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.

Effects of caudal fin stiffness on optimized forward swimming and turning maneuver in a robotic swimmer

In animal and robot swimmers of body and caudal fin (BCF) form, hydrodynamic thrust is mainly produced by their caudal fins, the stiffness of which has profound effects on both thrust and efficiency of swimming. Caudal fin stiffness also affects the motor control and resulting swimming gaits that correspond to optimal swimming performance; however, their relationship remains scarcely explored. Here using magnetic, modular, undulatory robots (μBots), we tested the effects of caudal fin stiffness on both forward swimming and turning maneuver. We developed six caudal fins with stiffness of more than three orders of difference. For aμBot equipped with each caudal fin (andμBot absent of caudal fin), we applied reinforcement learning in experiments to optimize the motor control for maximizing forward swimming speed or final heading change. The motor control ofμBot was generated by a central pattern generator for forward swimming or by a series of parameterized square waves for turning maneuver. In forward swimming, the variations in caudal fin stiffness gave rise to three modes of optimized motor frequencies and swimming gaits including no caudal fin (4.6 Hz), stiffness <10-4Pa m4(∼10.6 Hz) and stiffness >10-4Pa m4(∼8.4 Hz). Swimming speed, however, varied independently with the modes of swimming gaits, and reached maximal at stiffness of 0.23 × 10-4Pa m4, with theμBot without caudal fin achieving the lowest speed. In turning maneuver, caudal fin stiffness had considerable effects on the amplitudes of both initial head steering and subsequent recoil, as well as the final heading change. It had relatively minor effect on the turning motor program except for theμBots without caudal fin. Optimized forward swimming and turning maneuver shared an identical caudal fin stiffness and similar patterns of peduncle and caudal fin motion, suggesting simplicity in the form and function relationship inμBot swimming.

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.

Hydrodynamics of Butterfly-Mode Flapping Propulsion of Dolphin Pectoral Fins with Elliptical Trajectories

This article aims to numerically study the hydrodynamic performance of the bionic dolphin equipped with a pair of rigid pectoral fins. We use dynamic-grid technology and user-defined functions to simulate a novel butterfly-mode flapping propulsion of the fins. This pattern of propulsion is composed of three angular degrees of freedom including the pitch angle ϕp, the azimuth angle ϕa and the roll angle ϕr, which can be divided into four stages for analysis within a single cycle. The stroke of one single pectoral fin can be approximated as an ellipse trajectory, where the amplitudes of ϕa and ϕp, respectively, determine the major and minor axes of the ellipse. The fluid dynamics involved in the specific butterfly pattern is mathematically formulated, and numerical simulation is conducted to investigate the propulsion quantitatively. The results show that the dolphin with a higher water striking frequency f can acquire higher propulsion speed and efficiency. Furthermore, the shape of the ellipse trajectory under different conditions could also have different propulsion effects. The periodic generation and disappearance of vortex structures in the butterfly flapping mode show the evolution process of fluid flow around a pair of pectoral fins, which reveals the influence of motion parameters on fluid dynamics under different working conditions.

Bio-Inspired Aquatic Propulsion Mechanism Using Viscoelastic Fin Containing Fiber Composite Shear Thickening Fluid

Many propulsion mechanisms utilizing elastic fins inspired by the caudal fins of aquatic animals have been developed. However, these elastic fins possess a characteristic whereby the rigidity required to achieve propulsion force and speed increases as the oscillation velocity increases. Therefore, by adding an actuator including a variable stiffness mechanism to the fin it is possible to maintain the optimal stiffness at all times. However, if the aforementioned characteristics allowing the fin itself to change stiffness are present, the need for a variable stiffness mechanism is eliminated, leading to possibilities such as the simplification of the mechanism, improvements in fault tolerance, and enhancements in fin efficiency. The authors developed a fiber composite viscoelastic fin by adding fibers to a shear thickening fluid (STF) and examined the speed dependency of the fin's rigidity. In this work, we examined the structure and speed dependency of the fin's rigidity, as well as the propulsion characteristics in still water and in uniform flow. As a result, the fiber-containing fin containing the STF oobleck (an aqueous suspension of potato starch) demonstrated higher propulsion in still water and higher self-propelled equivalent speed in uniform water flow than elastic fins.

