Research Development on Fish Swimming
Chinese Journal of Mechanical Engineering volume 35, Article number: 114 (2022)
Fishes have learned how to achieve outstanding swimming performance through the evolution of hundreds of millions of years, which can provide bio-inspiration for robotic fish design. The premise of designing an excellent robotic fish include fully understanding of fish locomotion mechanism and grasp of the advanced control strategy in robot domain. In this paper, the research development on fish swimming is presented, aiming to offer a reference for the later research. First, the research methods including experimental methods and simulation methods are detailed. Then the current research directions including fish locomotion mechanism, structure and function research and bionic robotic fish are outlined. Fish locomotion mechanism is discussed from three views: macroscopic view to find a unified principle, microscopic view to include muscle activity and intermediate view to study the behaviors of single fish and fish school. Structure and function research is mainly concentrated from three aspects: fin research, lateral line system and body stiffness. Bionic robotic fish research focuses on actuation, materials and motion control. The paper concludes with the future trend that curvature control, machine learning and multiple robotic fish system will play a more important role in this field. Overall, the intensive and comprehensive research on fish swimming will decrease the gap between robotic fish and real fish and contribute to the broad application prospect of robotic fish.
Considering the outstanding swimming performance like high speed, high efficiency and low noise, fishes have been the excellent reference for autonomous underwater vehicle (AUV) designers. Bionic robotic fish can be applied in many field as an underwater mobile platform, such as water quality monitoring and animal tracking [1,2,3,4,5].
The fish locomotion research can be tracked back to Aristotle. However, until in early 1900s, the qualitative research made significant progress under collaborations of zoologists and engineers. In this stage, Breder made a classification of fish species based on swimming modes, later Gray put forward the famous paradox that the drag power experienced by a dolphin is larger than the estimated muscle power [6, 7]. The mathematically oriented scientists entered this field around 1950. They developed relevant theories and made it possible for quantitative studies of fish propulsion. Among these scientists, Lighthill, Taylor and Wu made a great contribution to fish hydrodynamics . Compared with the resistive drag model developed by Taylor and waving plate theory proposed by Wu, Lighthill’s large-amplitude elongated-body theory (LAEBT) is more realistic, intuitive and elegant, thus contributing to its wide application. A rigid robotic tuna made by Triantafyllou led to a wave of bionic robot fish research . Almost at the same time, the development of computational fluid dynamics (CFD) made it easier for fish swimming simulation. In the year around 2014, Autonomous soft-bodied robotic fish fabricated by Marchese marks the arrival of the era of soft robotic fish .
Fish locomotion research has increased exponentially in recent years. Some influential research teams and their main research directions are summarized and listed in Table 1. It can be found that the related research takes place mainly in the USA, China and Europe. In particular, MIT and Harvard University are still the sources of innovation. China has advantages in motion control and stiffness adjustment mechanism, but needs to take effort in biomechanics of fish swimming. Although significant progress on understand ding fish locomotion mechanism has been made and a large number of robotic fish prototypes aiming to improve locomotor performance has been fabricated, there remains a gap between robotic fish and real fish to be addressed. Therefore, it is necessary to review and summarize the recent research development of fish swimming, which can provide a reference for the further research.
For convenience of later description, some basic knowledge about fish propulsion is added here. Generally, the propulsion modes can be divided into body/caudal fin (BCF) propulsion and median/paired fin (MPF) propulsion. About 85% of fish employ BCF propulsion for regular propulsion . These fishes are further subdivided into three categories: anguilliform, carangiform, and thunniform modes .
This paper is organized as follows. Section 2 describes the research methods applied in fish locomotion. Section 3 presents the research directions at present. Section 4 discusses future trends. Finally, conclusions are summarized in Section 5.
2 Research Methods
Fish swimming is indeed a combination of active swimming and passive swimming. Internal biomechanics dominate the active swimming and external flow field influence the passive swimming, resulting in a fluid structure coupling (FSI) problem and then determining the final swimming performance. The following part will be detailed around this center.
The outline of experimental research on fish swimming is shown in Figure 1.
The swimming performance: For real fish, the most direct method to obtain swimming characteristics is video recording. Scientists can get abundant data through this observation and know better about the tail-beat frequencies, swimming speeds, turn rates, swimming motions and so on of different fish species. For the purpose of making full use of the kind of data, Feeny developed a complex modal analysis technique to describe the main modes of lateral displacement, and the associated frequency and wavelength .
The internal biomechanics: Vivo experiments are the most important way to comprehend muscle activity and neural activity of fish. By using electromyograms (EMGs), Hamlet analyzed the calcium kinematics between muscle activity and neural activity . Schwalbe studied the red muscle activity in bluegill sunfish . Jayne found the red muscle motor pattern . So far, compared with anguilliform fish, the neuro-musculo-mechanical model of carangiform fish and thunniform fish is far from perfect owing to its complexity.
The external flow field: The techniques of particle image velocimetry (PIV), digital particle image velocimetry (DPIV) and volumetric imaging system allow the visualization of flow field. F E Fish applied DPIV to get the vortex wake shed by fish tail . Lauder used volumetric imaging systems to get 3D instantaneous snapshots of wake flow patterns . Thandiackal used a modified PIV technique to obtain flow fields around the zebrafish body .
Nonetheless, quantifying time-varying forces and moments along the fish body in an experiment is still a challenge at present . In addition, some cases like altering individual parameters such as body shape, body stiffness cannot be achieved in real fish. To address these problems, three alternatives could be considered: foil research, simulation and robotic fish platform. The latter two will be presented in Sections 2.2 and 3.3, respectively.
Foil research: Because of the similarity between fish body and airfoil, fish can be simplified to periodically heaving and pitching foils in a steady free stream velocity . Triantafyllou concluded that the Strouhal number St (St = fA/U, where f is the tail-beat frequency, A is the peak-to-peak tail amplitude and U is the mean swimming speed) of optimal fish propulsion should be in the narrow range 0.2−0.4 . A further experiment carried about by Anderson validated the maximum efficiency can be reached in this interval . Lauder used a robotic flapping foil platform to explore relevant parameter effects . Alben found resonant-like peaks in the swimming speed as a function of foil rigidity . Paraz showed thrust generation mechanism by a heaving flexible foil . Van Buren analyzed the effect of flow speed on oscillating foils . To some extent, foil research can be regarded as a pilot study for fish swimming research.
Traditional theories like LAEBT are incompetent in a precise analysis. Nowadays, simulation methods are of two kinds in general: the dynamic model based on traditional theory and CFD method. The former focuses on the fish body and applies the traditional theory to simplify the forces exerted by external fluids, which is an improvement of traditional theories. The latter simplifies the internal body dynamics and highlights hydrodynamics, which treats fish swimming as a FSI problem. In view of the advantages and disadvantages of dynamic model and CFD method (shown in Figure 2), some researchers have combined the two methods together to study the integrated system with both undulatory body and flexible fins systematically [28, 29].
Dynamic model: The premise of applying this method is to obtain the approximation of hydrodynamic force distribution along fish body. Once hydrodynamic force formulas are determined, calculations of dynamic models can be then carried out. When fish swims, the pressure field leads to a form drag in the forward direction and a resistive force in the lateral direction. The reversed Kaman vortex street generates a reactive force at tail and momentum transfer between fish surface and flow produces a skin friction. The sum of skin friction and form drag is the total drag force acting on the fish body. Ehrenstein analyzed the skin friction theoretically . Lucas estimated the form drag in undulatory fish . Zhang studied the total drag and Verma computed the force distribution on fish surface [35, 36].
There are two major approaches to the dynamic model: beam model and multi-body dynamic model. Cheng developed the continuous beam model based on waving plate theory . Alvarado and Govindarajan established the Timoshenko beam model based on LAEBT [38, 39]. Piñeirua used the Euler–Bernoulli beam model to quantify the reactive and resistive contributions to the thrust . Boyer built the Cosserat beam model based on LAEBT . These models have four-order governing equations, which is hard to solve and limit the further application. Under such circumstances, a reduced dynamic model is usually used by introducing some approximation treatments. As for the multi-body dynamic model, Boyer has done much fruitful work in this field [41, 42]. Hongzhou Jiang and Zhao developed multi-body systems by capitalizing on decoupled natural orthogonal complement matrices and the Udwadia-Kalaba theory, respectively [43,44,45]. Bhalla incorporated a forced damped oscillation framework and resistive drag theory into a chain-link model to study undulatory propulsion . Multi-body dynamic models have an active role in control and motion planning of robotic fish.
CFD method: Some main CFD methods applied in fish locomotion are listed in Table 2. Koumoutsakos, Patankar, Battista, Borazjani and Weymouth made plenty of achievements in this area. Besides, the immersed boundary method (IBM) has become the main stream. Conventionally, the body-fitted mesh approach based on unstructured grids is used to cope with such FSI problem, which can achieve a sharp resolution of solid-fluid interface. However, it usually requires frequent remeshing, complex mesh techniques and high computational cost. IBM, first proposed by Peskin to study the heart valves, can overcome these difficulties by using a fixed Cartesian grid to discretize fluid domain and describing elastic body via a Lagrangian mesh . The drawback of this method is that it cannot resolve the solid-fluid interface sharply. To address this problem, the adaptive mesh refinement (AMR) approach is used to deploy these localized regions of high resolution. Different methods like Level-set immersed boundary method (LS-IBM) and sharp-interface IBM are developed to deal with complex immersed surface problems.
3 Research Directions
3.1 Fish Locomotion Mechanism
The outline of research on fish locomotion mechanism is shown in Figure 3.
3.1.1 Macroscopic View
Researchers hope to find a unified principle like the Strouhal number St to reveal the intrinsic mechanism of fish locomotion. Gazzola uncovered a power law Re~Swα through existing observation data and numerical methods, in which Re is Reynolds numbers and Sw is a dimensionless swimming number (see Eqs. (1) and (2)) . α equals 4/3 for laminar flows and 1 for turbulent flows.
where U is the swimming speed; L is the fish length; ν is the fluid kinematic viscosity; ω is the tail-beat angular frequency.
where β is the pitch angle.
3.1.2 Microscopic View
Scientists hope to use both muscle activity and neural activity to interpret fish locomotion mechanism. Williams and Tytell analyzed the neuromechanical model systematically by considering fully the nonlinear muscles, passive viscoelasticity and body stiffness [17, 81, 87, 88]. Patel established hydrodynamically resolved computational neuromechanics by combining the neuromechanical model into the CFD method . Ming and Zhao studied muscle activation patterns and muscle-contraction model of pre-strains, respectively [90, 91]. Tokić concluded the relationship between muscle efficiency and body size .
