Tunabot Flex: a tuna-inspired robot with body flexibility improves high-performance swimming

Gradients of properties increase the morphing and stiffening performance of bioinspired synthetic fin rays

State-of-the-art morphing materials are either very compliant to achieve large shape changes (flexible metamaterials, compliant mechanisms, hydrogels), or very stiff but with infinitesimal changes in shape that require large actuation forces (metallic or composite panels with piezoelectric actuation). Morphing efficiency and structural stiffness are therefore mutually exclusive properties in current engineering morphing materials, which limits the range of their applicability. Interestingly, natural fish fins do not contain muscles, yet they can morph to large amplitudes with minimal muscular actuation forces from the base while producing large hydrodynamic forces without collapsing. This sophisticated mechanical response has already inspired several synthetic fin rays with various applications. However, most 'synthetic' fin rays have only considered uniform properties and structures along the rays while in natural fin rays, gradients of properties are prominent. In this study, we designed, modeled, fabricated and tested synthetic fin rays with bioinspired gradients of properties. The rays were composed of two hemitrichs made of a stiff polymer, joined by a much softer core region made of elastomeric ligaments. Using combinations of experiments and nonlinear mechanical models, we found that gradients in both the core region and hemitrichs can increase the morphing and stiffening response of individual rays. Introducing a positive gradient of ligament density in the core region (the density of ligament increases towards the tip of the ray) decreased the actuation force required for morphing and increased overall flexural stiffness. Introducing a gradient of property in the hemitrichs, by tapering them, produced morphing deformations that were distributed over long distances along the length of the ray. These new insights on the interplay between material architecture and properties in nonlinear regimes of deformation can improve the designs of morphing structures that combine high morphing efficiency and high stiffness from external forces, with potential applications in aerospace or robotics.

A Fast Online Elastic-Spine-Based Stiffness Adjusting Mechanism for Fishlike Swimming

Fish tunes fishtail stiffness by coordinating its tendons, muscles, and other tissues to improve swimming performance. For robotic fish, achieving a fast and online fishlike stiffness adjustment over a large-scale range is of great significance for performance improvement. This article proposes an elastic-spine-based variable stiffness robotic fish, which adopts spring steel to emulate the fish spine, and its stiffness is adjusted by tuning the effective length of the elastic spine. The stiffness can be switched in the maximum adjustable range within 0.26 s. To optimize the motion performance of robotic fish by adjusting fishtail stiffness, a Kane-based dynamic model is proposed, based on which the stiffness adjustment strategy for multistage swimming is constructed. Simulations and experiments are conducted, including performance measurements and analyses in terms of swimming speed, thrust, and so on, and online stiffness adjustment-based multistage swimming, which verifies the feasibility of the proposed variable stiffness robotic fish. The maximum speed and lowest cost of transport for robotic fish are 0.43 m/s (equivalent to 0.81 BL/s) and 7.14 J/(kg·m), respectively.

Toward the Intelligent, Safe Exploration of a Biomimetic Underwater Robot: Modeling, Planning, and Control

Safe, underwater exploration in the ocean is a challenging task due to the complex environment, which often contains areas with dense coral reefs, uneven terrain, or many obstacles. To address this issue, an intelligent underwater exploration framework of a biomimetic robot is proposed in this paper, including an obstacle avoidance model, motion planner, and yaw controller. Firstly, with the aid of the onboard distance sensors in robotic fish, the obstacle detection model is established. On this basis, two types of obstacles, i.e., rectangular and circular, are considered, followed by the obstacle collision model's construction. Secondly, a deep reinforcement learning method is adopted to plan the plane motion, and the performances of different training setups are investigated. Thirdly, a backstepping method is applied to derive the yaw control law, in which a sigmoid function-based transition method is employed to smooth the planning output. Finally, a series of simulations are carried out to verify the effectiveness of the proposed method. The obtained results indicate that the biomimetic robot can not only achieve intelligent motion planning but also accomplish yaw control with obstacle avoidance, offering a valuable solution for underwater operation in the ocean.

Hydrodynamic analysis of fin-fin interactions in two-manta-ray schooling in the vertical plane

This study investigates the interaction of a two-manta-ray school using computational fluid dynamics simulations. The baseline case consists of two in-phase undulating three-dimensional manta models arranged in a stacked configuration. Various vertical stacked and streamwise staggered configurations are studied by altering the locations of the top manta in the upstream and downstream directions. Additionally, phase differences between the two mantas are considered. Simulations are conducted using an in-house developed incompressible flow solver with an immersed boundary method. The results reveal that the follower will significantly benefit from the upstroke vortices (UVs) and downstroke vortices depending on its streamwise separation. We find that placing the top manta 0.5 body length (BL) downstream of the bottom manta optimizes its utilization of UVs from the bottom manta, facilitating the formation of leading-edge vortices (LEVs) on the top manta's pectoral fins during the downstroke. This LEV strengthening mechanism, in turn, generates a forward suction force on the follower that results in a 72% higher cycle-averaged thrust than a solitary swimmer. This benefit harvested from UVs can be further improved by adjusting the phase of the top follower. By applying a phase difference ofπ/3to the top manta, the follower not only benefits from the UVs of the bottom manta but also leverages the auxiliary vortices during the upstroke, leading to stronger tip vortices and a more pronounced forward suction force. The newfound interaction observed in schooling studies offers significant insights that can aid in the development of robot formations inspired by manta rays.