A Comparative and Collaborative Study of the Hydrodynamics of Two Swimming Modes Applicable to Dolphins

This paper presents a hydrodynamics study that examines the comparison and collaboration of two swimming modes relevant to the universality of dolphins. This study utilizes a three-dimensional virtual swimmer model resembling a dolphin, which comprises a body and/or caudal fin (BCF) module, as well as a medium and/or paired fin (MPF) module, each equipped with predetermined kinematics. The manipulation of the dolphin to simulate various swimming modes is achieved through the application of overlapping grids in conjunction with the parallel hole cutting technique. The findings demonstrate that the swimming velocity and thrust attained through the single BCF mode consistently surpass those achieved through the single MPF mode and collaborative mode. Interestingly, the involvement of the MPF mode does not necessarily contribute to performance enhancement. Nevertheless, it is encouraging to note that adjusting the phase difference between the two modes can partially mitigate the limitations associated with the MPF mode. To further investigate the potential advantages of dual-mode collaboration, we conducted experiments by increasing the MPF frequency while keeping the BCF frequency constant, thus introducing the concept of frequency ratio (β). In comparison to the single BCF mode, the collaborative mode with a high β exhibits superior swimming velocity and thrust. Although its efficiency experiences a slight decrease, it tends to stabilize. The corresponding flow structure indirectly verifies the favorable impact of collaboration.

Shape memory alloy-driven undulatory locomotion of a soft biomimetic ray robot

The objective of this study was to imitate undulatory motion, which is a commonly observed swimming mechanism of rays, using a soft morphing actuator. To achieve the undulatory motion, an artificial muscle built with shape memory alloy-based soft actuators was exploited to control the shape-changing behavior of a soft fin membrane. Artificial undulating fins were divided into two categories according to the method of generating the wave motion: single and multiple actuator-driven fins. For empirical research on the transformation and propulsion behavior of each fin type, the design and construction of bound propulsors were undertaken to mimic the structural and behavioral aspects of animals. To visualize the effect of undulatory motion on the swimming efficiency test of the fin beat frequency, a simplified soft undulating fin with a rectangular propulsor was constructed and tested. Additionally, dynamic modeling of the fin tip in wave-traveling was conducted for comparison and optimization. To optimize the thrust and propulsion efficiency of robot speed, the effects of the wave amplitude control and actuator sequence on the fin behavior were examined. An untethered robot was constructed according to the experimental results of the propulsors. Both exhibited exceptional swimming efficiency and maneuverability. The multiple actuator-driven ray robot exhibited a maximum swimming speed of 0.25 body lengths per second which is almost a similar swimming speed with previously reported robots. The developed robot achieved directional swimming (forward and backward) and turning (including rotation). Underwater exploration in an artificial environment was performed using the robot.

Exploration of swimming performance for a biomimetic multi-joint robotic fish with a compliant passive joint

In this paper, a novel compliant joint with two identical torsion springs is proposed for a biomimetic multi-joint robotic fish, which enables imitatation of the swimming behavior of live fish. More importantly, a dynamic model based on the Lagrangian dynamic method is developed to explore the compliant passive mechanism. In the dynamic modeling, a simplified Morrison equation is utilized to analyze the hydrodynamic forces. Further, the parameter identification technique is employed to estimate numerous hydrodynamic parameters. The extensive experimental data with different situations match well with the simulation results, which verifies the effectiveness of the obtained dynamic model. Finally, motivated by the requirement for performance optimization, we firstly take advantage of a dynamic model to investigate the effect of joint stiffness and control parameters on the swimming speed and energy efficiency of a biomimetic multi-joint robotic fish. The results reveal that phase difference plays a primary role in improving efficiency and the compliant joint presents a more significant role in performance improvement when a smaller phase difference is given. Namely, at the largest actuation frequency, the maximum improvement of energy efficiency is obtained and surprisingly approximates 89%. Additionally, the maximum improvement in maximum swimming speed is about 0.19 body lengths per second. These findings demonstrate the potential of compliance in optimizing joint design and locomotion control for better performance.

Design and development of autonomous robotic fish for object detection and tracking

In this article, an autonomous robotic fish is designed for underwater operations like object detection and tracking along with collision avoidance. The computer-aided design model for prototype robotic fish is designed using the Solid Works® software to export an stereolithography (STL) file to MakerBot, a 3D printer, to manufacture the parts of robotic fish using polylactic acid thermoplastic polymer. The precise maneuverability of the robotic fish is achieved by the propulsion of a caudal fin. The oscillation of the caudal fin is controlled by a servomotor. A combination of visual and ultrasonic sensors is used to track the position and distance of the desired object with respect to the fish and also to avoid the obstacles. The robotic fish has the ability to detect an object up to a distance of 90 cm at normal exposure conditions. A computational fluid dynamics analysis is conducted to analyze the fluid hydrodynamics (flow rate of water and pressure) around the hull of a robotic fish and the drag force acting on it. A series of experimental results have shown the effectiveness of the designed underwater robotic fish.

