Stable formations of self-propelled fish-like swimmers induced by hydrodynamic interactions

Flow interactions lead to self-organized flight formations disrupted by self-amplifying waves

Collectively locomoting animals are often viewed as analogous to states of matter in that group-level phenomena emerge from individual-level interactions. Applying this framework to fish schools and bird flocks must account for visco-inertial flows as mediators of the physical interactions. Motivated by linear flight formations, here we show that pairwise flow interactions tend to promote crystalline or lattice-like arrangements, but such order is disrupted by unstably growing positional waves. Using robotic experiments on "mock flocks" of flapping wings in forward flight, we find that followers tend to lock into position behind a leader, but larger groups display flow-induced oscillatory modes - "flonons" - that grow in amplitude down the group and cause collisions. Force measurements and applied perturbations inform a wake interaction model that explains the self-ordering as mediated by spring-like forces and the self-amplification of disturbances as a resonance cascade. We further show that larger groups may be stabilized by introducing variability among individuals, which induces positional disorder while suppressing flonon amplification. These results derive from generic features including locomotor-flow phasing and nonreciprocal interactions with memory, and hence these phenomena may arise more generally in macroscale, flow-mediated collectives.

Target-Following Control of a Biomimetic Autonomous System Based on Predictive Reinforcement Learning

Biological fish often swim in a schooling manner, the mechanism of which comes from the fact that these schooling movements can improve the fishes' hydrodynamic efficiency. Inspired by this phenomenon, a target-following control framework for a biomimetic autonomous system is proposed in this paper. Firstly, a following motion model is established based on the mechanism of fish schooling swimming, in which the follower robotic fish keeps a certain distance and orientation from the leader robotic fish. Second, by incorporating a predictive concept into reinforcement learning, a predictive deep deterministic policy gradient-following controller is provided with the normalized state space, action space, reward, and prediction design. It can avoid overshoot to a certain extent. A nonlinear model predictive controller is designed and can be selected for the follower robotic fish, together with the predictive reinforcement learning. Finally, extensive simulations are conducted, including the fix point and dynamic target following for single robotic fish, as well as cooperative following with the leader robotic fish. The obtained results indicate the effectiveness of the proposed methods, providing a valuable sight for the cooperative control of underwater robots to explore the ocean.

The role of hydrodynamics in collective motions of fish schools and bioinspired underwater robots

Collective behaviour defines the lives of many animal species on the Earth. Underwater swarms span several orders of magnitude in size, from coral larvae and krill to tunas and dolphins. Agent-based algorithms have modelled collective movements of animal groups by use of social forces, which approximate the behaviour of individual animals. But details of how swarming individuals interact with the fluid environment are often under-examined. How do fluid forces shape aquatic swarms? How do fish use their flow-sensing capabilities to coordinate with their schooling mates? We propose viewing underwater collective behaviour from the framework of fluid stigmergy, which considers both physical interactions and information transfer in fluid environments. Understanding the role of hydrodynamics in aquatic collectives requires multi-disciplinary efforts across fluid mechanics, biology and biomimetic robotics. To facilitate future collaborations, we synthesize key studies in these fields.

Learning to school in dense configurations with multi-agent deep reinforcement learning

Fish are observed to school in different configurations. However, how and why fish maintain a stable schooling formation still remains unclear. This work presents a numerical study of the dense schooling of two free swimmers by a hybrid method of the multi-agent deep reinforcement learning and the immersed boundary-lattice Boltzmann method. Active control policies are developed by synchronously training the leader to swim at a given speed and orientation and the follower to hold close proximity to the leader. After training, the swimmers could resist the strong hydrodynamic force to remain in stable formations and meantime swim in desired path, only by their tail-beat flapping. The tail movement of the swimmers in the stable formations are irregular and asymmetrical, indicating the swimmers are carefully adjusting their body-kinematics to balance the hydrodynamic force. In addition, a significant decrease in the mean amplitude and the cost of transport is found for the followers, indicating these swimmers could maintain the swimming speed with less efforts. The results also show that the side-by-side formation is hydrodynamically more stable but energetically less efficient than other configurations, while the full-body staggered formation is energetically more efficient as a whole.