3.1.3 Intermediate View
Kinematics optimization: In face of massive observation data, researchers have limited information to determine which body movement is optimal. Numerical optimization can be helpful to overcome the above limiting constraint once the swimming optimization objectives are set. Swimming speed and efficiency are commonly used as optimization objectives. Due to the fact that swimming efficiency of a self-propelled flexible body is ill-defined, there is not a unified measure at present although scholars put forward different swimming efficiency measures respectively [93,94,95]. A further comparative research of different efficiency measures should be conducted like the work of Eguchi but it is beyond the scope of this paper .
Kern combined an ‘Evolution Strategy with Adaptation of the Covariance Matrix’ (CMA-ES) algorithm with hydrodynamics to get efficient and high-speed swimming motions of an anguilliform swimmer ; Van Rees utilized the same method to optimize kinematics and body shapes for undulatory swimmers . Nevertheless, this technique fails to consider the internal dynamics and is not suitable for swimming at high Reynolds numbers. Eloy Optimized undulatory swimming at high Reynolds number based on an improved linear system . Tokić obtained optimal shapes and motions of swimming animals by applying elongated-body theory and evolutionary optimization algorithms . The disadvantage of this model is that it only function for small-amplitude motion. Eloy found two kinds of optimal body shapes by using a reduced dynamic model, one with good swimming efficiency and the other with large stride lengths . But the latter body shapes do not exist in nature, so the effectiveness of the model needs further verification. Patankar studied the optimal wave length in BCF swimmers and found that a rigid body attached to an undulating fin leads to an increased efficiency in MPF swimmers [101, 102].
On the other hand, optimality and resonance are closely inter-related with the hypothesis that fish can use resonance to lift swimming efficiency [103,104,105]. When the tail-bear frequency reached around the body’s natural frequency, fish consumes a minimal negative work. However, their relationship and influencing factors should be further studied because different scholars yielded inconsistent results [106, 107].
Unsteady locomotor behaviors: Except for steady swimming, there are also other locomotor behaviors for specific purposes: fast start, turning locomotion and burst-and-coast swimming [108,109,110,111,112]. C-start is a typical escape response of prey for predator. Fishes first bend their body to C-shape and then recoil their body quickly to accelerate. Gazzola identified the C-start pattern which minimize the escape distance and Currier designed a robotic fish that can generates fast-start accelerations of more than 20g by utilizing a dynamic snap-through buckling mechanism [85, 113]. As for turning locomotion, a fundamental life function, fish can use it to change swimming direction frequently and flexibly for finding food or mates. Thandiackal estimated pressure forces and the mechanical work along the body during turning . Xin held that fish turn quickly on account of the directional control strategy of the swing of the head . Dabiri analyzed rotational mechanics of turning maneuvers . Feng revealed that thunniform fish have a poorer turning ability than anguilliform fish and carangiform fish . The burst-and-coast swimming, as an intermittent form of locomotion, which can confer energetic benefits, has two successive stages: active undulation powered by fish muscles followed by a prolonged unpowered gliding. Li showed that fish adjust the bursting-to-coasting ratio to maintain the demanded speed . Wang indicated that wake structures of burst-and-coast swimming are obviously different from these of continuous swimming . Dan Xia explored the energy-saving advantages of this intermittent locomotion . Verma discovered a range of intermittent-swimming patterns with multi-objective optimization . Akoz found the relationship between efficiency and a dimensionless heave ratio in intermittent swimming .
Fish school: The key to understanding fish-schooling behavior lies in making clear the role of fluid medium or flow structures [120,121,122,123]. A single fish can be a good analytical entry point. F E Fish held that the active flow control mechanism of swimming animals is to generate wake flow structures actively . Macias concluded that net thrust appears in reverse Von Kármán wakes . Khalid and Zhang studied the wake structure in different Reynolds numbers, respectively [125, 126]. However, Floryan deduced that wake structures are not a reliable method to study swimming performance . The role of fluid medium for single fish still needs an in-depth study. On the other hand, with respect to the hypothesis that fish can exploit the neighbor–induced flow to save energy, different researches about fish school have been conducted. Li analyzed the interference of vorticity and pressure fields of a fish school . If two fish are arranged in an in-line configuration, the follower can reduce up to 30% energy cost and the leader benefits energetically only for small distances by exploiting independent pitch control of its caudal fin [83, 129, 130]. Moreover, pitching motions can increase the group efficiency while heaving motions can lead to a slight increase in the swimming speed . In this in-line configuration, Dai discussed the effect of the horizontal spacing and vertical spacing between two fish ; Verma improved coordinated patterns through deep reinforcement learning ; Li found that the follower can exhibit ‘vortex phase matching’ strategy . In addition, Chao studied the tandem, parallel and staggered arrangements of two fish . Dai, Li and Ashraf simulated the tandem, the phalanx, the diamond and the rectangle configurations for three fish or four fish, respectively [131, 135,136,137]. In spite of these achievements, scholars still do not reach a unified conclusion on the efficiency of fish school.
3.2 Structure and Function Research
IT has to be admitted that fish are such a fascinating aquatic animal that almost every part of the body has been studied more or less. For example, the research team of Li Wen fabricated an underwater robot with of strong adhesion capability by fully understanding the function of adhesive discs in remoras [138, 139]. They also studied the function of shark skin denticles and designed an artificial shark skin that reduces the cost of transport by 5% . Weymouth designed a size-changing robotic swimmer by using the jet pulsing mechanism in octopuses . Long Jr, Chao and Nesteruk analyzed the evolution, asymmetric geometry and the effect on efficiency for fish shape profile independently [142,143,144]. Thus, it is difficult to give an overall review in this aspect. Nevertheless, we attempt to classify this research into the following three categories roughly. Note that structure and function research is definitely not confined to the following types.
3.2.1 Fin Research
Among fish fins (shown in Figure 4), the most effective fin should be the caudal fin, which plays a key role in self-propelled locomotion. Besides, other soft appendages of fish, such as anal fin, dorsal fin and pectoral fins, also play an important role in precise fish swimming research, although they are usually ignored in past studies for the purpose of simplicity. Scholars expect to study the fins to improve swimming performance to some extent. The main fin research types are summarized and listed in Table 3. It shows that researches are more concentrated on the computational model and the integral study of body-fin system.
3.2.2 Lateral Line System
Biologists have discovered that fish can obtain surrounding fluid environment information by lateral line system (LLS) to achieve some basic activities including hunting, swarming and obstacle avoidance. LLS has two perceptual functions: one is the identification of the flow direction and flow speed by surface nerve mound, and the other is pressure gradient sensation by duct nerve mound . More details about the flow-sensing mechanism of these two mounds can be referred to Ref. . Inspired by the nature, different artificial LLS systems that are equipped with a pressure sensor array have been developed to sense the fluid environment (shown in Figure 5). Guijie Liu investigated the effect of speed and flow angle and studied not only near-field detection but also the AUV’s pitch motion parameters perception [169, 170]. Although the sensing capability has been achieved, the sensitivity and stability of these current systems need to be further improved. The sensor configuration, the flow field perception algorithm and state recognition are the keys to be addressed. Verma studied the optimal spatial placement of these sensors and found that a high density of sensors should be located in the head and other sensors only need to be distributed along with the body uniformly . Guijie Liu used pressure difference matrix to identify the flow field, Tang utilized the free surface wave equation to percept the vibrating sphere and Maertens combined potential flow model with a linear analysis of the boundary layer to improve the existing object identification algorithm [172,173,174]. As for state recognition, a back propagation neural network and convolutional neural network are applied to predict the flow information quickly [169, 170], respectively. In addition, Gao held that vorticity control can be conducted precisely based on LLS when fish swim in schools .
3.2.3 Body Stiffness
Fish can modulates body stiffness actively to adjust its swimming performance through muscles, tendons and other biological tissues [179,180,181]. Through testing biological structures, Long Jr supported the biological hypothesis that fish swimming behaviors are controlled by the body stiffness and the stiffness can be altered by the vertebral column . Ardian Jusufi built a platform to modulate the whole body stiffness by changing the pressure of soft pneumatic actuators (SPA) that are attached to a flexible panel [183,184,185]. These experimental results shows that there exist complicated interactive effects of both the frequency and stiffness on fish swimming performance. Tytell utilized a neuromechanical model to examine the role of body stiffness and found that fish can tune its body stiffness by appropriately timed muscle contractions to achieve maximum speed . Furtherly, he put forward a nondimensional effective flexibility (see Eq. (4)) to study the comprehensive effect of scaling flexibility and consequently to estimate the relevant resonant frequency.
where ρ is the fluid density, h is the average height of fish, l is the length, f is the tail-beat frequency and EI is the bending modulus.
Floryan obtained the optimal flexibility distribution along with the body of simmers through a linear inviscid model . They discovered that significant thrust gain can be made and a resonance can be triggered by tuning the stiffness. The stiffness of their model are characterized by Eq. (5). Using this scaling stiffness, Luo studied the effect of stiffness of both fish body and caudal fin .
where E is the Young’s modulus and U is the swimming speed.
The biological principle and the effect of stiffness on swimming performance have been described above. Then, the stiffness adjustment mechanisms are introduced (see Figure 6). Xu Dong proposed a variable stiffness mechanism based on the negative work. He adopted a fuzzy controller to mimic this mechanism and describe the relationship between stiffness and negative work . The result shows that energy consumption during fish swimming is reduced and the propulsion efficiency is improved. Hongzhou Jiang applied a variant of redundant planar rotational parallel mechanisms—a variable stiffness decoupled mechanism based on mechanically adjustable compliance and controllable equilibrium position actuator (MACCEPA) to develop a robotic fish with large stiffness variation [190, 191]. Moreover, he fabricated a tensegrity robotic fish, which is composed of a series of rigid segments connected with tensegrity joints. The stiffness of each segment of which can be altered in theory .
3.3 Bionic Robotic Fish
Some bionic robotic fishes for specific research purposes have been mentioned above. Generally, robotic fish development has experienced three periods: rigid robotic fish, compliant robotic fish and soft robotic fish. This section deals mainly with the actuation, material and motion control of robotic fish.