Fluid-structure interaction modeling on a 3D ray-strengthened caudal fin

In this paper, we present a numerical model capable of solving the fluid-structure interaction problems involved in the dynamics of skeleton-reinforced fish fins. In this model, the fluid dynamics is simulated by solving the Navier-Stokes equations using a finite-volume method based on an overset, multi-block structured grid system. The bony rays embedded in the fin are modeled as nonlinear Euler-Bernoulli beams. To demonstrate the capability of this model, we numerically investigate the effect of various ray stiffness distributions on the deformation and propulsion performance of a 3D caudal fin. Our numerical results show that with specific ray stiffness distributions, certain caudal fin deformation patterns observed in real fish (e.g. the cupping deformation) can be reproduced through passive structural deformations. Among the four different stiffness distributions (uniform, cupping, W-shape and heterocercal) considered here, we find that the cupping distribution requires the least power expenditure. The uniform distribution, on the other hand, performs the best in terms of thrust generation and efficiency. The uniform stiffness distribution, per se, also leads to 'cupping' deformation patterns with relatively smaller phase differences between various rays. The present model paves the way for future work on dynamics of skeleton-reinforced membranes.

Curvature-induced stiffening of a fish fin

How fish modulate their fin stiffness during locomotive manoeuvres remains unknown. We show that changing the fin's curvature modulates its stiffness. Modelling the fin as bendable bony rays held together by a membrane, we deduce that fin curvature is manifested as a misalignment of the principal bending axes between neighbouring rays. An external force causes neighbouring rays to bend and splay apart, and thus stretches the membrane. This coupling between bending the rays and stretching the membrane underlies the increase in stiffness. Using three-dimensional reconstruction of a mackerel (Scomber japonicus) pectoral fin for illustration, we calculate the range of stiffnesses this fin is expected to span by changing curvature. The three-dimensional reconstruction shows that, even in its geometrically flat state, a functional curvature is embedded within the fin microstructure owing to the morphology of individual rays. As the ability of a propulsive surface to transmit force to the surrounding fluid is limited by its stiffness, the fin curvature controls the coupling between the fish and its surrounding fluid. Thereby, our results provide mechanical underpinnings and morphological predictions for the hypothesis that the spanned range of fin stiffnesses correlates with the behaviour and the ecological niche of the fish.

Effects of stiffness distribution and spanwise deformation on the dynamics of a ray-supported caudal fin

Using a fluid-structure interaction model, we study the effect of ray stiffness distribution on the deformation and performance of a caudal fin. By prescribing a simple swaying motion, our results show that through passive structural deformation alone it is possible to reproduce some complicated fin movements (e.g. the cup and 'W'-shape deformations) observed in real fish. Moreover, it has been numerically shown that, compared with a fin with uniform ray stiffness, at the same (average) ray stiffness fins with nonuniform stiffness distribution may achieve further performance enhancement, e.g. increase in propulsion efficiency and decrease in lateral force generation. This is attributed to spanwise deformations caused by phase differences between different rays.

Investigation of Collective Behaviour and Electrocommunication in the Weakly Electric Fish, Mormyrus rume, through a biomimetic Robotic Dummy Fish

A robotic fish has been developed to create a mixed bio-hybrid system made up of weakly electric fish and a mobile dummy fish. Weakly electric fish are capable of interacting with each other via sequences of self-generated electric signals during electrocommunication. Here we present the design of an artificial dummy fish, which is subsequently tested in behavioural experiments. The robot consists of two parts: a flexible tail that can move at different frequencies and amplitudes, performing a carangiform oscillation, and a rigid head containing the motor for the tail oscillation. The dummy fish mimics the weakly electric fish Mormyrus rume in morphology, size and electric signal generation. In order to study electrical interactions, the dummy fish is equipped with ten electrodes that record electric signals of nearby real fish and generate electric dipole fields around itself that are similar to those produced by real fish in both waveform and sequence. Behavioural experiments demonstrate that the dummy fish is able to recruit both single individuals and groups of M. rume from a shelter into an exposed area. The development of an artificial dummy fish may help to understand fundamental aspects of collective behaviour in weakly electric fish and the properties necessary to initiate and sustain it in closed-loop feedback experiments based on electrocommunication.