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.

Design and Analysis of a Novel Bionic Tensegrity Robotic Fish with a Continuum Body

Biological fish exhibit remarkable adaptability and exceptional swimming performance through their powerful and flexible bodies. Therefore, designing a continuum flexible body is significantly important for the development of a robotic fish. However, it is still challenging to replicate these functions of a biological body due to the limitations of actuation and material. In this paper, based on a tensegrity structure, we propose a bionic design scheme for a continuum robotic fish body with a property of stiffness variation. Its detailed structures and actuation principles are also presented. A mathematical model was established to analyze the bending characteristics of the tensegrity structure, which demonstrates the feasibility of mimicking the fish-like oscillation propulsion. Additionally, the stiffness variation mechanism is also exhibited experimentally to validate the effectiveness of the designed tensegrity fish body. Finally, a novel bionic robotic fish design scheme is proposed, integrating an electronic module-equipped fish head, a tensegrity body, and a flexible tail with a caudal fin. Subsequently, a prototype was developed. Extensive experiments were conducted to explore how control parameters and stiffness variation influence swimming velocity and turning performance. The obtained results reveal that the oscillation amplitude, frequency, and stiffness variation of the tensegrity robotic fish play crucial roles in swimming motions. With the stiffness variation, the developed tensegrity robotic fish achieves a maximum swimming velocity of 295 mm/s (0.84 body length per second, BL/s). Moreover, the bionic tensegrity robotic fish also performs a steering motion with a minimum turning radius of 230 mm (0.68 BL) and an angular velocity of 46.6°/s. The conducted studies will shed light on the novel design of a continuum robotic fish equipped with stiffness variation mechanisms.

Fish can use coordinated fin motions to recapture their own vortex wake energy

During swimming, many fishes use pectoral fins for propulsion and, in the process, move substantial amounts of water rearward. However, the effect that this upstream wake has on the caudal fin remains largely unexplored. By coordinating motions of the caudal fin with the pectoral fins, fishes have the potential to create constructive flow interactions which may act to partially recapture the upstream energy lost in the pectoral fin wake. Using experimentally derived velocity and pressure fields for the silver mojarra (Eucinostomus argenteus), we show that pectoral-caudal fin (PCF) coordination enables the circulation and interception of pectoral fin wake vortices by the caudal fin. This acts to transfer energy to the caudal fin and enhance its hydrodynamic efficiency at swimming speeds where this behaviour occurs. We also find that mojarras commonly use PCF coordination in nature. The results offer new insights into the evolutionary drivers and behavioural plasticity of fish swimming as well as for developing more capable bioinspired underwater vehicles.

Complex Modal Characteristic Analysis of a Tensegrity Robotic Fish's Body Waves

A bionic robotic fish based on compliant structure can excite the natural modes of vibration, thereby mimicking the body waves of real fish to generate thrust and realize undulate propulsion. The fish body wave is a result of the fish body's mechanical characteristics interacting with the surrounding fluid. Thoroughly analyzing the complex modal characteristics in such robotic fish contributes to a better understanding of the locomotion behavior, consequently enhancing the swimming performance. Therefore, the complex orthogonal decomposition (COD) method is used in this article. The traveling index is used to quantitatively describe the difference between the real and imaginary modes of the fish body wave. It is defined as the reciprocal of the condition number between the real and imaginary components. After introducing the BCF (body and/or caudal fin) the fish's body wave curves and the COD method, the structural design and parameter configuration of the tensegrity robotic fish are introduced. The complex modal characteristics of the tensegrity robotic fish and real fish are analyzed. The results show that their traveling indexes are close, with two similar complex mode shapes. Subsequently, the relationship between the traveling index and swimming performance is expressed using indicators reflecting linear correlation (correlation coefficient (Rc) and p value). Based on this correlation, a preliminary optimization strategy for the traveling index is proposed, with the potential to improve the swimming performance of the robotic fish.

Performance Optimization for Bionic Robotic Dolphin with Active Variable Stiffness Control

Aquatic animals such as fish and cetaceans can actively modulate their body stiffness with muscle to achieve excellent swimming performance under different situations. However, it is still challenging for a robotic swimmer with bionic propulsion mode to dynamically adjust its body stiffness to improve the swimming speed due to the difficulties in designing an effective stiffness adjustment structure. In this paper, based on the special torque mode of a motor, we propose an active variable stiffness control method for a robotic dolphin to pursue better swimming speed. Different from a variable stiffness structure design, a torque control strategy for the caudal motor is employed to imitate the physical property of a torsion spring to act as the variable stiffness component. In addition, we also establish a dynamic model with the Lagrangian method to explore the variable stiffness mechanism. Extensive experiments have validated the dynamic model, and then the relationships between frequency and stiffness on swimming performance are presented. More importantly, through integrating the dynamic model and torque actuation mode-based variable stiffness mechanism, the online performance optimization scheme can be easily realized, providing valuable guidance in coordinating system parameters. Finally, experiments have demonstrated the stiffness adjustment capability of the caudal joint, validating the effectiveness of the proposed control method. The results also reveal that stiffness plays an essential role in swimming motion, and the active stiffness adjustment can significantly contribute to performance improvement in both speed and efficiency. Namely, with the adjustment of stiffness, the maximum speed of our robotic dolphin achieves up to 1.12 body length per second (BL/s) at 2.88 Hz increasing by 0.44 BL/s. Additionally, the efficiency is also improved by 37%. The conducted works will offer some new insights into the stiffness adjustment of robotic swimmers for better swimming performance.