3.3.1 Actuations and Materials
Almost all the robotic fish can be tracked back to RoboTuna designed by Triantafyllou. The development of rigid robotic fish is shown in Table 4 and Figure 7. The main driving mode includes motor drive and hydraulic drive. The motor can be further divided into three types: steering engine, servomotor, DC (Direct current) motor. The advantages of motor drive are that it can achieve precise predefined motion and high-frequency oscillation and can provide high power, while this kind of drive has large noise, high power consumption and complex structure. Hydraulic drive can bring about large driving torque, but the shortcoming is that it needs a complete hydraulic system. Both of the above drive modes need large space. To mimic the body wave of real fish, rigid robotic fish always is composed of rigid links and rotation joints. Single link is the simplest design that uses a single motor to drive the caudal fin. By contrast, multiple links can imitate the fish skeletons better and gives the robotic fish a higher degree of freedom. However, this multiple-link structure is difficult to control. As for the material of rigid robotic fish, it does not have high elastic deformation capability due to high stiffness. There are three types of material usually used: metals like aluminum and steel, plastic like polystyrene, PVC and plexiglass and composite like carbon fiber.
Compliant robotic fish is a transitional stage between rigid robotic fish and soft robotic fish, which is typical featured by soft materials and traditional drive mode. Therefore, deformation can happen passively. Soft materials have a large elastic deformation and can recover to original shape. Rubber like silicone and latex and metals like spring steel and cables are usually applied in compliant robotic fish. On the other hand, soft materials can be used to protect actuators and waterproof. There exist three kinds of research types on compliant robotic fish (see Figure 8): (1) robotic fish composed of rigid body and compliant tail [202,203,204,205]; (2) robotic fish composed of rigid tail and compliant body ; (3) a whole compliant device [38, 207]. Zhong designed a novel robotic fish with wire-driven active body and compliant tail, which outperforms many rigid robotic fish . The maximum swimming speed is up to 2.15 BL/s, the highest Froude efficiency to 97% and the average turning rate to 63°/s. Interestingly, some researchers found resonance phenomenon in swimming speed, thrust and efficiency [38, 203, 206].
Soft robotic fish with a continuously deformable body can exhibit continuum motions that conventional rigid-bodied robotic fish cannot achieve, which has become a new hotspot. The soft materials have been introduced above. The biggest difference from the above two kinds of robotic fish is the soft actuation. Soft actuators applied in robotic fish are summarized and listed in Table 5 and Figure 9. All the actuators except FEA belong to functional material actuations. FEA plays a key role in soft robotics field and was used to robotic fish first by Marchese . The high complexity and nonlinearity of FEA make the dynamics modeling challenging. Zhou established a theoretical model to predict the bending angle of a bi-directionally FEA . Tao Wang developed a universal model for FEA based on constant curvature assumption and Lagrangian approach and further proposed a nonlinear robust control model based on system identification [209, 210]. Optimizations aiming to improve the FEA performance have also been made. Hu evaluated the effect of structure parameters such as input pressure, the wall thickness and the gap between chambers to optimize the performance of FEA . Yang adopted a new form of free bottom of FEA and thus improved the bending capacity of FEA . Li proposed a fiber-reinforced FEA that can bear high pressure up to 400 kPa . Consequently, some FEA variations are applied in robotic fishes. Feng used a fiber-reinforced FEA array to generate body wave of anguilliform fish . Frame manufactured jellyfish robot with eight FEAs extending radially from its center . Joshi replaced FEAs of jellyfish robot with soft pneumatic composite actuators which consists of FEAs and thin steel springs .
3.3.2 Motion Control
Motion control can be roughly divided into two classes: open-loop control for body wave generation and close-loop control based on dynamic models. Open-loop control always fits the body wave by designing predefined multiple-link kinematics or using functional material actuations. In another way, central pattern generator (CPG) method can generate periodic signals for joints directly without sensory feedback. Inspired by the biological neural network, CPGs are analogue to an array of coupled neurons that produce oscillatory signals . Although it lacks enough theoretical basis, CPG control has been widely used in bionic engineering [227,228,229,230,231]. Due to no feedback in open-loop control, it cannot reach the desired motion compared with close-loop control. As for close-loop control, speed control, depth control, attitude control, path following and target tracking are emphatically introduced below (see Table 6).
Speed control: Precise speed control of robotic fish is essential for motion control and motion planning. Xu JX’s team of National University of Singapore has done much work on the speed control and has proposed several control methods, including SMC, data-driven model and iterative learning method.
Depth control: Vertical movement is also important besides horizontal motion, which can help fulfill many tasks, such as seabed mapping, ocean exploration. As shown in Table 6, Zhang adopted fuzzy logic method to control depth by changing the angle of pectoral fin . Shen applied fuzzy PID control to change the center of gravity for depth control . In the work of Junzhi Yu, SMC and fuzzy control are combined to regulate the depth of robotic dolphin . It can be seen that fuzzy control is often used in depth control.
Attitude control: Attitude includes three aspects: roll, pitch and yaw. Most relative studies researches focus on the single attitude control. Yuan and Cao designed SMO and self-tuning fuzzy strategy for heading control of robotic dolphin, respectively [235, 236]. Meurer used nonlinear PD controller for yaw control of compliant robotic fish . Tian developed an ADRC strategy to track the target pose .
Path tracking: According to different targets, path tracking includes two aspects: way-point tracking, path following. Junzhi Yu’s team of Chinese Academy of Sciences has made many efforts in this field. As for way-point tracking, Yu successfully applied point-to-point control algorithm in four-link robotic fish . Kopman implemented PID control for a two-link robotic fish . As for path following, Yu’s team developed a series of methods successively, including BS technique, LOS method, ADRC and fuzzy-linear model.
Target tracking: Target tracking faces the challenges of complex fluid environments such as weak light, limited field of view and obstacles. Hu gave a decentralized control methods for two vision-based robotic fish to fulfill the tasks of target tracking and collision avoidance . Chen used BS technique to develop a target tracking control framework and Yu designed a target tracking control scheme that combines sliding-mode fuzzy control and multiple-stage directional control [241, 242]
4 Research Trend
4.1 Curvature Control
Theory Basis: Past studies always attempted to develop a comprehensive swimming model including muscle activity, passive viscoelasticity and fluid mechanics. Although much progress on muscle model has been made by EMGs, the neuro-musculo-mechanical model, owing to its complexity, is still far from perfect especially for carangiform fish and thunniform fish. McMillen held that neuromuscular systems produce an intrinsic shape determined by its preferred curvature . Therefore, the internal moment can be described in Eq. (6) based on linear constitutive relation. The hypothesis indeed treat fish swimming as a beam actuated by a preferred curvature. It is remarked that the curvature presented in swimming process does not equal the preferred curvature, which reflects the active/passive swimming mechanism.
where κ is preferred curvature that is the function of time t and arc-length along fish body centerline s. φ is the local incident angle between tangent of centerline and the horizontal axis. The subscript denotes the derivative with respect to s or/and t. δ is viscoelastic damping coefficient.
The equations of fish locomotion can be thus obtained based on the conservation of linear and angular momentum. The question then arises naturally: which preferred curvature is appropriate? The problem can be solved by optimization once the optimization objectives are set. The preferred curvature distribution along fish body can be determined finally.
Experimental Analysis: For simplicity, the preferred curvature distribution can be treated as approximate piecewise constant curvature (APCC). Cheng developed an APCC equivalent model: APCC 2L-5R model (L means links and R means rotation joints), which can be used in rigid robotic fish design . In this way, the kinematics of rigid links is equivalent to the continuum robot. On the other hand, for soft robotic fish, we can utilize the idea of Luo Ming as a reference . He first developed a dynamic model for soft robots actuated by FEA. The model contains soft bending segments and short rigid links. Second, he designed a variation of FEA, tested the relationship between curvature and pressure input and improved dynamic response. At last, he used a modular approach to fabricate each segment of soft robot and adopted open-loop control to achieve the desired motion. This framework has been applied in a pressure-operated soft robotic snake successfully. Yet, when this framework is ported to soft robotic fish, the slow dynamic response highly up to 1−2 s consequently induces the low tail-beat frequency. It can be solved by changing the structure parameter to improve the dynamic response of FEA. Moreover, the close-loop control should be considered if precise motion is required.
4.2 Machine Learning
At present, machine learning (ML) is deeply changing every aspect of scientific and technical field and fish swimming research is no exception. The advantage of ML is to address problems for which the optimal theoretical solution method is unknown. Even though ML is computationally costly, especially when it involves FSI models, it develops rapidly in the aspects of fluid mechanics and robots. The methods used in ML include deep learning (DL), reinforcement learning (RL) and deep reinforcement learning (DRL). In the aspect of fluid mechanics, ML can extract information from a large amount of data and reveal the underlying mechanism of fluid mechanics. Petros’s team of ETH Zurich used RL to study fish school problem in 2014 and gave an overview of research development and promising opportunities of ML for fluid mechanics [254, 255]. Raissi studied the application of DL in vortex induced vibrations . Rabault studied the application of DRL in active flow control and shape optimization and Xu utilized DRL to find out the optimal control strategy for rotating cylinders [257, 258]. Jiao trained fish to learn how to swim in potential flow based on RL . Still, the research on fish locomotion mechanism based on ML is not near enough. There are vast prospects in waiting for us to explore. As for robots, Liu discussed the application of RL in robotic fish . Thuruthel introduced ML-based motion control for soft robot and Cho applied RL to generate a CPG-based motion control of a robotic salamander [261, 262]. For soft robotic fish, ML can improve the survival possibilities by adapting to complex underwater environment. In addition, robotic fish can learn various motion skills autonomously through ML.
4.3 Multiple Robotic Fish System
The coordinated planning and control of multiple robotic fish system has not been fully addressed in the past studies and still is a challenging task at present . Compared with single robotic fish, multiple robotic fish system can deal with complex underwater tasks and save work time. There are two difficulties to overcome: interaction mechanism of real fish school and cooperative communication of multiple robotic fish system. The former can give insights into the active flow control mechanism to save energy and the latter can help to share collected information. Artificial intelligence (AI) will play a more important role in these two areas in the future. Both attitude adjustment in fish school and swarm intelligence strategy in coordinated control require the outstanding learning ability of AI.