How Non-Uniform Stiffness Affects the Propulsion Performance of a Biomimetic Robotic Fish

Live fish in nature exhibit various stiffness characteristics. The anguilliform swimmer, like eels, has a relatively flexible body, while the thunniform swimmer, like the swordfishes, has a much stiffer body. Correspondingly, in the design of biomimetic robotic fish, how to balance the non-uniform stiffness to achieve better propulsion performance is an essential question needed to be answered. In this paper, we conduct an experimental study on this question. First, a customized experimental platform is built, which eases the adjustment of the non-uniform stiffness ratio, the stiffness of the flexible part, the flapping frequency, and the flapping amplitude. Second, extensive experiments are carried out, finding that to maximize the propulsion performance of the biomimetic robotic fish, the non-uniform stiffness ratio is required to adapt to different locomotor parameters. Specifically, the non-uniform stiffness ratio needs to be reduced when the robotic fish works at low frequency, and it needs to be increased when the robotic fish works at high frequency. Finally, detailed discussions are given to further analyze the experimental results. Overall, this study can shed light on the design of a non-uniform biomimetic robotic fish, which helps to increase its propulsion performance.

Fluid-structure interaction of bio-inspired flexible slender structures: a review of selected topics

Flexible slender structures are ubiquitous in biological systems and engineering applications. Fluid-structure interaction (FSI) plays a key role in the dynamics of such structures immersed in fluids. Here, we survey recent studies on highly simplified bio-inspired models (either mathematical or mechanical) that aim to revealthe flow physics associated with FSI. Various models from different sources of biological inspiration are included, namely flexible flapping foil inspired by fish and insects, deformable membrane inspired by jellyfish and cephalopods, beating filaments inspired by flagella and cilia of microorganisms, and flexible wall-mounted filaments inspired by terrestrial and aquatic plants. Suggestions on directions for future research are also provided.

Stable Schooling Formations Emerge from the Combined Effect of the Active Control and Passive Self-Organization

This work presents a numerical study of the collective motion of two freely-swimming swimmers by a hybrid method of the deep reinforcement learning method (DRL) and the immersed boundary-lattice Boltzmann method (IB-LBM). An active control policy is developed by training a fish-like swimmer to swim at an average speed of 0.4 L/T and an average orientation angle of 0∘. After training, the swimmer is able to restore the desired swimming speed and orientation from moderate external perturbation. Then the control policy is adopted by two identical swimmers in the collective swimming. Stable side-by-side, in-line and staggered formations are achieved according to the initial positions. The stable side-by-side swimming area of the follower is concentrated to a small area left or right to the leader with an average distance of 1.35 L. The stable in-line area is concentrated to a small area about 0.25 L behind the leader. A detailed analysis shows that both the active control and passive self-organization play an important role in the emergence of the stable schooling formations, while the active control works for maintaining the speed and orientation in case the swimmers collide or depart from each other and the passive self-organization works for emerging a stable schooling configuration. The result supports the Lighthill conjecture and also highlights the importance of the active control.

Hydrodynamic advantages of in-line schooling

Fish benefit energetically when swimming in groups, which is reflected in lower tail-beat frequencies for maintaining a given speed. Recent studies further show that fish save the most energy when swimming behind their neighbor such that both the leader and the follower benefit. However, the mechanisms underlying such hydrodynamic advantages have thus far not been established conclusively. The long-standing drafting hypothesis-reduction of drag forces by judicious positioning in regions of reduced oncoming flow-fails to explain advantages of in-line schooling described in this work. We present an alternate hypothesis for the hydrodynamic benefits of in-line swimming based on enhancement of propulsive thrust. Specifically, we show that an idealized school consisting of in-line pitching foils gains hydrodynamic benefits via two mechanisms that are rooted in the undulatory jet leaving the leading foil and impinging on the trailing foil: (i) leading-edge suction on the trailer foil, and (ii) added-mass push on the leader foil. Our results demonstrate that the savings in power can reach as high as 70% for a school swimming in a compact arrangement. Informed by these findings, we designed a modification of the tail propulsor that yielded power savings of up to 56% in a self-propelled autonomous swimming robot. Our findings provide insights into hydrodynamic advantages of fish schooling, and also enable bioinspired designs for significantly more efficient propulsion systems that can harvest some of their energy left in the flow.