Nonbiomorphic Passively Adaptive Swimming Robot Enables Agile Propulsion in Cluttered Aquatic Environments

Aquatic swimmers, whether natural or artificial, leverage their maneuverability and morphological adaptability to operate successfully in diverse, complex underwater environments. Maneuverability allows swimmers the agility to change speed and direction within a constrained operating space, while morphological adaptability allows their bodies to deform as they avoid obstacles and pass through narrow gaps. In this work, we design a soft, modular, nonbiomorphic swimming robot that emulates the maneuverability and adaptability of biological swimmers. This tethered swimming robot is actuated by a two degree-of-freedom (2-DOF) cable-driven mechanism that enables not only common maneuvers, such as undulatory surging and pitch/yaw rotations, but also a roll rotation maneuver that is steady and controllable. This simple 2-DOF system demonstrates full 3D swimming abilities in a space-constrained underwater test bed. The soft compliant body and passive foldable fins of the swimming robot lend to its morphological adaptability, allowing it to move through narrow gaps, channels, and tunnels and to avoid obstacles without the need for a low-level feedback control strategy. The passive adaptability and maneuvering capabilities of our swimming robot offer a new approach to achieving underwater navigation in complex real-world settings.

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.

Identification of the trade-off between speed and efficiency in undulatory swimming using a bio-inspired robot

Anguilliform swimmers, like eels or lampreys, are highly efficient swimmers. Key to understanding their performances is the relationship between the body's kinematics and resulting swimming speed and efficiency. But, we cannot prescribe kinematics to living fish, and it is challenging to measure their power consumption. Here, we characterise the swimming speed and cost of transport of a free-swimming undulatory bio-inspired robot as we vary its kinematic parameters, including joint amplitude, body wavelength, and frequency. We identify a trade-off between speed and efficiency. Speed, in terms of stride length, increases for increasing maximum tail angle, described by the newly proposed specific tail amplitude and reaches a maximum value around the specific tail amplitude of unity. Efficiency, in terms of the cost of transport, is affected by the whole-body motion. Cost of transport decreases for increasing travelling wave-like kinematics, and lower specific tail amplitudes. Our results suggest that live eels tend to choose efficiency over speed and provide insights into the key characteristics affecting undulatory swimming performance.

Physics-informed reinforcement learning for motion control of a fish-like swimming robot

Motion control of fish-like swimming robots presents many challenges due to the unstructured environment and unmodelled governing physics of the fluid-robot interaction. Commonly used low-fidelity control models using simplified formulas for drag and lift forces do not capture key physics that can play an important role in the dynamics of small-sized robots with limited actuation. Deep Reinforcement Learning (DRL) holds considerable promise for motion control of robots with complex dynamics. Reinforcement learning methods require large amounts of training data exploring a large subset of the relevant state space, which can be expensive, time consuming, or unsafe to obtain. Data from simulations can be used in the initial stages of DRL, but in the case of swimming robots, the complexity of fluid-body interactions makes large numbers of simulations infeasible from the perspective of time and computational resources. Surrogate models that capture the primary physics of the system can be a useful starting point for training a DRL agent which is subsequently transferred to train with a higher fidelity simulation. We demonstrate the utility of such physics-informed reinforcement learning to train a policy that can enable velocity and path tracking for a planar swimming (fish-like) rigid Joukowski hydrofoil. This is done through a curriculum where the DRL agent is first trained to track limit cycles in a velocity space for a representative nonholonomic system, and then transferred to train on a small simulation data set of the swimmer. The results show the utility of physics-informed reinforcement learning for the control of fish-like swimming robots.

Computational Study of Stiffness-Tuning Strategies in Anguilliform Fish

Biological evidence demonstrates that fish can tune their body stiffness to improve thrust and efficiency during swimming locomotion. However, the stiffness-tuning strategies that maximize swimming speed or efficiency are still unclear. In the present study, a musculo-skeletal model of anguilliform fish is developed to study the properties of variable stiffness, in which the planar serial-parallel mechanism is used to model the body structure. The calcium ion model is adopted to simulate muscular activities and generate muscle force. Further, the relations among the forward speed, the swimming efficiency, and Young's modulus of the fish body are investigated. The results show that for certain body stiffness, the swimming speed and efficiency are increased with the tail-beat frequency until reaching the maximum value and then decreased. The peak speed and efficiency are also increased with the amplitude of muscle actuation. Anguilliform fish tend to vary their body stiffness to improve the swimming speed and efficiency at a high tail-beat frequency or small amplitude of muscle actuation. Furthermore, the midline motions of anguilliform fish are analyzed by the complex orthogonal decomposition (COD) method, and the discussions of fish motions associated with the variable body stiffness and the tail-beat frequency are also presented. Overall, the optimal swimming performance of anguilliform fish benefits from the matching relationships among the muscle actuation, the body stiffness, and the tail-beat frequency.