Researchers hope to design an AUV with excellent capabilities like high speed, high efficiency and low noise through studying fish swimming mechanism. Thus, the relevant research can be generally divided into two classes: fish locomotion mechanism from a science perspective and bionic robotic fish from an engineering perspective. Although much progress has been made, the gap between bionic robotic fish and real fish is still apparent. In this article, the research development on fish swimming is presented. Research methods, current research direction and future research trend are detailed. The internal biomechanics of fish is investigated by Vivo experiments and is treated as a beam or multi-body system in the mathematical model. The external fluid information is obtained by PIV or DPIV experiments and is simulated by CFD. The comprehensive study of fish swimming can be simplified to foil research that can provide qualitative analysis. For single fish, certainly, unsteady locomotor behaviors reflecting maneuverability such as fast start, turning locomotion and burst-and-coast swimming and steady swimming performance reflecting speed and efficiency are the focus of research. While the fish school research put emphasis on the active flow control and swarm energy saving. On the other hand, Robotic fish development has experienced three periods: rigid robotic fish, compliant robotic fish and soft robotic fish. Hence, the actuations and materials have been greatly changed. As for the motion control of bionic fish, the overview of the speed control, depth control, attitude control, path following and target tracking are introduced. In the future, AI will help researchers to understand fish swimming mechanism and design intelligent motion control strategies. With the development of soft robot on material and basic theory, curvature control in bionic robotic fish based on the preferred curvature hypothesis can be realized. We hope that this review can help scholars to understand the recent research development of fish swimming and provide a reference for the further research.
Z X Wu, J C Liu, J Z Yu, et al. Development of a novel robotic dolphin and its application to water quality monitoring. IEEE/ASME Transactions on Mechatronics, 2017, 22(5): 2130-2140.
O Ennasr, C Holbrook, D W Hondorp, et al. Characterization of acoustic detection efficiency using a gliding robotic fish as a mobile receiver platform. Animal Biotelemetry, 2020, 8(1): 1-13.
R K Katzschmann, J DelPreto, R MacCurdy, et al. Exploration of underwater life with an acoustically controlled soft robotic fish. Science Robotics, 2018, 3(16): eaar3449.
Z B Xue, L L Li, Y X Song. The research of maneuverability modeling and environmental monitoring based on a robotic dolphin. Applied Bionics and Biomechanics, 2021, 2021: 4203914.
D K Wainwright, G V Lauder. Tunas as a high-performance fish platform for inspiring the next generation of autonomous underwater vehicles. Bioinspiration & Biomimetics, 2020, 15(3): 035007.
M I Lamas, C G Rodriguez. Hydrodynamics of biomimetic marine propulsion and trends in computational simulations. Journal of Marine Science and Engineering, 2020, 8(7): 479.
D Scaradozzi, G Palmieri, D Costa, et al. BCF swimming locomotion for autonomous underwater robots: a review and a novel solution to improve control and efficiency. Ocean Engineering, 2017, 130: 437-453.
Y L Yu, K J Huang. Scaling law of fish undulatory propulsion. Physics of Fluids, 2021, 33(6): 061905.
M S Triantafyllou, G S Triantafyllou. An efficient swimming machine. Scientific American, 1995, 272(3): 64-70.
A D Marchese, C D Onal, D Rus. Autonomous soft robotic fish capable of escape maneuvers using fluidic elastomer actuators. Soft Robotics, 2014, 1(1): 75-87.
R Wang, S Wang, Y Wang, et al. Development and motion control of biomimetic underwater robots: A survey. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2022, 52(2): 833-844.
F R Xie, Q Y Zuo, Q L Chen, et al. Designs of the biomimetic robotic fishes performing body and/or caudal fin (BCF) swimming locomotion: A review. Journal of Intelligent & Robotic Systems, 2021, 102(1): 1-19.
G V Lauder. Fish locomotion: recent advances and new directions. Annual Review of Marine Science, 2015, 7: 521-545.
T McMillen, T Williams, P Holmes. Nonlinear muscles, passive viscoelasticity and body taper conspire to create neuromechanical phase lags in anguilliform swimmers. PLoS Computational Biology, 2008, 4(8): e1000157.
S Alben, C Witt, T V Baker, et al. Dynamics of freely swimming flexible foils. Physics of Fluids, 2012, 24(5): 051901.
M Tanha. Complex modal analysis of carangiform swimming kinematics. East Lansing MI: Michigan State University, 2018. https://www.proquest.com/dissertations-theses/complex-modal-analysis-carangiform-swimming/docview/2100023891/se-2?accountid=28855.
C L Hamlet, K A Hoffman, E D Tytell, et al. The role of curvature feedback in the energetics and dynamics of lamprey swimming: A closed-loop model. PLoS Computational Biology, 2018, 14(8): e1006324.
M A B Schwalbe, A L Boden, T N Wise, et al. Red muscle activity in bluegill sunfish Lepomis macrochirus during forward accelerations. Scientific Reports, 2019, 9(1): 1-13.
B Jayne, G Lauder. Red muscle motor patterns during steady swimming in largemouth bass: effects of speed and correlations with axial kinematics. The Journal of Experimental Biology, 1995, 198(7): 1575-1587.
F E Fish, G V Lauder. Passive and active flow control by swimming fishes and mammals. Annual Review of Fluid Mechanics, 2006, 38: 193-224.
R Thandiackal, G V Lauder. How zebrafish turn: Analysis of pressure force dynamics and mechanical work. Journal of Experimental Biology, 2020, 223(16): jeb223230.
K N Lucas, J O Dabiri, G V Lauder. A pressure-based force and torque prediction technique for the study of fish-like swimming. PloS One, 2017, 12(12): e0189225.
T Van Buren, D Floryan, A T Bode-Oke, et al. Foil shapes for efficient fish-like propulsion. AIAA Scitech 2019 Forum, San Diego, California, January 7–11, 2019: 1379.
J M Anderson, K Streitlien, D S Barrett, et al. Oscillating foils of high propulsive efficiency. Journal of Fluid Mechanics, 1998, 360: 41-72.
G V Lauder, J Lim, R Shelton, et al. Robotic models for studying undulatory locomotion in fishes. Marine Technology Society Journal, 2011, 45(4): 41-55.
F Paraz, L Schouveiler, C Eloy. Thrust generation by a heaving flexible foil: Resonance, nonlinearities, and optimality. Physics of Fluids, 2016, 28(1): 011903.
T Van Buren, D Floryan, N Wei, et al. Flow speed has little impact on propulsive characteristics of oscillating foils. Physical Review Fluids, 2018, 3(1): 013103.
S Cinquemani, G Bianchi, F Resta. A coupled CFD and multibody analysis of the hydrodynamics of batoid fish. Bioinspiration, Biomimetics, and Bioreplication X. Proc. of SPIE, April 22, 2020: 11374: 113740B-1.
R X Li, Q Xiao, Y C Liu, et al. A multi-body dynamics based numerical modelling tool for solving aquatic biomimetic problems. Bioinspiration & Biomimetics, 2018, 13(5): 056001.
M Porez, F Boyer, A J Ijspeert. Improved Lighthill fish swimming model for bio-inspired robots: Modeling, computational aspects and experimental comparisons. The International Journal of Robotics Research, 2014, 33(10): 1322-1341.
F Boyer, M Porez, A Leroyer. Poincaré–Cosserat equations for the Lighthill three-dimensional large amplitude elongated body theory: Application to robotics. Journal of Nonlinear Science, 2010, 20(1): 47-79.
A P S Bhalla, R Bale, B E Griffith, et al. Fully resolved immersed electrohydrodynamics for particle motion, electrolocation, and self-propulsion. Journal of Computational Physics, 2014, 256: 88-108.
U Ehrenstein, C Eloy. Skin friction on a moving wall and its implications for swimming animals. Journal of Fluid Mechanics, 2013, 718: 321-346.
K N Lucas, G V Lauder, E D Tytell. Airfoil-like mechanics generate thrust on the anterior body of swimming fishes. Proceedings of the National Academy of Sciences, 2020, 117(19): 10585-10592.
D Zhang, J M van der Hoop, V Petrov, et al. Simulated and experimental estimates of hydrodynamic drag from bio-logging tags. Marine Mammal Science, 2020, 36(1): 136-157.
S Verma, G Abbati, G Novati, et al. Computing the force distribution on the surface of complex, deforming geometries using vortex methods and brinkman penalization. International Journal for Numerical Methods in Fluids, 2017, 85(8): 484-501.
J Y Cheng, T J Pedley, J D Altringham. A continuous dynamic beam model for swimming fish. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences, 1998, 353(1371): 981-997.
P P A Valdivia y Alvarado. Design of biomimetic compliant devices for locomotion in liquid environments. Massachusetts Institute of Technology, 2007, http://hdl.handle.net/1721.1/38927.
G Govindarajan. An investigation to identify the thrust in flapping and undulatory motion of smart Timoshenko beam. Journal of Marine Science and Technology, 2020, 25(3): 743-756.
M Piñeirua, B Thiria, R Godoy-Diana. Modelling of an actuated elastic swimmer. Journal of Fluid Mechanics, 2017, 829: 731-750.
F Boyer, M Porez. Multibody system dynamics for bio-inspired locomotion: from geometric structures to computational aspects. Bioinspiration & Biomimetics, 2015, 10(2): 025007.
F Renda, F Giorgio-Serchi, F Boyer, et al. A unified multi-soft-body dynamic model for underwater soft robots. The International Journal of Robotics Research, 2018, 37(6): 648-666.
Y W Liu, H Z Jiang, Q Huang, et al. Investigation of the resonant effect in carangiform locomotion. 2020 6th International Conference on Mechatronics and Robotics Engineering (ICMRE), Barcelona, Spain, February 12–15, 2020: 58–62.
H Z Jiang, Y W Liu. Nonlinear analysis of compliant robotic fish locomotion. Journal of Vibration and Control, 2021: 1077546321997608.
H Zhao, S C Zhen, Y H Chen. Dynamic modeling and simulation of multi-body systems using the Udwadia-Kalaba theory. Chinese Journal of Mechanical Engineering, 2013, 26(5): 839-850.
A P S Bhalla, B E Griffith, N A Patankar. A forced damped oscillation framework for undulatory swimming provides new insights into how propulsion arises in active and passive swimming. PLoS Computational Biology, 2013, 9(6): e1003097.
C S Peskin. The immersed boundary method. Acta Numerica, 2002, 11: 479-517.
S Kern, P Koumoutsakos. Simulations of optimized anguilliform swimming. Journal of Experimental Biology, 2006, 209(24): 4841-4857.
D Xia, Q F Yin, Z H Li, et al. Numerical study on the hydrodynamics of porpoising behavior in dolphins. Ocean Engineering, 2021, 229: 108985.