A numerical study of fish adaption behaviors in complex environments with a deep reinforcement learning and immersed boundary-lattice Boltzmann method

Fish adaption behaviors in complex environments are of great importance in improving the performance of underwater vehicles. This work presents a numerical study of the adaption behaviors of self-propelled fish in complex environments by developing a numerical framework of deep learning and immersed boundary-lattice Boltzmann method (IB-LBM). In this framework, the fish swimming in a viscous incompressible flow is simulated with an IB-LBM which is validated by conducting two benchmark problems including a uniform flow over a stationary cylinder and a self-propelled anguilliform swimming in a quiescent flow. Furthermore, a deep recurrent Q-network (DRQN) is incorporated with the IB-LBM to train the fish model to adapt its motion to optimally achieve a specific task, such as prey capture, rheotaxis and Kármán gaiting. Compared to existing learning models for fish, this work incorporates the fish position, velocity and acceleration into the state space in the DRQN; and it considers the amplitude and frequency action spaces as well as the historical effects. This framework makes use of the high computational efficiency of the IB-LBM which is of crucial importance for the effective coupling with learning algorithms. Applications of the proposed numerical framework in point-to-point swimming in quiescent flow and position holding both in a uniform stream and a Kármán vortex street demonstrate the strategies used to adapt to different situations.

Diving into a Simple Anguilliform Swimmer’s Sensitivity

Computational models of aquatic locomotion range from modest individual simple swimmers in 2D to sophisticated 3D multi-swimmer models that attempt to parse collective behavioral dynamics. Each of these models contain a multitude of model input parameters to which its outputs are inherently dependent, that is, various performance metrics. In this work, the swimming performance’s sensitivity to parameters is investigated for an idealized, simple anguilliform swimming model in 2D. The swimmer considered here propagates forward by dynamically varying its body curvature, similar to motion of a Caenorhabditis elegans. The parameter sensitivities were explored with respect to the fluid scale (Reynolds number), stroke (undulation) frequency, as well as a kinematic parameter controlling the velocity and acceleration of each upstroke and downstroke. The input Reynolds number and stroke frequencies sampled were from [450, 2200] and [1, 3] Hz, respectively. In total, 5000 fluid–structure interaction simulations were performed, each with a unique parameter combination selected via a Sobol sequence, in order to conduct global sensitivity analysis. Results indicate that the swimmer’s performance is most sensitive to variations in its stroke frequency. Trends in swimming performance were discovered by projecting the performance data onto particular 2D subspaces. Pareto-like optimal fronts were identified. This work is a natural extension of the parameter explorations of the same model from Battista in 2020.

Swimming Through Parameter Subspaces of a Simple Anguilliform Swimmer

Computational scientists have investigated swimming performance across a multitude of different systems for decades. Most models depend on numerous model input parameters and performance is sensitive to those parameters. In this article, parameter subspaces are qualitatively identified in which there exists enhanced swimming performance for an idealized, simple swimming model that resembles a Caenorhabditis elegans, an organism that exhibits an anguilliform mode of locomotion. The computational model uses the immersed boundary method to solve the fluid-interaction system. The 1D swimmer propagates itself forward by dynamically changing its preferred body curvature. Observations indicate that the swimmer’s performance appears more sensitive to fluid scale and stroke frequency, rather than variations in the velocity and acceleration of either its upstroke or downstroke as a whole. Pareto-like optimal fronts were also identified within the data for the cost of transport and swimming speed. While this methodology allows one to locate robust parameter subspaces for desired performance in a straight-forward manner, it comes at the cost of simulating orders of magnitude more simulations than traditional fluid–structure interaction studies.