Research and Experiment on a Bionic Fish Based on High-Frequency Vibration Characteristics

This paper takes the high-frequency vibration characteristics of a bionic robot fish as the research object. Through research on the vibration characteristics of a bionic fish, we quantified the role of voltage and beat frequency in high-speed and stable swimming. We proposed a new type of electromagnetic drive. The tail is made of 0° silica gel to simulate the elastic characteristics of fish muscles. We completed a series of experimental studies on the vibration characteristics of biomimetic robotic fish. Through the single-joint fishtail underwater experiment, the influence of vibration characteristics on parameters during swimming was discussed. In terms of control, the central mode generator control method (CPG) control model is adopted, and a replacement layer is designed in combination with particle swarm optimization (PSO). By changing the elastic modulus of the fishtail, the fishtail resonates with the vibrator, and the swimming efficiency of the bionic fish is improved. Finally, through the prototype experiment, it is found that the bionic robot fish can achieve high-speed swimming through high-frequency vibration.

Pleobot: a modular robotic solution for metachronal swimming

Metachronal propulsion is widespread in aquatic swarming organisms to achieve performance and maneuverability at intermediate Reynolds numbers. Studying only live organisms limits our understanding of the mechanisms driving these abilities. Thus, we present the design, manufacture, and validation of the Pleobot-a unique krill-inspired robotic swimming appendage constituting the first platform to study metachronal propulsion comprehensively. We combine a multi-link 3D printed mechanism with active and passive actuation of the joints to generate natural kinematics. Using force and fluid flow measurements in parallel with biological data, we show the link between the flow around the appendage and thrust. Further, we provide the first account of a leading-edge suction effect contributing to lift during the power stroke. The repeatability and modularity of the Pleobot enable the independent manipulation of particular motions and traits to test hypotheses central to understanding the relationship between form and function. Lastly, we outline future directions for the Pleobot, including adapting morphological features. We foresee a broad appeal to a wide array of scientific disciplines, from fundamental studies in ecology, biology, and engineering, to developing new bio-inspired platforms for studying oceans across the solar system.

Cost of Transport of Undulating Fin Propulsion

Autonomous robots are used to inspect, repair and maintain underwater assets. These tasks require energy-efficient robots, including efficient movement to extend available operational time. To examine the suitability of a propulsion system based on undulating fins, we built two robots with one and two fins, respectively, and conducted a parametric study for combinations of frequency, amplitude, wavenumber and fin shapes in free-swimming experiments, measuring steady-state swimming speed, power consumption and cost of transport. The following trends emerged for both robots. Swimming speed was more strongly affected by frequency than amplitude across the examined wavenumbers and fin heights. Power consumption was sensitive to frequency at low wavenumbers, and increasingly sensitive to amplitude at high wavenumbers. This increasing sensitivity of amplitude was more pronounced in tall rather than short fins. Cost of transport showed a complex relation with fin size and kinematics and changed drastically across the mapped parameter space. At equal fin kinematics as the single-finned robot, the double-finned robot swam slightly faster (>10%) with slightly lower power consumption (<20%) and cost of transport (<40%). Overall, the robots perform similarly to finned biological swimmers and other bio-inspired robots, but do not outperform robots with conventional propulsion systems.

Platform development and gliding optimization of a robotic flying fish with morphing pectoral fins

The aquatic-aerial robot with the free interface crossing can enhance adaptability in complex aquatic environments. However, its design is extremely challenging for the striking discrepancies in propulsion principles. The flying fish in nature exhibits remarkable multi-modal cross-domain locomotion capability, such as high-maneuvers swimming, agile water-air crossing, and long-distance gliding, providing extensive inspiration. In this paper, we present a unique aquatic-aerial robotic flying fish with powerful propulsion and a pair of morphing wing-like pectoral fins to realize cross-domain motion. Furthermore, to explore the gliding mechanism of flying fish, a dynamic model with a morphing structure of pectoral fins is established, and a double deep Q-network-based control strategy is proposed to optimize the gliding distance. Finally, experiments were conducted to analyze the locomotion of the robotic flying fish. The results suggest that the robotic flying fish can successfully perform the 'fish leaping and wing spreading' cross-domain locomotion with an exiting speed of 1.55 m s^-1(5.9 body lengths per second, BL/s) and a crossing time of 0.233 s indicating its great potential in cross-domain. Simulation results have validated the effectiveness of the proposed control strategy and indicated that the dynamical adjustment of morphing pectoral fins contributes to improving the gliding distance. The maximum gliding distance has increased by 7.2%. This study will offer some significant insights into the system design and performance optimization of aquatic-aerial robots.