D Xia, W S Chen, J K Liu, et al. Using spanwise flexibility of caudal fin to improve swimming performance for small fishlike robots. Journal of Hydrodynamics, 2018, 30(5): 859-871.
Z H Li, D Xia, J B Cao, et al. Hydrodynamics study of dolphin’s self-yaw motion realized by spanwise flexibility of caudal fin. Journal of Ocean Engineering and Science, 2021.
N Y Li, H X Liu, Y M Su. Numerical study on the hydrodynamics of thunniform bio-inspired swimming under self-propulsion. PLoS One, 2017, 12(3): e0174740.
G S Su, H L Shen, N Y Li, et al. Numerical investigation of the hydrodynamics of stingray swimming under self-propulsion. Journal of Fluids and Structures, 2021, 106: 103383.
S Verma, P Hadjidoukas, P Wirth, et al. Multi-objective optimization of artificial swimmers. 2017 IEEE Congress on Evolutionary Computation (CEC), Donostia, Spain, June 5–8, 2017: 1037–1046.
S Verma, P Hadjidoukas, P Wirth, et al. Pareto optimal swimmers. Proceedings of the Platform for Advanced Scientific Computing Conference, Lugano, Switzerland, June 26–28, 2017: 1–11.
D A P Reid, H Hildenbrandt, J T Padding, et al. Fluid dynamics of moving fish in a two-dimensional multiparticle collision dynamics model. Physical Review E, 2012, 85(2): 021901.
N Thekkethil, A Sharma, A Agrawal. Three-dimensional biological hydrodynamics study on various types of batoid fishlike locomotion. Physical Review Fluids, 2020, 5(2): 023101.
A A Shirgaonkar, M A MacIver, N A Patankar. A new mathematical formulation and fast algorithm for fully resolved simulation of self-propulsion. Journal of Computational Physics, 2009, 228(7): 2366-2390.
P N Sun, A Colagrossi, A M Zhang. Numerical simulation of the self-propulsive motion of a fishlike swimming foil using the δ+-SPH model. Theoretical and Applied Mechanics Letters, 2018, 8(2): 115-125.
J G Miles, N A Battista. Naut your everyday jellyfish model: exploring how tentacles and oral arms impact locomotion. Fluids, 2019, 4(3): 169.
J G Miles, N A Battista. Exploring the sensitivity in jellyfish locomotion under variations in scale, frequency, and duty cycle. Journal of Mathematical Biology, 2021, 83(5): 1-34.
N A Battista. Swimming through parameter subspaces of a simple anguilliform swimmer. Integrative and Comparative Biology, 2020, 60(5): 1221-1235.
N A Battista. Fluid-structure interaction for the classroom: interpolation, hearts, and swimming! SIAM Review, 2021, 63(1): 181-207.
A Hemmati, U Senturk, T Van Buren, et al. The performance of a new immersed boundary method on simulating underwater locomotion and swimming. Tenth International Symposium on Turbulence and Shear Flow Phenomena, Chicago, Illinois, July 7–9, 2017: 235–240.
N Nangia, H Johansen, N A Patankar, et al. A moving control volume approach to computing hydrodynamic forces and torques on immersed bodies. Journal of Computational Physics, 2017, 347: 437-462.
D Zhang, G Pan, L M Chao, et al. Mechanisms influencing the efficiency of aquatic locomotion. Modern Physics Letters B, 2018, 32(25): 1850299.
D Zhang, L M Chao, G Pan. Ground effect on a self-propelled undulatory foil. Modern Physics Letters B, 2018, 32(11): 1850135.
N Thekkethil, A Sharma, A Agrawal. Unified hydrodynamics study for various types of fishes-like undulating rigid hydrofoil in a free stream flow. Physics of Fluids, 2018, 30(7): 077107.
N Thekkethil, A Sharma, A Agrawal. Self-propulsion of fishes-like undulating hydrofoil: A unified kinematics based unsteady hydrodynamics study. Journal of Fluids and Structures, 2020, 93: 102875.
Z Cui, H Z Jiang. Numerical study of complex modal characteristics in anguilliform mode of fish swimming. Journal of Mechanical Science and Technology, 2021, 35(10): 4511-4521.
Z Cui, Z Yang, L Shen, et al. Complex modal analysis of the movements of swimming fish propelled by body and/or caudal fin. Wave Motion, 2018, 78: 83-97.
Z Cui, X S Gu, K K Li, et al. CFD studies of the effects of waveform on swimming performance of carangiform fish. Applied Sciences, 2017, 7(2): 149.
P Han, J S Wang, F E Fish, et al. Kinematics and hydrodynamics of a dolphin in forward swimming. AIAA Aviation 2020 Forum, Virtual Event, June 15–19, 2020: 3015. https://doi.org/10.2514/6.2020-3015.
J S Wang, H Tran, M Christino, et al. Hydrodynamics and flow characterization of tuna-inspired propulsion in forward swimming. Fluids Engineering Division Summer Meeting, San Francisco, California, July 28–August 1, 2019: V001T01A025. https://doi.org/10.1115/AJKFluids2019-5472.
J S Wang, V Pavlov, Z P Lou, et al. Computational investigation of thrust production of a dolphin at various swimming speeds. Fluids Engineering Division Summer Meeting, August 10–12, 2021: V001T02A044. https://doi.org/10.1115/FEDSM2021-65792.
A N Zurman-Nasution, B Ganapathisubramani, G D Weymouth. Influence of three-dimensionality on propulsive flapping. Journal of Fluid Mechanics, 2020, 886: A25.
N S Lagopoulos, G D Weymouth, B Ganapathisubramani. Universal scaling law for drag-to-thrust wake transition in flapping foils. Journal of Fluid Mechanics, 2019, 872: R1.
I Borazjani, F Sotiropoulos. Numerical investigation of the hydrodynamics of anguilliform swimming in the transitional and inertial flow regimes. Journal of Experimental Biology, 2009, 212(4): 576-592.
S A Ghaffari, S Viazzo, K Schneider, et al. Simulation of forced deformable bodies interacting with two-dimensional incompressible flows: Application to fish-like swimming. International Journal of Heat and Fluid Flow, 2015, 51: 88-109.
M Bergmann, A Iollo. Modeling and simulation of fish-like swimming. Journal of Computational Physics, 2011, 230(2): 329-348.
C Hamlet, L J Fauci, E D Tytell. The effect of intrinsic muscular nonlinearities on the energetics of locomotion in a computational model of an anguilliform swimmer. Journal of Theoretical Biology, 2015, 385: 119-129.
M Gazzola, M Argentina, L Mahadevan. Scaling macroscopic aquatic locomotion. Nature Physics, 2014, 10(10): 758-761.
G Novati, S Verma, D Alexeev, et al. Synchronisation through learning for two self-propelled swimmers. Bioinspiration & Biomimetics, 2017, 12(3): 036001.
G Tokić, D K P Yue. Optimal shape and motion of undulatory swimming organisms. Proceedings of the Royal Society B: Biological Sciences, 2012, 279(1740): 3065-3074.
M Gazzola, W M Van Rees, P Koumoutsakos. C-start: optimal start of larval fish. Journal of Fluid Mechanics, 2012, 698: 5-18.
A J Wiens, A E Hosoi. Self-similar kinematics among efficient slender swimmers. Journal of Fluid Mechanics, 2018, 840: 106-130.
T L Williams, T McMillen. Strategies for swimming: explorations of the behaviour of a neuro-musculo-mechanical model of the lamprey. Biology Open, 2015, 4(3): 253-258.
C Wagenbach. Biological beam bending: How lamprey muscles can change the viscoelastic properties of their bodies. Medford, MA: Tufts University, 2018. https://www.proquest.com/dissertations-theses/biological-beam-bending-how-lamprey-muscles-can/docview/2027407928/se-2?accountid=28855.
N K Patel, A P S Bhalla, N A Patankar. A new constraint-based formulation for hydrodynamically resolved computational neuromechanics of swimming animals. Journal of Computational Physics, 2018, 375: 684-716.
T Y Ming, B W Jin, J L Song, et al. 3D computational models explain muscle activation patterns and energetic functions of internal structures in fish swimming. PLoS Computational Biology, 2019, 15(9): e1006883.
Z J Zhao, L Dou. Modeling and simulation of the intermittent swimming gait with the muscle-contraction model of pre-strains. Ocean Engineering, 2020, 207: 107391.
G Tokić, D K P Yue. Energetics of optimal undulatory swimming organisms. PLOS Computational Biology, 2019, 15(10): e1007387.
Y Q Xu, Y T Peet. Optimum gaits of 2D thunniform locomotion for efficient swimming and performance of fish pair. 2018 Fluid Dynamics Conference, Atlanta, Georgia, June 25–29, 2018: 2915.
R Tong, Z X Wu, D Chen, et al. Design and optimization of an untethered high-performance robotic tuna. IEEE/ASME Transactions on Mechatronics, 2022. https://doi.org/10.1109/TMECH.2022.3150982.
L C Xu, F B Tian, J C S Lai, et al. Optimal efficiency and heaving velocity in flapping foil propulsion. AIAA Journal, 2021, 59(6): 2143-2154.
G Eguchi, Y Aoki, S Torisawa, et al. Mechanical efficiency of fish thrust induced by tail beating: comparison between kinetic energy and metabolic energy. Journal of Aero Aqua Bio-mechanisms, 2019, 8(1): 54-62.
S Kern. Bioinspired optimization algorithms for the design of anguilliform swimmers. Zurich: ETH Zurich, 2007. https://doi.org/10.3929/ethz-a-005566433.
W M Van Rees, M Gazzola, P Koumoutsakos. Optimal morphokinematics for undulatory swimmers at intermediate Reynolds numbers. Journal of Fluid Mechanics, 2015, 775: 178-188.
C Eloy, L Schouveiler. Optimisation of two-dimensional undulatory swimming at high Reynolds number. International Journal of Non-Linear Mechanics, 2011, 46(4): 568-576.
C Eloy. On the best design for undulatory swimming. Journal of Fluid Mechanics, 2013, 717: 48-89.
N Nangia, R Bale, N Chen, et al. Optimal specific wavelength for maximum thrust production in undulatory propulsion. PloS One, 2017, 12(6): e0179727.
B Sprinkle, R Bale, A P S Bhalla, et al. Hydrodynamic optimality of balistiform and gymnotiform locomotion. European Journal of Computational Mechanics, 2017, 26(1-2): 31-43.
T Bujard, F Giorgio-Serchi, G D Weymouth. A resonant squid-inspired robot unlocks biological propulsive efficiency. Science Robotics, 2021, 6(50): eabd2971.