Optimal chordwise stiffness profiles of self-propelled flapping fins

The versatility of fish to adapt to different swimming requirements is attributed to their complex muscular system. Fish modulate their fin stiffness and shape for maximized performance. In this paper, optimal chordwise stiffness profiles that maximize the propulsive performance have been predicted using theoretical studies. An experimental setup has been fabricated to measure the stiffness profiles of real fish caudal fins. Chordwise varying stiffness robotic fins fabricated using carbon fiber reinforced composites (CFRC) have been tested in the water tunnel to evaluate their performance over constant stiffness fins. It is observed that the varying stiffness fins produce larger thrusts and efficiencies compared to constant stiffness fins for all the operating conditions considered in this work. A comparison of the digital image correlation (DIC) measured deformations of the fins showed that the better performance of varying stiffness fins is due to their larger curvatures and trailing edge amplitudes. These theoretical and experimental studies provide a greater understanding of the role of stiffness in fish fins for locomotion.

Application of Taguchi Method in the Optimization of Swimming Capability for Robotic Fish

In this paper, we applied the Taguchi method to evaluate the maximum swimming speed of a robotic fish under the limitation of the output of the motor. Four factors were considered in the optimization: the caudal-fin aspect ratio, the caudal fin stiffness, the oscillating frequency and the stiffness of the spring that transmits forces from the actuators to the foil. Because of the power limitations, the parameter's space was irregular. Since the Taguchi method requires a regular parameter space, we divided the parameter space into a regular space and the remaining irregular spaces. Within only 25 trials, the frequency and the spring stiffness were determined as the main factors in the regular space by the orthogonal design. Six more trials were carried out in the remaining irregular space with a higher frequency and spring stiffness. The fastest swimming speed of 870 mm/s, approximately 2.6 BL ( Body Lengths)/ s, was acquired, when the frequency reached 12 Hz and with infinite spring stiffness. This method is efficient for exploring the maximum locomotor capabilities of robotic fish and may also be useful for other robots as no modelling is required.

Investigation of Fish Caudal Fin Locomotion Using a Bio-Inspired Robotic Model

Due to its advantages of realizing repeatable experiments, collecting data and isolating key factors, the bio-robotic model is becoming increasingly important in the study of biomechanics. The caudal fin of fish has long been understood to be central to propulsion performance, yet its contribution to manoeuverability, especially for homocercal caudal fin, has not been studied in depth. In the research outlined in this paper, we designed and fabricated a robotic caudal fin to mimic the morphology and the three-dimensional (3D) locomotion of the tail of the Bluegill Sunfish ( Lepomis macrochirus). We applied heave and pitch motions to the robot to model the movement of the caudal peduncle of its biological counterpart. Force measurements and 2D and 3D digital particle image velocimetry were then conducted under different movement patterns and flow speeds. From the force data, we found the addition of the 3D caudal fin locomotion significantly enhanced the lift force magnitude. The phase difference between the caudal fin ray and peduncle motion was a key factor in simultaneously controlling the thrust and lift. The increased flow speed had a negative impact on the generation of lift force. From the average 2D velocity field, we observed that the vortex wake directed water both axially and vertically, and formed a jet-like structure with notable wake velocity. The 3D instantaneous velocity field at 0.6 T indicated the 3D motion of the caudal fin may result in asymmetry wake flow patterns relative to the mid-sagittal plane and change the heading direction of the shedding vortexes. Based on these results, we hypothesized that live fish may actively tune the movement between the caudal fin rays and the peduncle to change the wake structure behind the tail and hence obtain different thrust and lift forces, which contributes to its high manoeuvrability.

Evolutionary multiobjective design of a flexible caudal fin for robotic fish

Robotic fish accomplish swimming by deforming their bodies or other fin-like appendages. As an emerging class of embedded computing system, robotic fish are anticipated to play an important role in environmental monitoring, inspection of underwater structures, tracking of hazardous wastes and oil spills, and the study of live fish behaviors. While integration of flexible materials (into the fins and/or body) holds the promise of improved swimming performance (in terms of both speed and maneuverability) for these robots, such components also introduce significant design challenges due to the complex material mechanics and hydrodynamic interactions. The problem is further exacerbated by the need for the robots to meet multiple objectives (e.g., both speed and energy efficiency). In this paper, we propose an evolutionary multiobjective optimization approach to the design and control of a robotic fish with a flexible caudal fin. Specifically, we use the NSGA-II algorithm to investigate morphological and control parameter values that optimize swimming speed and power usage. Several evolved fin designs are validated experimentally with a small robotic fish, where fins of different stiffness values and sizes are printed with a multi-material 3D printer. Experimental results confirm the effectiveness of the proposed design approach in balancing the two competing objectives.