A Survey on Reinforcement Learning Methods in Bionic Underwater Robots

Bionic robots possess inherent advantages for underwater operations, and research on motion control and intelligent decision making has expanded their application scope. In recent years, the application of reinforcement learning algorithms in the field of bionic underwater robots has gained considerable attention, and continues to grow. In this paper, we present a comprehensive survey of the accomplishments of reinforcement learning algorithms in the field of bionic underwater robots. Firstly, we classify existing reinforcement learning methods and introduce control tasks and decision making tasks based on the composition of bionic underwater robots. We further discuss the advantages and challenges of reinforcement learning for bionic robots in underwater environments. Secondly, we review the establishment of existing reinforcement learning algorithms for bionic underwater robots from different task perspectives. Thirdly, we explore the existing training and deployment solutions of reinforcement learning algorithms for bionic underwater robots, focusing on the challenges posed by complex underwater environments and underactuated bionic robots. Finally, the limitations and future development directions of reinforcement learning in the field of bionic underwater robots are discussed. This survey provides a foundation for exploring reinforcement learning control and decision making methods for bionic underwater robots, and provides insights for future research.

Biomimetic Soft Underwater Robot Inspired by the Red Muscle and Tendon Structure of Fish

Underwater robots are becoming increasingly important in various fields. Fish robots are attracting attention as an alternative to the screw-type robots currently in use. We developed a compact robot with a high swimming performance by mimicking the anatomical structure of fish. In this paper, we focus on the red muscles, tendons, and vertebrae used for steady swimming of fish. A robot was fabricated by replacing the red muscle structure with shape memory alloy wires and rigid body links. In our previous work, undulation motions with various phase differences and backward quadratically increasing inter-vertebral bending angles were confirmed in the air, while the swimming performance in insulating fluid was poor. To improve the swimming performance, an improved robot was designed that mimics the muscle contractions of mackerel using a pulley mechanism, with the robot named UEC Mackerel. In swimming experiments using the improved robot, a maximum swimming speed of 25.8 mm/s (0.11 BL/s) was recorded, which is comparable to that of other soft-swimming robots. In addition, the cost of transport (COT), representing the energy consumption required for robot movement, was calculated, and a minimum COT of 0.08 was recorded, which is comparable to that of an actual fish.

A novel wave-like crawling robot has excellent swimming capabilities

Multiple animals ranging from micro-meter scale bacteria to meter scale vertebrates rely on undulatory motion to propel themselves on land and in the water. This type of locomotion also appears in amphibious animals such as sea snakes and salamanders. While undulatory motion can be used for both crawling and swimming, it requires the coordination of multiple joints so that only a few robots have the ability to mimic this motion. Here, we report a new minimalistic method for both crawling and swimming based on producing a wave motion in the sagittal (vertical) plane. A robotic prototype AmphiSAW was developed to demonstrate this methodology in a variety of scenarios. AmphiSAW (using its wave mechanism only) crawled at 1.5 B s^-1and swam at 0.74 B s^-1. The robot can be fitted with legs or wheels at the front, which can further increase its performance especially when crawling on uneven terrains. In addition to its high speeds, the robot has the lowest cost of transport among all amphibious robots reported in literature.

A Bioinspired Cownose Ray Robot for Seabed Exploration

This article presents the design and the experimental tests of a bioinspired robot mimicking the cownose ray. These fish swim by moving their large and flat pectoral fins, creating a wave that pushes backward the surrounding water so that the fish is propelled forward due to momentum conservation. The robot inspired by these animals has a rigid central body, housing motors, batteries, and electronics, and flexible pectoral fins made of silicone rubber. Each of them is actuated by a servomotor driving a link inside the leading edge, and the traveling wave is reproduced thanks to the flexibility of the fin itself. In addition to the pectoral fins, two small rigid caudal fins are present to improve the robot's maneuverability. The robot has been designed, built, and tested underwater, and the experiments have shown that the locomotion principle is valid and that the robot is able to swim forward, perform left and right turns, and do floating or diving maneuvers.

Bioinspired Propulsion System for a Thunniform Robotic Fish

The paper describes a bioinspired propulsion system for a robotic fish model. The system is based on a combination of an elastic chord with a tail fin fixed on it. The tail fin is connected to a servomotor by two symmetric movable thrusts simulating muscle contractions. The propulsion system provides the oscillatory tail movement with controllable amplitude and frequency. Tail oscillations translate into the movement of the robotic fish implementing the thunniform principle of locomotion. The shape of the body and the tail fin of the robotic fish were designed using a computational model simulating a virtual body in an aquatic medium. A prototype of a robotic fish was constructed and tested in experimental conditions. Dependencies of fish velocity on the dynamic characteristics of tail oscillations were analyzed. In particular, it was found that the robot's speed increased as the frequency of tail fin oscillations grew. We also found that for fixed frequencies, an increase in the oscillation amplitude lead to an increase in the swimming speed only up to a certain threshold. Further growth of the oscillation amplitude lead to a weak increase in speed at higher energy costs.

A tale of two fish tails: does a forked tail really perform better than a truncate tail when cruising?