E Demirer, Y C Wang, A Erturk, et al. Effect of actuation method on hydrodynamics of elastic plates oscillating at resonance. Journal of Fluid Mechanics, 2021, 910: A4.
D Floryan, C W Rowley. Clarifying the relationship between efficiency and resonance for flexible inertial swimmers. Journal of Fluid Mechanics, 2018, 853: 271-300.
M Gazzola, M Argentina, L Mahadevan. Gait and speed selection in slender inertial swimmers. Proceedings of the National Academy of Sciences, 2015, 112(13): 3874-3879.
E D Tytell, C Y Hsu, L J Fauci. The role of mechanical resonance in the neural control of swimming in fishes. Zoology, 2014, 117(1): 48-56.
R Thandiackal, C H White, H Bart-Smith, et al. Tuna robotics: hydrodynamics of rapid linear accelerations. Proceedings of the Royal Society B, 2021, 288(1945): 20202726.
G Li, I Ashraf, B François, et al. Burst-and-coast swimmers optimize gait by adapting unique intrinsic cycle. Communications Biology, 2021, 4(1): 1-7.
X H Li, J Y Gu, Z Q Yao. Numerical study on the hydrodynamics of tuna morphing median fins during C-turn behaviors. Ocean Engineering, 2021, 236: 109547.
Z H Yang, W J Gong, H Chen, et al. Research on the turning maneuverability of a bionic robotic dolphin. IEEE Access, 2022, 10: 7368-7383.
S Gupta, N Thekkethil, A Agrawal, et al. Body-caudal fin fish-inspired self-propulsion study on burst-and-coast and continuous swimming of a hydrofoil model. Physics of Fluids, 2021, 33(9): 091905.
T M Currier, S Lheron, Y Modarres-Sadeghi. A bio-inspired robotic fish utilizes the snap-through buckling of its spine to generate accelerations of more than 20g. Bioinspiration & Biomimetics, 2020, 15(5): 055006.
Z Q Xin, C J Wu. Vorticity dynamics and control of the turning locomotion of 3D bionic fish. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2018, 232(14): 2524-2535.
J O Dabiri, S P Colin, B J Gemmell, et al. Jellyfish and fish solve the challenges of turning dynamics similarly to achieve high maneuverability. Fluids, 2020, 5(3): 106.
Y K Feng, H X Liu, Y Y Su, et al. Numerical study on the hydrodynamics of C-turn maneuvering of a tuna-like fish body under self-propulsion. Journal of Fluids and Structures, 2020, 94: 102954.
J S Wang, P Han, X L Deng, et al. Effects of flapping waveforms on the performance of burst-and-coast swimming in viscous flows. 2018 AIAA Aerospace Sciences Meeting, Kissimmee, Florida, January 8–12, 2018: 0812.
D Xia, W S Chen, J K Liu, et al. The energy-saving advantages of burst-and-glide mode for thunniform swimming. Journal of Hydrodynamics, 2018, 30(6): 1072-1082.
E Akoz, A Mivehchi, K W Moored. Intermittent unsteady propulsion with a combined heaving and pitching foil. Physical Review Fluids, 2021, 6(4): 043101.
C Wei, Q Hu, T J Zhang, et al. Passive hydrodynamic interactions in minimal fish schools. Ocean Engineering, 2022, 247: 110574.
M Saadat, F Berlinger, A Sheshmani, et al. Hydrodynamic advantages of in-line schooling. Bioinspiration & Biomimetics, 2021, 16(4): 046002.
S Heydari, E Kanso. School cohesion, speed and efficiency are modulated by the swimmers flapping motion. Journal of Fluid Mechanics, 2021, 922: A27.
P Han, Y Pan, G Liu, et al. Propulsive performance and vortex wakes of multiple tandem foils pitching in-line. Journal of Fluids and Structures, 2022, 108: 103422.
M M Macias, I F Souza, A C P B Junior, et al. Three-dimensional viscous wake flow in fish swimming-A CFD study. Mechanics Research Communications, 2020, 107: 103547.
M S U Khalid, J Wang, H Dong, et al. Flow transitions and mapping for undulating swimmers. Physical Review Fluids, 2020, 5(6): 063104.
D Zhang, G Pan, L M Chao, et al. Effects of Reynolds number and thickness on an undulatory self-propelled foil. Physics of Fluids, 2018, 30(7): 071902.
D Floryan, T Van Buren, A J Smits. Swimmers’ wake structures are not reliable indicators of swimming performance. Bioinspiration & Biomimetics, 2020, 15(2): 024001.
G Li, D Kolomenskiy, H Liu, et al. On the interference of vorticity and pressure fields of a minimal fish school. Journal of Aero Aqua Bio-mechanisms, 2019, 8(1): 27-33.
A P Maertens, A Gao, M S Triantafyllou. Optimal undulatory swimming for a single fish-like body and for a pair of interacting swimmers. Journal of Fluid Mechanics, 2017, 813: 301-345.
A Gao, M S Triantafyllou. Independent caudal fin actuation enables high energy extraction and control in two-dimensional fish-like group swimming. Journal of Fluid Mechanics, 2018, 850: 304-335.
L Z Dai, G W He, X Zhang, et al. Stable formations of self-propelled fish-like swimmers induced by hydrodynamic interactions. Journal of The Royal Society Interface, 2018, 15(147): 20180490.
S Verma, G Novati, P Koumoutsakos. Efficient collective swimming by harnessing vortices through deep reinforcement learning. Proceedings of the National Academy of Sciences, 2018, 115(23): 5849-5854.
L Li, M Nagy, J M Graving, et al. Vortex phase matching as a strategy for schooling in robots and in fish. Nature Communications, 2020, 11(1): 1-9.
L M Chao, G Pan, D Zhang, et al. On the thrust generation and wake structures of two travelling-wavy foils. Ocean Engineering, 2019, 183: 167-174.
S M Li, C Li, L Y Xu, et al. Numerical simulation and analysis of fish-like robots swarm. Applied Sciences, 2019, 9(8): 1652.
S M Li, C Li, L Y Xu, et al. The research on efficiency of bionic robotic fish cruising formation. 2019 IEEE International Conference on Real-time Computing and Robotics (RCAR), Irkutsk, Russia, August 4–9, 2019: 379–384.
I Ashraf, R Godoy-Diana, J Halloy, et al. Synchronization and collective swimming patterns in fish (Hemigrammus bleheri). Journal of the Royal Society Interface, 2016, 13(123): 20160734.
Y P Wang, X B Yang, Y F Chen, et al. A biorobotic adhesive disc for underwater hitchhiking inspired by the remora suckerfish. Science Robotics, 2017, 2(10): eaan8072.
S Q Wang, L Li, W Zhao, et al. A biomimetic remora disc with tunable, reversible adhesion for surface sliding and skimming. Bioinspiration & Biomimetics, 2022, 17(3): 036001.
L Wen, J C Weaver, P J M Thornycroft, et al. Hydrodynamic function of biomimetic shark skin: effect of denticle pattern and spacing. Bioinspiration & Biomimetics, 2015, 10(6): 066010.
F Giorgio-Serchi, A K Lidtke, G D Weymouth. A soft aquatic actuator for unsteady peak power amplification. IEEE/ASME Transactions on Mechatronics, 2018, 23(6): 2968-2973.
J H Long Jr, M E Porter, R G Root, et al. Go reconfigure: how fish change shape as they swim and evolve. Integrative and Comparative Biology, 2010, 50(6): 1120-1139.
L M Chao, G Pan, D Zhang. Effect of the asymmetric geometry on the wake structures of a pitching foil. Chinese Physics B, 2018, 27(11): 114701.
I Nesteruk, G Passoni, A Redaelli. Shape of aquatic animals and their swimming efficiency. Journal of Marine Biology, 2014, 2014: 470715.
S Reddy, S Sen, C Har. Effect of flexural stiffness distribution of a fin on propulsion performance. Mechanism and Machine Theory, 2018, 129: 218-231.
R Ramamurti, J Geder, K Viswanath, et al. Propulsion characteristics of flapping caudal fins and its upstream interaction with pectoral fins. AIAA Scitech 2019 Forum, San Diego, California, January 7–11, 2019: 1618.
R Mittal, H B Dong, M Bozkurttas, et al. Locomotion with flexible propulsors: II. Computational modeling of pectoral fin swimming in sunfish. Bioinspiration & Biomimetics, 2006, 1(4): S35.
J S Wang, D K Wainwright, R E Lindengren, et al. Tuna locomotion: a computational hydrodynamic analysis of finlet function. Journal of the Royal Society Interface, 2020, 17(165): 20190590.
A P Mignano, S Kadapa, J L Tangorra, et al. Passing the wake: using multiple fins to shape forces for swimming. Biomimetics, 2019, 4(1): 23.
G Liu, B Geng, X D Zheng, et al. An image-guided computational approach to inversely determine in vivo material properties and model flow-structure interactions of fish fins. Journal of Computational Physics, 2019, 392: 578-593.
F Boyer, M Porez, F Morsli, et al. Locomotion dynamics for bio-inspired robots with soft appendages: Application to flapping flight and passive swimming. Journal of Nonlinear Science, 2017, 27(4): 1121-1154.
Y Luo, Q Xiao, G Y Shi, et al. A fluid–structure interaction solver for the study on a passively deformed fish fin with non-uniformly distributed stiffness. Journal of Fluids and Structures, 2020, 92: 102778.
W B Wu. Locomotion of a flexible plate: How the boundary condition of the leading edge affects the self-propulsion performance. European Journal of Mechanics-B/Fluids, 2020, 84: 40-50.
C Y Zhang, H B Huang, X Y Lu. Effect of trailing-edge shape on the self-propulsive performance of heaving flexible plates. Journal of Fluid Mechanics, 2020, 887: A7.
A Matta, J Bayandor, F Battaglia, et al. Effects of fish caudal fin sweep angle and kinematics on thrust production during low-speed thunniform swimming. Biology Open, 2019, 8(7): bio040626.
D Siebelts, A Kater, T Meurer. Modeling and motion planning for an artificial fishtail. IFAC-PapersOnLine, 2018, 51(2): 319-324.
P Liu, S Q Wang, R R Liu, et al. Effects of St and Re on propulsive performance of bionic oscillating caudal fin. Ocean Engineering, 2020, 217: 107933.
