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

Self-deployable contracting-cord metamaterials with tunable mechanical properties

Recent advances in active materials and fabrication techniques have enabled the production of cyclically self-deployable metamaterials with an expanded functionality space. However, designing metamaterials that possess continuously tunable mechanical properties after self-deployment remains a challenge, notwithstanding its importance. Inspired by push puppets, we introduce an efficient design strategy to create reversibly self-deployable metamaterials with continuously tunable post-deployment stiffness and damping. Our metamaterial comprises contracting actuators threaded through beads with matching conical concavo-convex interfaces in networked chains. The slack network conforms to arbitrary shapes, but when actuated, it self-assembles into a preprogrammed configuration with beads gathered together. Further contraction of the actuators can dynamically tune the assembly's mechanical properties through the beads' particle jamming, while maintaining the overall structure with minimal change. We show that, after deployment, such metamaterials exhibit pronounced tunability in bending-dominated configurations: they can become more than 35 times stiffer and change their damping capability by over 50%. Through systematic analysis, we find that the beads' conical angle can introduce geometric nonlinearity, which has a major effect on the self-deployability and tunability of the metamaterial. Our work provides routes towards reversibly self-deployable, lightweight, and tunable metamaterials, with potential applications in soft robotics, reconfigurable architectures, and space engineering.

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.

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

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

Performance Optimization for Bionic Robotic Dolphin with Active Variable Stiffness Control

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

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.

A Torque Control Strategy for a Robotic Dolphin Platform Based on Angle of Attack Feedback

Biological fish can always sense the state of water flow and regulate the angle of attack in time, so as to maintain the highest movement efficiency during periodic flapping. The biological adjustment of the caudal fin's angle of attack (AoA) depends on the contraction/relaxation of the tail muscles, accompanying the variation in tail stiffness. During an interaction with external fluid, it helps to maintain the optimal angle of attack during movement, to improve the propulsion performance. Inspired by this, this paper proposes a tail joint motion control scheme based on AoA feedback for the high-speed swimming of bionic dolphins. Firstly, the kinematic characteristics of the designed robot dolphin are analyzed, and the hardware basis is clarified. Second, aiming at the deficiency of the tail motor, which cannot effectively cooperate with the waist joint motor during high-frequency movement, a compensation model for the friction force and latex skin-restoring force is designed, and a joint angle control algorithm based on fuzzy inference is proposed to realize the tracking of the desired joint angle for the tail joint in torque mode. In addition, a tail joint closed-loop control scheme based on angle of attack feedback is proposed to improve the motion performance. Finally, experiments verify the effectiveness of the proposed motion control scheme.

Experimental analysis of the sweepback angle effect on the thrust generation of a robotic penguin wing

Penguins have evolved excellent swimming skills as diving birds, benefiting from their agile wings. This paper experimentally analyzes the effects of the wing sweepback angle on thrust generation using a robotic penguin wing. A developed wing mechanism that can realize penguin-like flapping and feathering motion was used for actuating five alternative wing models, with different sweepback angles ranging from 0° to 50°. Force measurements under a steady water flow were conducted for both fixed and flapping states for all wing models. The results showed that small sweepback angles of 30° or less in the fixed state caused a steep lift curve and a moderate sweepback angle of 30° produced the largest lift-to-drag ratio. In the flapping state, the smaller sweepback wings generated a larger net thrust for the same wing motion, whereas the larger-sweepback wings produced more thrust under the same Strouhal number. The findings also revealed that larger sweepback wings more easily achieve the maximum net thrust in terms of less angle-of-attack control. In contrast, the hydrodynamic efficiency was not greatly affected by the sweepback. Regardless of the sweepback, the trend of the efficiency increasing with increasing flow speed indicates that the penguin wings can be more suitable for high-speed locomotion for higher hydrodynamic efficiency.

Thrust Improvement of a Biomimetic Robotic Fish by Using a Deformable Caudal Fin

In nature, live fish has various deformable fins which are capable to promote the swimming speed, efficiency, stability, and thrust generation. However, this feature is rarely possessed by current man-made biomimetic robotic fishes. In this paper, a novel deformable caudal fin platform is proposed to improve thrust generation of biomimetic robotic fish. First, the design of the deformable caudal fin is given, which includes a servo motor, a gear-based transmission mechanism, fin bones, and silica membrane. Second, an improved Central Pattern Generator (CPG) model was developed to coordinately control the flapping of the tail and the deformation of the caudal fin. More specifically, three deformation patterns, i.e., conventional nondeformable mode, sinusoidal-based mode, instant mode, of the caudal fin are investigated. Third, extensive experiments are conducted to explore the effects of deformation of the caudal fin on the thrust generation of the biomimetic robotic fish. It was found that the instant mode of the caudal fin has the largest thrust, which sees a 27.5% improvement compared to the conventional nondeformable mode, followed by the sinusoidal-based mode, which also sees an 18.2% improvement. This work provides a novel way to design and control the deformation of the caudal fin, which sheds light on the development of high-performance biomimetic robotic fish.