Many fishes use their tail as the main thrust producer during swimming. This fin's diversity in shape and size influences its physical interactions with water as well as its ecological functions. Two distinct tail morphologies are common in bony fishes: flat, truncate tails which are best suited for fast accelerations via drag forces, and forked tails that promote economical, fast cruising by generating lift-based thrust. This assumption is based primarily on studies of the lunate caudal fin of Scombrids (i.e. tuna, mackerel), which is comparatively stiff and exhibits an airfoil-type cross-section. However, this is not representative of the more commonly observed and taxonomically widespread flexible forked tail, yet similar assumptions about economical cruising are widely accepted. Here, we present the first comparative experimental study of forked versus truncate tail shape and compare the fluid mechanical properties and energetics of two common nearshore fish species. We examined the hypothesis that forked tails provide a hydrodynamic advantage over truncate tails at typical cruising speeds. Using experimentally derived pressure fields, we show that the forked tail produces thrust via acceleration reaction forces like the truncate tail during cruising but at increased energetic costs. This reduced efficiency corresponds to differences in the performance of the two tail geometries and body kinematics to maintain similar overall thrust outputs. Our results offer insights into the benefits and tradeoffs of two common fish tail morphologies and shed light on the functional morphology of fish swimming to guide the development of bio-inspired underwater technologies.

Role of the caudal peduncle in a fish-inspired robotic model: how changing stiffness and angle of attack affects swimming performance

In fish, the tail is a key element of propulsive anatomy that contributes to thrust during swimming. Fish possess the ability to alter tail stiffness, surface area and conformation. Specifically, the region at the base of the tail, the caudal peduncle, is proposed to be a key location of fish stiffness modulation during locomotion. Most previous analyses have focused on the overall body or tail stiffness, and not on the effects of changing stiffness specifically at the base of the tail in fish and robotic models. We used both computational fluid dynamics analysis and experimental measurements of propulsive forces in physical models with different peduncle stiffnesses to analyze the effect of altering stiffness on the tail angle of attack and propulsive force and efficiency. By changing the motion program input to the tail, we were able to alter the phase relationship between the front and back tail sections between 0° and 330°. Computational simulations showed that power consumption was nearly minimized and thrust production was nearly maximized at the kinematic pattern whereφ= 270°, the approximate phase lag observed in the experimental foils and in free swimming tuna. We observed reduced thrust and efficiency at high angles of attack, suggesting that the tail driven during these motion programs experiences stalling and loss of lift. However, there is no single peduncle stiffness that consistently maximizes performance, particularly in physical models. This result highlights the fact that the optimal caudal peduncle stiffness is highly context dependent. Therefore, incorporating the ability to control peduncle stiffness in future robotic models of fish propulsion promises to increase the ability of robots to approach the performance of fish.

OpenFish: Biomimetic design of a soft robotic fish for high speed locomotion

We present OpenFish: an open source soft robotic fish which is optimized for speed and efficiency. The soft robotic fish uses a combination of an active and passive tail segment to accurately mimic the thunniform swimming mode. Through the implementation of a novel propulsion system that is capable of achieving higher oscillation frequencies with a more sinusoidal waveform, the open source soft robotic fish achieves a top speed of 0.85 m / s . Hereby, it outperforms the previously reported fastest soft robotic fish by 27 % . Besides the propulsion system, the optimization of the fish morphology played a crucial role in achieving this speed. In this work, a detailed description of the design, construction and customization of the soft robotic fish is presented. Hereby, we hope this open source design will accelerate future research and developments in soft robotic fish.

Fish-inspired segment models for undulatory steady swimming

Many aquatic animals swim by undulatory body movements and understanding the diversity of these movements could unlock the potential for designing better underwater robots. Here, we analyzed the steady swimming kinematics of a diverse group of fish species to investigate whether their undulatory movements can be represented using a series of interconnected multi-segment models, and if so, to identify the key factors driving the segment configuration of the models. Our results show that the steady swimming kinematics of fishes can be described successfully using parsimonious models, 83% of which had fewer than five segments. In these models, the anterior segments were significantly longer than the posterior segments, and there was a direct link between segment configuration and swimming kinematics, body shape, and Reynolds number. The models representing eel-like fishes with elongated bodies and fishes swimming at high Reynolds numbers had more segments and less segment length variability along the body than the models representing other fishes. These fishes recruited their anterior bodies to a greater extent, initiating the undulatory wave more anteriorly. Two shape parameters, related to axial and overall body thickness, predicted segment configuration with moderate to high success rate. We found that head morphology was a good predictor of its segment length. While there was a large variation in head segments, the length of tail segments was similar across all models. Given that fishes exhibited variable caudal fin shapes, the consistency of tail segments could be a result of an evolutionary constraint tuned for high propulsive efficiency. The bio-inspired multi-segment models presented in this study highlight the key bending points along the body and can be used to decide on the placement of actuators in fish-inspired robots, to model hydrodynamic forces in theoretical and computational studies, or for predicting muscle activation patterns during swimming.