A Hussein, S A Ragab, H E Taha, et al. Optimal tail kinematics for fish-like locomotion using the unsteady vortex lattice method. 2018 AIAA Aerospace Sciences Meeting, Kissimmee, Florida, January 8–12, 2018: 0311.
T T Nguyen, B R Lee, T Q Vo. Dynamic analysis of a robotic fish propelled by flexible folding pectoral fins. Robotica, 2020, 38(4): 699-718.
X F Zhou, Z H Li, Y Y Zhu, et al. Effect of pectoral fin flapping motion on swimming performance of robotic dolphin. 2020 IEEE International Conference on Mechatronics and Automation (ICMA), Beijing, China, October 13–16, 2020: 880–885.
L Wen, Z Y Ren, V Di Santo, et al. Understanding fish linear acceleration using an undulatory biorobotic model with soft fluidic elastomer actuated morphing median fins. Soft Robotics, 2018, 5(4): 375-388.
S Z Wang, X Zhang, G W He. Numerical simulation of a three-dimensional fish-like body swimming with finlets. Communications in Computational Physics, 2012, 11(4): 1323-1333.
J L Tangorra, A P Mignano, G N Carryon, et al. Biologically derived models of the sunfish for experimental investigations of multi-fin swimming. 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, San Francisco, California, September 25–30, 2011: 580–587.
R X Li, Q Xiao, Y C Liu, et al. Computational investigation on a self-propelled pufferfish driven by multiple fins. Ocean Engineering, 2020, 197: 106908.
G Liu, Y Ren, H B Dong, et al. Computational analysis of vortex dynamics and performance enhancement due to body–fin and fin–fin interactions in fish-like locomotion. Journal of Fluid Mechanics, 2017, 829: 65-88.
Z J Zhao, L Dou. Effects of the structural relationships between the fish body and caudal fin on the propulsive performance of fish. Ocean Engineering, 2019, 186: 106117.
G J Liu, M M Wang, A Y Wang, et al. Research on flow field perception based on artificial lateral line sensor system. Sensors, 2018, 18(3): 838.
Y G Jiang, Z Q Ma, D Y Zhang. Flow field perception based on the fish lateral line system. Bioinspiration & Biomimetics, 2019, 14(4): 041001.
G J Liu, M M Wang, L Xu, et al. A new bionic lateral line system applied to pitch motion parameters perception for autonomous underwater vehicles. Applied Ocean Research, 2020, 99: 102142.
G J Liu, H H Hao, T T Yang, et al. Flow field perception of a moving carrier based on an artificial lateral line system. Sensors, 2020, 20(5): 1512.
S Verma, C Papadimitriou, N Lüthen, et al. Optimal sensor placement for artificial swimmers. Journal of Fluid Mechanics, 2020, 884: A24.
G J Liu, S K Liu, S R Wang, et al. Research on artificial lateral line perception of flow field based on pressure difference matrix. Journal of Bionic Engineering, 2019, 16(6): 1007-1018.
Z J Tang, Z Wang, J Q Lu, et al. Underwater robot detection system based on fish’s lateral line. Electronics, 2019, 8(5): 566.
A P Maertens, M S Triantafyllou. The boundary layer instability of a gliding fish helps rather than prevents object identification. Journal of Fluid Mechanics, 2014, 757: 179-207.
A A R Gao. Sensing and control for fishlike propulsion in unsteady environments. Cambridge MA: Massachusetts Institute of Technology, 2018.
R Venturelli, O Akanyeti, F Visentin, et al. Hydrodynamic pressure sensing with an artificial lateral line in steady and unsteady flows. Bioinspiration & Biomimetics, 2012, 7(3): 036004.
X W Zheng, C Wang, R F Fan, et al. Artificial lateral line based local sensing between two adjacent robotic fish. Bioinspiration & Biomimetics, 2017, 13(1): 016002.
O Akanyeti, L D Chambers, J Ježov, et al. Self-motion effects on hydrodynamic pressure sensing: Part I. Forward–backward motion. Bioinspiration & Biomimetics, 2013, 8(2): 026001.
D B Quinn, G V Lauder. Tunable stiffness in fish robotics: mechanisms and advantages. Bioinspiration & Biomimetics, 2021, 17(1): 011002.
Q Zhong, J Zhu, F E Fish, et al. Tunable stiffness enables fast and efficient swimming in fish-like robots. Science Robotics, 2021, 6(57): eabe4088.
T L Wang, Z Y Ren, W Q Hu, et al. Effect of body stiffness distribution on larval fish–like efficient undulatory swimming. Science Advances, 2021, 7(19): eabf7364.
J H Long Jr, N M Krenitsky, S F Roberts, et al. Testing biomimetic structures in bioinspired robots: How vertebrae control the stiffness of the body and the behavior of fish-like swimmers. Integrative and Comparative Biology, 2011, 51(1): 158-175.
B Wright, D M Vogt, R J Wood, et al. Soft sensors for curvature estimation under water in a soft robotic fish. 2019 2nd IEEE International Conference on Soft Robotics (RoboSoft), Seoul, South Korea, April 14–18, 2019: 367–371.
A Jusufi, D M Vogt, R J Wood, et al. Undulatory swimming performance and body stiffness modulation in a soft robotic fish-inspired physical model. Soft Robotics, 2017, 4(3): 202-210.
Z Wolf, A Jusufi, D M Vogt, et al. Fish-like aquatic propulsion studied using a pneumatically-actuated soft-robotic model. Bioinspiration & Biomimetics, 2020, 15(4): 046008.
E D Tytell, C Y Hsu, T L Williams, et al. Interactions between internal forces, body stiffness, and fluid environment in a neuromechanical model of lamprey swimming. Proceedings of the National Academy of Sciences, 2010, 107(46): 19832-19837.
D Floryan, C W Rowley. Distributed flexibility in inertial swimmers. Journal of Fluid Mechanics, 2020, 888: A24.
Y Luo, Q Xiao, G Y Shi, et al. The effect of variable stiffness of tuna-like fish body and fin on swimming performance. Bioinspiration & Biomimetics, 2020, 16(1): 016003.
D Xu, H N Zeng, X Peng, et al. A stiffness adjustment mechanism based on negative work for high-efficient propulsion of robotic fish. Journal of Bionic Engineering, 2018, 15(2): 270-282.
K K Li, H Z Jiang, S Y Wang, et al. A soft robotic fish with variable-stiffness decoupled mechanisms. Journal of Bionic Engineering, 2018, 15(4): 599-609.
K K Li, H Z Jiang, J F H, et al. Variable-stiffness decoupling of redundant planar rotational parallel mechanisms with crossed legs. Journal of Vibration and Control, 2018, 24(23): 5525–5533.
B X Chen, H Z Jiang. Swimming performance of a tensegrity robotic fish. Soft Robotics, 2019, 6(4): 520-531.
D S Barrett. The design of a flexible hull undersea vehicle propelled by an oscillating foil. Cambridge MA: Massachusetts Institute of Technology, 1994.
J M Anderson, N K Chhabra. Maneuvering and stability performance of a robotic tuna. Integrative and Comparative Biology, 2002, 42(1): 118-126.
J H Liang, T M Wang, Wang S, et al. Experiment of robofish aided underwater archaeology. 2005 IEEE International Conference on Robotics and Biomimetics (ROBIO), Shatin, HK, China, July 5–9, 2005: 499–504.
J D Liu. Modelling and online optimisation of robotic fish behaviours. Saarbrücken: LAMBERT Academic Publishing, 2013.
T M Wang, L Wen, J H Liang, et al. Fuzzy vorticity control of a biomimetic robotic fish using a flapping lunate tail. Journal of Bionic Engineering, 2010, 7(1): 56-65.
Z S Su, J Z Yu, M Tan, et al. Implementing flexible and fast turning maneuvers of a multijoint robotic fish. IEEE/ASME Transactions on Mechatronics, 2013, 19(1): 329-338.
R X Du, Z Li, K Youcef-Toumi, et al. Robot fish: Bio-inspired fishlike underwater robots. Berlin: Springer Science & Business Media, 2015.
L Li, Lv J, W Chen, et al. Application of Taguchi method in the optimization of swimming capability for robotic fish. International Journal of Advanced Robotic Systems, 2016, 13(3): 102.
C H White, G V Lauder, H Bart-Smith. Tunabot flex: A tuna-inspired robot with body flexibility improves high-performance swimming. Bioinspiration & Biomimetics, 2021, 16(2): 026019.
Y Zhong, Z Li, R X Du. A novel robot fish with wire-driven active body and compliant tail. IEEE/ASME Transactions on Mechatronics, 2017, 22(4): 1633-1643.
P L Nguyen, B R Lee, K K Ahn. Thrust and swimming speed analysis of fish robot with non-uniform flexible tail. Journal of Bionic Engineering, 2016, 13(1): 73-83.
V Kopman, J Laut, F Acquaviva, et al. Dynamic modeling of a robotic fish propelled by a compliant tail. IEEE Journal of Oceanic Engineering, 2014, 40(1): 209-221.
J X Wang, P K McKinley, X B Tan. Dynamic modeling of robotic fish with a base-actuated flexible tail. Journal of Dynamic Systems, Measurement, and Control, 2015, 137(1): 011004.
H El Daou, T Salumäe, L D Chambers, et al. Modelling of a biologically inspired robotic fish driven by compliant parts. Bioinspiration & Biomimetics, 2014, 9(1): 016010.
A J Wahab. A framework for design, modeling, and identification of compliant biomimetic swimmers. Cambridge MA: Massachusetts Institute of Technology, 2008.
W Zhou, Y Q Li. Modeling and analysis of soft pneumatic actuator with symmetrical chambers used for bionic robotic fish. Soft Robotics, 2020, 7(2): 168-178.
T Wang, Y C Zhang, Y P Zhu, et al. A computationally efficient dynamical model of fluidic soft actuators and its experimental verification. Mechatronics, 2019, 58: 1-8.
T Wang, Y C Zhang, Z Chen, et al. Parameter identification and model-based nonlinear robust control of fluidic soft bending actuators. IEEE/ASME Transactions on Mechatronics, 2019, 24(3): 1346-1355.
W P Hu, R Mutlu, W H Li, et al. A structural optimisation method for a soft pneumatic actuator. Robotics, 2018, 7(2): 24.
F Yang, Q Ruan, Y M Man, et al. Design and optimize of a novel segmented soft pneumatic actuator. IEEE Access, 2020, 8: 122304-122313.
