajectories near the density interface.  Noted differences with simulated trajectories and a consideration of the potential hydrodynamic cues indicate that copepod behavior response has a substantial influence on the swimming trajectories in the internal wave region.   

A vortex sheet-based hydrodynamic model of fish swimming

Hydrodynamic models of fish can help elucidate a range of swimming phenomena, such as schooling and rheotaxis. Particularly enticing is the vortex dipole model, which offers an elegant representation of the flow physics at a modest computational cost. The model assumes the flow to be incompressible, irrotational, and inviscid, while the fish is treated as a dipole consisting of a pair of point vortices of equal and opposite strength. Despite its technical value and promise, this modeling paradigm does not fully capture major characteristics of the flow field around a swimming fish, featuring a high velocity region in the wake and the emergence and advection of local vorticities. To address these limitations, we explore an alternative hydrodynamic model, in which we explicitly take into consideration the wake generated by fish. Specifically, the time-averaged flow surrounding the fish is modeled as a pair of vortex sheets with spatially decaying strength, separated by a finite distance. The parameters of each vortex sheet and the distance between the sheets are determined by calibrating on a numerical simulation of a fish swimming in a channel. We demonstrate the feasibility of the proposed modeling scheme in the study of hydrodynamic interactions between multiple fish.   

Benefits of concurrent metachronal cycles as observed in Americamysis bahia

Studies of metachronal swimming in crustaceans have previously focused on organisms whose pleopods on the same abdominal segment beat in tandem with each other resulting in one, 5-paddle metachronal stroke. In contrast, the mysid shrimp Americamysis bahia’s pleopods on the same abdominal segment beat independently of each other resulting in a metachronal stroke comprised of two, 5-paddle metachronal cycles that are 180° out-of-phase with each other running the length of the body. Free-swimming A. bahia were recorded with high-speed cameras to obtain high-resolution data of pleopod kinematics and resulting swimming behavior. Although A. bahia primarily rely on their thoracic appendages for swimming, they occasionally use their pleopods to achieve swim speeds up to 12 body lengths per second. Time series of speed during one metachronal stroke in 5-paddle euphausiids show a periodic increase corresponding to the power stroke of the longest paddle. This phenomena is absent in A. bahia suggesting that more paddles in a metachronal stroke result in smoother swimming. A. bahia also achieve faster normalized swim speeds than euphausiids and analysis of non-dimensional parameters, including Strouhal number and advance ratio, indicate that pleopodal swimming in A. bahia is tuned to achieve normalized swim speeds greater than 9 body length per second.

On the Varying Tail-Beat Frequency in High-Density Fish School

Fish schooling has been studied thoroughly in order to understand their physical strengths and benefits. It has been proven that schooling creates a hydrodynamic benefit for individual fish in a school as well as providing protection from predators.  In this study, numerical simulations utilizing an immersed-boundary-method-based incompressible Navier-Stokes flow solver are used to investigate the impact of undulation frequency on two-dimensional fish-like bodies swimming with carangiform locomotion in a high-density diamond-shaped school. Frequencies were selected to range from 0.46 to 1.11 Hz. This research analyzes the impact on individual fish performance as well as overall school average values by examining thrust coefficient, power coefficient, and propulsive efficiency. As the undulation frequency of the school is increased, the results come to a peak efficiency that the school can operate at. As the frequency continues to increase, the thrust and power consumption significantly increases while the average propulsive efficiency decreases due to the affected downstream momentum and wake structure of the school. The insights revealed from this study will contribute to a better understanding of physical mechanisms used by fish schools as well as providing new information to be used for bio-inspired underwater swarm robots.   

Optimal elastic filaments for viscous propulsion

Oscillating elastic slender filaments are used as a mode of swimming by many eukaryotic cells, thus inspiring the design of many different artificial microswimmers. The time-varying shape of the elastic filament is what determines the efficiency of its viscous propulsion, and that shape depends critically on the spatial distribution of the bending rigidity along the filament. In this talk, we discuss the optimal designs of elastic filaments (i.e. their optimal bending rigidity) that maximise their propulsive forces under different geometrical constraints.   

Surfing Turbulence: a strategy for plankton navigation

We explain how microswimmers, such as planktonic organisms, can use a local measure of velocity

gradients of the flow to navigate efficiently in complex 3D flows. Following the observation that

despite its chaotic properties turbulence present exploitable correlation times, we derive an analytic

strategy, solution of a local optimum, that we test in simulated 3D homogeneous isotropic turbulence.

Given a fixed target direction, this strategy allows microswimmers to surf the surrounding flow and

increase their velocity along this direction, up to 100% in best cases. Best results are obtained for

low swimming velocities (of the order of the Kolmogorov velocity) that are in agreement with

various biological plankton species swimming velocities.   

Brachistochronous motion of a flat plate parallel to its surface immersed in a fluid

We determine the globally minimum time T needed to translate a thin submerged flat plate a given distance parallel to its surface within a work budget. The Reynolds number for the flow is assumed to be large so that the drag on the plate arises from skin friction in a thin viscous boundary layer. The minimum is determined using a steepest descent, where an adjoint formulation is used to compute the gradients. Because the equations governing fluid mechanics for this problem are nonlinear, multiple local minima could exist. Exploiting the quadratic nature of the objective function and the constraining differential equations, we derive and apply a "spectral condition" to show the converged local optimum to be a global one. The condition states that the optimum is global if the Hessian of the Lagrangian in the state variables constructed using the converged adjoint field is positive semi-definite at every instance. The globally optimum kinematics of the plate starts from rest with speed proportional to t^1/4 and comes to rest with speed proportional to (T-t)^1/4 as a function of time t. For distances much longer than the plate, the work-minimizing kinematics consists of an optimum startup, a constant-speed cruising, and an optimum stopping.   

Not Participating

An experimental set-up has been designed to study the propulsive performance of a pitching symmetric foil near the water free surface. The system is actuated by a servo that rotates sinusoidally with different amplitudes and frequencies. Kinematics are measured using a precision potentiometer, whilst a six-axis load cell and a torque sensor provide hydrodynamic loads. A time resolved Particle Image Velocimetry system is used to study the flow generated by the moving foil in two planes, one parallel to the trailing edge and another perpendicular to the rotating shaft.

 

We will show how thrust, side force, power and efficiency, are influenced by the proximity of the foil to the free surface, by adjusting the gap between the upper edge of the foil and the water surface. The gap is varied from a condition in which there is virtually no influence of the free surface, to a point at which the upper edge of the foil is at the free surface. The interactions that take place at the free surface alter substantially the performance of the system.