A fish-like soft-robotic model generates a diversity of swimming patterns

Fish display a versatile array of swimming patterns, and frequently demonstrate the ability to switch between these patterns altering kinematics as necessary. Many hard and soft robotic systems have sought to understand a variety of aspects pertaining to undulatory swimming, but most have been built to focus solely on a subset of those swimming patterns. We have expanded upon a previous soft robotic model, the pneufish, so that it can now simulate a variety of swimming patterns, much like a real fish. We explore the performance space available for this longer soft robotic model, which we call the quad-pneufish, with particular attention to the effects on lateral forces and z-torques produced during locomotion. We show that the quad-pneufish is capable of achieving a variety of midline patterns - including more realistic, fish-like patterns - and introducing a slight amount of co-activation between the left and right sides maintains forward thrust while decreasing lateral forces, indicating an increase in swimming efficiency. Robotic systems that are capable of producing an array of swimming movement patterns hold promise as experimental platforms for studying the diversity of fish locomotor patterns.

Bioinspired morphing fins to provide optimal maneuverability, stability, and response to turbulence in rigid hull AUVs

By adopting bioinspired morphing fins, we demonstrate how to achieve good directional stability, exceptional maneuverability, and minimal adverse response to turbulent flow, properties that are highly desirable for rigid hull AUVs, but are presently difficult to achieve because they impose contradictory requirements. We outline the theory and design for switching between operating with sufficient stability that ensures a steady course in the presence of disturbances, with low corrective control action; reverting to high maneuverability to execute very rapid course and depth changes, improving turning rate by 25% up to 50%; and ensuring at all times that angular responses to external turbulence are minimized. We then demonstrate the developments through tests on a 1 m long autonomous underwater vehicle, namedMorpheus. The vehicle is capable of dynamically changing its stability-maneuverability qualities by using tuna-inspired morphing fins, which can be deployed, deflected and retracted, as needed. A series of free-swimming experiments and maneuvering simulations, combined with mathematical analysis, led to the design of optimal retractable morphing fins.

Robotics as a Comparative Method in Ecology and Evolutionary Biology

Comparative biologists have typically used one or more of the following methods to assist in evaluating the proposed functional and performance significance of individual traits: comparative phylogenetic analysis, direct interspecific comparison among species, genetic modification, experimental alteration of morphology (for example by surgically modifying traits), and ecological manipulation where individual organisms are transplanted to a different environment. But comparing organisms as the endpoints of an evolutionary process involves the ceteris paribus assumption: that all traits other than the one(s) of interest are held constant. In a properly controlled experimental study, only the variable of interest changes among the groups being compared. The theme of this paper is that the use of robotic or mechanical models offers an additional tool in comparative biology that helps to minimize the effect of uncontrolled variables by allowing direct manipulation of the trait of interest against a constant background. The structure and movement pattern of mechanical devices can be altered in ways not possible in studies of living animals, facilitating testing hypotheses of the functional and performance significant of individual traits. Robotic models of organismal design are particularly useful in three arenas: (1) controlling variation to allow modification only of the trait of interest, (2) the direct measurement of energetic costs of individual traits, and (3) quantification of the performance landscape. Obtaining data in these three areas is extremely difficult through the study of living organisms alone, and the use of robotic models can reveal unexpected effects. Controlling for all variables except for the length of a swimming flexible object reveals substantial non-linear effects that vary with stiffness. Quantification of the swimming performance surface reveals that there are two peaks with comparable efficiency, greatly complicating the inference of performance from morphology alone. Organisms and their ecological interactions are complex, and dissecting this complexity to understand the effects of individual traits is a grand challenge in ecology and evolutionary biology. Robotics has great promise as a "comparative method," allowing better-controlled comparative studies to analyze the many interacting elements that make up complex behaviors, ecological interactions, and evolutionary histories.

Bio-Inspired Propulsion: Towards Understanding the Role of Pectoral Fin Kinematics in Manta-like Swimming

Through computational fluid dynamics (CFD) simulations of a model manta ray body, the hydrodynamic role of manta-like bioinspired flapping is investigated. The manta ray model motion is reconstructed from synchronized high-resolution videos of manta ray swimming. Rotation angles of the model skeletal joints are altered to scale the pitching and bending, resulting in eight models with different pectoral fin pitching and bending ratios. Simulations are performed using an in-house developed immersed boundary method-based numerical solver. Pectoral fin pitching ratio (PR) is found to have significant implications in the thrust and efficiency of the manta model. This occurs due to more optimal vortex formation and shedding caused by the lower pitching ratio. Leading edge vortexes (LEVs) formed on the bottom of the fin, a characteristic of the higher PR cases, produced parasitic low pressure that hinders thrust force. Lowering the PR reduces the influence of this vortex while another LEV that forms on the top surface of the fin strengthens it. A moderately high bending ratio (BR) can slightly reduce power consumption. Finally, by combining a moderately high BR = 0.83 with PR = 0.67, further performance improvements can be made. This enhanced understanding of manta-inspired propulsive mechanics fills a gap in our understanding of the manta-like mobuliform locomotion. This motivates a new generation of manta-inspired robots that can mimic the high speed and efficiency of their biological counterpart.