Mechatronic design and locomotion control of a robotic thunniform swimmer for fast cruising

This paper presents mechatronic design and locomotion control of a biomimetic robotic fish that swims using thunniform kinematics for fast cruising. Propulsion of the robotic fish is realized with a parallel four-bar propulsive mechanism that delivers combined translational and rotational motion to a lunate caudal fin. A central pattern generator controller, composed of two unidirectionally coupled Hopf oscillators, is employed to generate robust, smooth and coordinated oscillatory control signals for the tail joints. In order to maintain correct phase relation between joints during fast tail beating, a novel phase adjusting mechanism is proposed and incorporated into the controller. The attitude of the robotic fish in fast swimming is stabilized using an attitude and heading reference system unit and a pair of pitching pectoral fins. The maximum speed of the robotic fish can reach 2.0 m s(-1), which is the fastest speed that robotic fishes have achieved. Its outstanding swimming performance presents possibilities for deployment to real-world exploration, probe and survey missions.

Design of a variable-stiffness flapping mechanism for maximizing the thrust of a bio-inspired underwater robot

Compliance can increase the thrust generated by the fin of a bio-inspired underwater vehicle. To improve the performance of a compliant fin, the compliance should change with the operating conditions; a fin should become stiffer as the oscillating frequency increases. This paper presents a novel variable-stiffness flapping (VaSF) mechanism that can change its stiffness to maximize the thrust of a bio-inspired underwater robot. The mechanism is designed on the basis of an endoskeleton structure, composed of compliant and rigid segments alternately connected in series. To determine the attachment point of tendons, the anatomy of a dolphin's fluke is considered. Two tendons run through the mechanism to adjust the stiffness. The fluke becomes stiffer when the tendons are pulled to compress the structure. The thrust generated by a prototype mechanism is measured under different conditions to show that the thrust can be maximized by changing the stiffness. The thrust of the VaSF device can approximately triple at a certain frequency just by changing the stiffness. This VaSF mechanism can be used to improve the efficiency of a bio-inspired underwater robot that uses compliance.

Modelling of a biologically inspired robotic fish driven by compliant parts

Inspired by biological swimmers such as fish, a robot composed of a rigid head, a compliant body and a rigid caudal fin was built. It has the geometrical properties of a subcarangiform swimmer of the same size. The head houses a servo-motor which actuates the compliant body and the caudal fin. It achieves this by applying a concentrated moment on a point near the compliant body base. In this paper, the dynamics of the compliant body driving the robotic fish is modelled and experimentally validated. Lighthill's elongated body theory is used to define the hydrodynamic forces on the compliant part and Rayleigh proportional damping is used to model damping. Based on the assumed modes method, an energetic approach is used to write the equations of motion of the compliant body and to compute the relationship between the applied moment and the resulting lateral deflections. Experiments on the compliant body were carried out to validate the model predictions. The results showed that a good match was achieved between the measured and predicted deformations. A discussion of the swimming motions between the real fish and the robot is presented.

A bioinspired autonomous swimming robot as a tool for studying goal-directed locomotion

The bioinspired approach has been key in combining the disciplines of robotics with neuroscience in an effective and promising fashion. Indeed, certain aspects in the field of neuroscience, such as goal-directed locomotion and behaviour selection, can be validated through robotic artefacts. In particular, swimming is a functionally important behaviour where neuromuscular structures, neural control architecture and operation can be replicated artificially following models from biology and neuroscience. In this article, we present a biomimetic system inspired by the lamprey, an early vertebrate that locomotes using anguilliform swimming. The artefact possesses extra- and proprioceptive sensory receptors, muscle-like actuation, distributed embedded control and a vision system. Experiments on optimised swimming and on goal-directed locomotion are reported, as well as the assessment of the performance of the system, which shows high energy efficiency and adaptive behaviour. While the focus is on providing a robotic platform for testing biological models, the reported system can also be of major relevance for the development of engineering system applications.