Collective Behavior in Wild Zebrafish

Anthropogenic change is expected to alter environments at alarming rates. To predict the impact of modified environments on social behavior, we must study the relationship between environmental features and collective behavior in a genetically tractable model, zebrafish (Danio rerio). Here, we conducted a field study to examine the relationship between salient environmental features and collective behavior in four populations of zebrafish. We found zebrafish in flowing water formed volatile groups, whereas those in still water had more consistent membership and leadership. Groups in fast-flowing water were large (up to 2000 fish) and tightly knit with short nearest neighbor distances, whereas group sizes were smaller (11 fish/group) with more space between individual fish in still and slow-flowing water. These observations point to a possible profound role of water flow in influencing collective behavior in wild zebrafish.

CFD-based multi-objective controller optimization for soft robotic fish with muscle-like actuation

Soft robots take advantage of rich nonlinear dynamics and large degrees of freedom to perform actions often by novel means beyond the capability of conventional rigid robots. Nevertheless, there are considerable challenges in analysis, design, and optimization of soft robots due to their complex behaviors. This is especially true for soft robotic swimmers whose dynamics are determined by highly nonlinear fluid-structure interactions. We present a holistic computational framework that employs a multi-objective evolutionary method to optimize feedback controllers for maneuvers of a soft robotic fish under artificial muscle actuation. The resultant fluid-structure interactions are fully solved by using a novel fictitious domain/active strain method. In particular, we consider a two-dimensional elastic plate with finite thickness, subjected to active contractile strains on both sides of the body. Compared to the conventional approaches that require specifying the entire-body curvature variation, we demonstrate that imposing contractile active strains locally can produce various swimming gaits, such as forwarding swimming and turning, using far fewer control parameters. The parameters of a pair of proportional-integral-derivative (PID) controllers, used to control the amplitude and the bias of the active strains, respectively, are optimized for tracking a moving target involving different trajectories and Reynolds numbers, with three objectives, tracking error, cost of transport, and elastic strain energy. The resulting Pareto fronts of the multi-objective optimization problem reveal the correlation and trade-off among the objectives and offer key insight into the design and control of soft swimmers.

On the energetics and stability of a minimal fish school

The physical basis for fish schooling is examined using three-dimensional numerical simulations of a pair of swimming fish, with kinematics and geometry obtained from experimental data. Energy expenditure and efficiency are evaluated using a cost of transport function, while the effect of schooling on the stability of each swimmer is examined by probing the lateral force and the lateral and longitudinal force fluctuations. We construct full maps of the aforementioned quantities as functions of the spatial pattern of the swimming fish pair and show that both energy expenditure and stability can be invoked as possible reasons for the swimming patterns and tail-beat synchronization observed in real fish. Our results suggest that high cost of transport zones should be avoided by the fish. Wake capture may be energetically unfavorable in the absence of kinematic adjustment. We hereby hypothesize that fish may restrain from wake capturing and, instead, adopt side-to-side configuration as a conservative strategy, when the conditions of wake energy harvesting are not satisfied. To maintain a stable school configuration, compromise between propulsive efficiency and stability, as well as between school members, ought to be considered.

Numerical Simulation and Analysis of Fish-Like Robots Swarm

Artificial fish-like robot is an important branch of underwater robot research. At present, most of fish-like robot research focuses on single robot mechanism behavior, some research pays attention to the influence of the hydro-environment on robot crowds but does not reach a unified conclusion on the efficiency of fish-like robots swarm. In this work, the fish-like robots swarm is studied by numerical simulation. Four different formations, including the tandem, the phalanx, the diamond, and the rectangle are conducted by changing the spacing between fishes. The results show that at close spacing, the fish in the back can obtain a large wake from the front fish, but suffers large lateral power loss from the lateral fish. On the contrary, when the spacing is large, both the wake and pressure caused by the front and side fishes become small. In terms of the average swimming efficiency of fish swarms, we find that when the fish spacing is less than 1.25 L (L is the length of the fish body), the tandem swarm is the best choice. When the spacing is 1.25 L , the tandem, diamond and rectangle swarms have similar efficiency. When the spacing is larger than 1.25 L , the rectangle swarm is more efficient than other formations. The findings will provide significant guidance for the control of fish-like robots swarm.