H L Li, J T Yao, P Zhou, et al. High-force soft pneumatic actuators based on novel casting method for robotic applications. Sensors and Actuators A: Physical, 2020, 306: 111957.
H Feng, Y Sun, P A Todd, et al. Body wave generation for anguilliform locomotion using a fiber-reinforced soft fluidic elastomer actuator array toward the development of the eel-inspired underwater soft robot. Soft Robotics, 2020, 7(2): 233-250.
J Frame, N Lopez, O Curet, et al. Thrust force characterization of free-swimming soft robotic jellyfish. Bioinspiration & Biomimetics, 2018, 13(6): 064001.
A Joshi, A Kulkarni, Y Tadesse. FludoJelly: Experimental study on jellyfish-like soft robot enabled by soft pneumatic composite (SPC). Robotics, 2019, 8(3): 56.
J Shintake, V Cacucciolo, H Shea, et al. Soft biomimetic fish robot made of dielectric elastomer actuators. Soft Robotics, 2018, 5(4): 466-474.
T F Li, G R Li, Y M Liang, et al. Fast-moving soft electronic fish. Science Advances, 2017, 3(4): e1602045.
J J U Hubbard. Design and characterization of sectored (Patterned) IPMC actuators for propulsion and maneuvering in bio-inspired underwater systems. Reno: University of Nevada, 2011.
Z Q Ye, P Q Hou, Z Chen. 2D maneuverable robotic fish propelled by multiple ionic polymer–metal composite artificial fins. International Journal of Intelligent Robotics and Applications, 2017, 1(2): 195-208.
X J Chen, H Shigemune, H Sawada. An untethered bionic robotic fish using SMA actuators. 2020 IEEE International Conference on Mechatronics and Automation (ICMA), Beijing, China, October 13–16, 2020: 1768–1773.
Z L Wang, G R Hang, J Li, et al. A micro-robot fish with embedded SMA wire actuated flexible biomimetic fin. Sensors and Actuators A: Physical, 2008, 144(2): 354-360.
D A Paley, N M Wereley. Bioinspired sensing, actuation, and control in underwater soft robotic systems. Cham: Springer Nature Switzerland AG, 2021. https://doi.org/10.1007/978-3-030-50476-2.
R Salazar, A Campos, V Fuentes, et al. A review on the modeling, materials, and actuators of aquatic unmanned vehicles. Ocean Engineering, 2019, 172: 257-285.
F B Zhu, C L Zhang, J Qian, et al. Mechanics of dielectric elastomers: materials, structures, and devices. Journal of Zhejiang University-Science A, 2016, 17(1): 1-21.
J Z Yu, M Wang, H F Dong, et al. Motion control and motion coordination of bionic robotic fish: A review. Journal of Bionic Engineering, 2018, 15(4): 579-598.
R Tong, Z X Wu, J Wang, et al. Online optimization of normalized CPGs for a multi-joint robotic fish. 2021 40th Chinese Control Conference (CCC), Shanghai, China, July 26–28, 2021: 4205–4210.
F R Xie, R X Du. Central pattern generator control for a biomimetic robot fish in maneuvering. 2018 IEEE International Conference on Robotics and Biomimetics (ROBIO), Kuala Lumpur, Malaysia, December 12–15, 2018: 268–273.
F R Xie, Y Zhong, R X Du, et al. Central pattern generator (CPG) control of a biomimetic robot fish for multimodal swimming. Journal of Bionic Engineering, 2019, 16(2): 222-234.
J Y Chen, B Yin, C C Wang, et al. Bioinspired closed-loop CPG-based control of a robot fish for obstacle avoidance and direction tracking. Journal of Bionic Engineering, 2021, 18(1): 171-183.
J C Liu, C Zhang, Z N Liu, et al. Design and analysis of a novel tendon-driven continuum robotic dolphin. Bioinspiration & Biomimetics, 2021, 16(6): 065002.
L Zhang, W Zhao, Y H Hu, et al. Development and depth control of biomimetic robotic fish. 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems, San Diego, California, October 29–November 2, 2007: 3560–3565.
F Shen, Z Q Cao, C Zhou, et al. Depth control for robotic dolphin based on fuzzy PID control. International Journal of Offshore and Polar Engineering, 2013, 23(03): 166-171.
J Z Yu, J C Liu, Z X Wu, et al. Depth control of a bioinspired robotic dolphin based on sliding-mode fuzzy control method. IEEE Transactions on Industrial Electronics, 2017, 65(3): 2429-2438.
J Yuan, Z X Wu, J Z Yu, et al. Sliding mode observer-based heading control for a gliding robotic dolphin. IEEE Transactions on Industrial Electronics, 2017, 64(8): 6815-6824.
Z Q Cao, F Shen, C Zhou, et al. Heading control for a robotic dolphin based on a self-tuning fuzzy strategy. International Journal of Advanced Robotic Systems, 2016, 13(1): 28.
C Meurer, A Simha, Ü Kotta, et al. Nonlinear orientation controller for a compliant robotic fish based on asymmetric actuation. 2019 International Conference on Robotics and Automation (ICRA), Montreal, Quebec, May 20–24, 2019: 4688–4694.
R Y Tian, L Li, W Wang, et al. CFD based parameter tuning for motion control of robotic fish. Bioinspiration & Biomimetics, 2020, 15(2): 026008.
J Z Yu, M Tan, Wang S, et al. Development of a biomimetic robotic fish and its control algorithm. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2004, 34(4): 1798-1810.
Y H Hu, W Zhao, L Wang. Vision-based target tracking and collision avoidance for two autonomous robotic fish. IEEE Transactions on Industrial Electronics, 2009, 56(5): 1401-1410.
S L Chen, J X Wang, X B Tan. Backstepping-based hybrid target tracking control for a carangiform robotic fish. Dynamic Systems and Control Conference, Palo Alto, California, October 21–23, 2013: V002T32A005.
J Z Yu, F H Sun, D Xu, et al. Embedded vision-guided 3-D tracking control for robotic fish. IEEE Transactions on Industrial Electronics, 2015, 63(1): 355-363.
S Verma, J X Xu, Q Y Ren, et al. A comparison of robotic fish speed control based on analytical and empirical models. IECON 2016-42nd Annual Conference of the IEEE Industrial Electronics Society, Florence, Italy, October 23–26, 2016: 6055–6060.
X F Li, Q Y Ren, J X Xu. Precise speed tracking control of a robotic fish via iterative learning control. IEEE Transactions on Industrial Electronics, 2015, 63(4): 2221-2228.
T Yuan, Z Y Ren, K N Hu, et al. A Kalman filter based force-feedback control system for hydrodynamic investigation of unsteady aquatic propulsion. 2017 IEEE International Conference on Robotics and Biomimetics (ROBIO), Macau, China, December 5–8, 2017: 1214–1219.
P F Zhang, Z X Wu, Y Meng, et al. Nonlinear model predictive position control for a tail-actuated robotic fish. Nonlinear Dynamics, 2020, 101(4): 2235-2247.
J Pan, J C Liu, J Z Yu. Path-following control of an amphibious robotic fish using fuzzy-linear model predictive control approach. 2020 IEEE International Conference on Mechatronics and Automation (ICMA), Beijing, China, October 13–16, 2020: 886–891.
S Du, C Zhou, J Z Yu, et al. A modified line-of-sight method for path tracking applied to robotic fish. 2020 IEEE International Conference on Mechatronics and Automation (ICMA), Beijing, China, October 13–16, 2020: 809–814.
R Wang, S Wang, Y Wang, et al. Path following for a biomimetic underwater vehicle based on ADRC. 2017 IEEE International Conference on Robotics and Automation (ICRA), Singapore, May 29–June 3, 2017: 3519–3524.
R Wang, S Wang, Y Wang, et al. A paradigm for path following control of a ribbon-fin propelled biomimetic underwater vehicle. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2017, 49(3): 482-493.
J Z Yu, M Tan. Motion control of biomimetic swimming robots. Singapore: Springer Nature Singapore Pte Ltd., 2020. https://doi.org/10.1007/978-981-13-8771-5.
H Cheng, H D Liu, X Q Wang, et al. Approximate piecewise constant curvature equivalent model and their application to continuum robot configuration estimation. 2020 IEEE International Conference on Systems, Man, and Cybernetics (SMC), Toronto, Ontario, October 11–14, 2020: 1929–1936.
M Luo. Pressure-operated soft robotic snake modeling, control, and motion planning. Worcester MA: Worcester Polytechnic Institute, 2017.
M Gazzola, B Hejazialhosseini, P Koumoutsakos. Reinforcement learning and wavelet adapted vortex methods for simulations of self-propelled swimmers. SIAM Journal on Scientific Computing, 2014, 36(3): B622-B639.
S L Brunton, B R Noack, P Koumoutsakos. Machine learning for fluid mechanics. Annual Review of Fluid Mechanics, 2020, 52: 477-508.
M Raissi, Z C Wang, M S Triantafyllou, et al. Deep learning of vortex-induced vibrations. Journal of Fluid Mechanics, 2019, 861: 119-137.
J Rabault, F Ren, W Zhang, et al. Deep reinforcement learning in fluid mechanics: A promising method for both active flow control and shape optimization. Journal of Hydrodynamics, 2020, 32(2): 234-246.
H Xu, W Zhang, J Deng, et al. Active flow control with rotating cylinders by an artificial neural network trained by deep reinforcement learning. Journal of Hydrodynamics, 2020, 32(2): 254-258.
Y S Jiao, F Ling, S Heydari, et al. Learning to swim in potential flow. Physical Review Fluids, 2021, 6(5): 050505.
N Nedjah, L D S Coelho, L D M Mourelle. Mobile robots: The evolutionary approach. Berlin: Springer Science & Business Media, 2007.
T G Thuruthel. Machine learning approaches for control of soft robots. Pisa: Sant'Anna School of Advanced Studies, 2019.
Y Cho, S Manzoor, Y Choi. Adaptation to environmental change using reinforcement learning for robotic salamander. Intelligent Service Robotics, 2019, 12(3): 209-218.
The authors sincerely thanks to Tong Li for English language checking.
Supported by National Natural Science Foundation of China (Grant No. 51275127).
The authors declare no competing financial interests.
About this article
Cite this article
Liu, Y., Jiang, H. Research Development on Fish Swimming. Chin. J. Mech. Eng. 35, 114 (2022). https://doi.org/10.1186/s10033-022-00791-4
- Fish swimming
- Kinematics optimization
- Motion control
- Bionic robotic fish
- Fish locomotion mechanism