Tunable stiffness in fish robotics: mechanisms and advantages

One of the emerging themes of fish-inspired robotics is flexibility. Adding flexibility to the body, joints, or fins of fish-inspired robots can significantly improve thrust and/or efficiency during locomotion. However, the optimal stiffness depends on variables such as swimming speed, so there is no one 'best' stiffness that maximizes efficiency in all conditions. Fish are thought to solve this problem by using muscular activity to tune their body and fin stiffness in real-time. Inspired by fish, some recent robots sport polymer actuators, adjustable leaf springs, or artificial tendons that tune stiffness mechanically. Models and water channel tests are providing a theoretical framework for stiffness-tuning strategies that devices can implement. The strategies can be thought of as analogous to car transmissions, which allow users to improve efficiency by tuning gear ratio with driving speed. We provide an overview of the latest discoveries about (1) the propulsive benefits of flexibility, particularlytunableflexibility, and (2) the mechanisms and strategies that fish and fish-inspired robots use to tune stiffness while swimming.

The performance of a flapping foil for a self-propelled fishlike body

Several fish species propel by oscillating the tail, while the remaining part of the body essentially contributes to the overall drag. Since in this case thrust and drag are in a way separable, most attention was focused on the study of propulsive efficiency for flapping foils under a prescribed stream. We claim here that the swimming performance should be evaluated, as for undulating fish whose drag and thrust are severely entangled, by turning to self-propelled locomotion to find the proper speed and the cost of transport for a given fishlike body. As a major finding, the minimum value of this quantity corresponds to a locomotion speed in a range markedly different from the one associated with the optimal efficiency of the propulsor. A large value of the feathering parameter characterizes the minimum cost of transport while the optimal efficiency is related to a large effective angle of attack. We adopt here a simple two-dimensional model for both inviscid and viscous flows to proof the above statements in the case of self-propelled axial swimming. We believe that such an easy approach gives a way for a direct extension to fully free swimming and to real-life configurations.

An introduction to an evolutionary tail: EvoDevo, structure and function of post-anal appendages

Although tails are common and versatile appendages that contribute to evolutionary success of animals in a broad range of ways, a scientific synthesis on the topic had yet to be initiated. For our Society for Integrative and Comparative Biology (SICB) symposium we brought together researchers from different areas of expertise (e.g., robotosists, biomechanists, functional morphologists, and evolutionary and developmental biologists), to highlight their research but also to emphasize the interdisciplinary nature of this topic. The four main themes that emerged based on the research presented in this symposium are: 1) How do we define a tail? 2) Development and regeneration inform evolutionary origins of tails, 3) Identifying key characteristics highlights functional morphology of tails, 4) Tail multi-functionality leads to the development of bioinspired technology. We discuss the research provided within this symposium, in light of these four themes. We showcase the broad diversity of current tail research and lay an important foundational framework for future interdisciplinary research on tails with this timely symposium.

Automatic segmentation of fish midlines for optimizing robot design

While fish use continuous and flexible bodies to propel themselves, fish robots are often made from interconnected segments. How many segments do robots need to represent fish movements accurately? We propose a new method to automatically determine parsimonious robot models from actual fish data. We first identify key bending points (i.e., joint positions) along the body and then study the concerted movement of the segments so that the difference between actual fish and modelled bending kinematics is minimized. To demonstrate the utility of our method, we analyse the steady swimming kinematics of 10 morphologically distinct fish species. Broadly classified as sub-carangiform (e.g., rainbow trout) and carangiform (e.g., crevalle jack) swimmers, these species exhibit variations in the way they undulate when traditional parameters (including head and tail beat amplitudes, body wavelength and maximum curvature along the body) are considered. We show that five segments are sufficient to describe the kinematics with at least 99% accuracy. For optimal performance, segments should progressively get shorter towards the tail. We also show that locations where bending moments are applied vary among species, possibly because of differences in morphology. More specifically, we find that wider fish have shorter head segments. We discover that once bending points are factored in, the kinematics differences observed in these species collapse into a single undulatory pattern. The amplitude and timing of how body segments move entirely depend on their respective joint positions along the body. Head and body segments are also coupled in a timely manner, which depends on the position of the most anterior joint. Our findings provide a mechanistic understanding of how morphology relates to kinematics and highlight the importance of head control, which is often overlooked in current robot designs.

Tuna robotics: hydrodynamics of rapid linear accelerations

Fish routinely accelerate during locomotor manoeuvres, yet little is known about the dynamics of acceleration performance. Thunniform fish use their lunate caudal fin to generate lift-based thrust during steady swimming, but the lift is limited during acceleration from rest because required oncoming flows are slow. To investigate what other thrust-generating mechanisms occur during this behaviour, we used the robotic system termed Tunabot Flex, which is a research platform featuring yellowfin tuna-inspired body and tail profiles. We generated linear accelerations from rest of various magnitudes (maximum acceleration of [Formula: see text] at [Formula: see text] tail beat frequency) and recorded instantaneous electrical power consumption. Using particle image velocimetry data, we quantified body kinematics and flow patterns to then compute surface pressures, thrust forces and mechanical power output along the body through time. We found that the head generates net drag and that the posterior body generates significant thrust, which reveals an additional propulsion mechanism to the lift-based caudal fin in this thunniform swimmer during linear accelerations from rest. Studying fish acceleration performance with an experimental platform capable of simultaneously measuring electrical power consumption, kinematics, fluid flow and mechanical power output provides a new opportunity to understand unsteady locomotor behaviours in both fishes and bioinspired aquatic robotic systems.