Design and implementation of a swimming robot with pectoral fins only

The use of swimming robots has increased widely in recent years due to the need of using them in situations where human intervention is difficult or not allowed. Exploring depths of seas, military interventions, or entering areas where the amount of water pollution is high that may threaten the lives of divers. In such cases, the best alternative for humans is to use swimming robots. This paper presents a swimming robot based on Labriform swimming mode. First, it starts with an analytical study of the effect of the fins shape on the performance of a robotic fish. The suggested design of the pectoral fins is concave. The effect of such a design would help largely in achieving the highest thrust in comparison to flat designs provided in the literature. Secondly, a variation in the velocity between the power and recovery strokes is accomplished and a maximum thrust can be obtained when the velocity of the power stroke is three times the velocity of recovery stroke. Thirdly, the kinematics and dynamics of the swimming robot are derived and an evaluation of the total hydrodynamic forces that are exerted on the robot’s body is studied via the computational fluid dynamics method from SOLIDWORKS® platform. Finally, the obtained results are compared to other designs in the literature in terms of some dimensionless numbers of biological fish to examine the efficiency. The proposed design has been validated theoretically and examined experimentally. The results of the simulation and practical experiments confirmed the validity of the design.

Tunable stiffness in fish robotics: mechanisms and advantages

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

Design and analysis of a novel tendon-driven continuum robotic dolphin

In this paper, a novel continuum robotic dolphin termed 'ConRoDolI' is proposed and developed. The biomimetic robot features dual tendon driving continuum mechanisms that are utilized to replicate the twisting and bending motions of the dolphin's caudal vertebrae and thoracic vertebrae. More importantly, a central pattern generator based kinematics is analyzed to yield stable dolphin-like swimming. In the meantime, the relationship between the backbone shape and both the tendon length as well as position and orientation are explored. Furthermore, multimodal swimming gaits are designed to pave the way for a three-dimensional (3D) swimming decoupling solution, involving forwarding swimming, multiple yaw patterns, and multiple pitch patterns. All of these endow the robotic dolphin with 3D maneuverability. Finally, extensive experiments demonstrate the feasibility of the proposed biomimetic mechatronic design and control approach. The forward swimming speed is 0.44 body lengths per second (BL/s). The steering radius of the robot is about 0.11 BL with an angular velocity of 10°/s and the diving speed is about 0.13 BL/s. The average propulsion efficiency is about 0.6 with the maximum is over 0.8. The obtained results shed light on the improvement of aquatic maneuverability associated with new-concept underwater vehicles.

Tunable stiffness enables fast and efficient swimming in fish-like robots

Fish maintain high swimming efficiencies over a wide range of speeds. A key to this achievement is their flexibility, yet even flexible robotic fish trail real fish in terms of performance. Here, we explore how fish leverage tunable flexibility by using their muscles to modulate the stiffness of their tails to achieve efficient swimming. We derived a model that explains how and why tuning stiffness affects performance. We show that to maximize efficiency, muscle tension should scale with swimming speed squared, offering a simple tuning strategy for fish-like robots. Tuning stiffness can double swimming efficiency at tuna-like frequencies and speeds (0 to 6 hertz; 0 to 2 body lengths per second). Energy savings increase with frequency, suggesting that high-frequency fish-like robots have the most to gain from tuning stiffness.

Variable Rigidity Module with a Flexible Thermoelectric Device for Bidirectional Temperature Control

Dynamic stiffness tuning is a promising approach for shape reconfigurable systems that must adapt their flexibility in response to changing operational requirements. Among stiffness tuning technologies, phase change materials are particularly promising because they are size scalable and can be powered using portable electronics. However, the long transition time required for phase change is a great limitation for most applications. In this study, we address this by introducing a rapidly responsive variable rigidity module with a low melting point material and flexible thermoelectric device (f-TED). The f-TED can conduct bidirectional temperature control; thereby, both heating and cooling were accomplished in a single device. By performing local cooling, the phase transition time from liquid to solid is reduced by 77%. The module in its rigid state shows 14.7 × higher bending stiffness than in the soft state. The results can contribute to greatly widening the application of phase transition materials for variable rigidity.

Tendon-Driven Jamming Mechanism for Configurable Variable Stiffness

Stiffness transition of a soft continuum body is an essential feature for dexterous interaction with an unstructured environment. Softness ensures safe interaction, whereas rigidness generates high force for movement or manipulation. Vacuum-based granular jamming is a widely used technique for on-line stiffness transition because of its high reconfigurability and intuitive driving method. However, vacuum driving method produces limited force levels, and the heavy weight and bulky size are unfavorable for portable applications. In this work, we propose a tendon-driven jamming mechanism for configurable variable stiffness. Compared with a vacuum system, an electric motor-tendon drive system has the benefits of force, bandwidth, size, and weight, but has different force characteristics for distribution, directionality, and transmissibility. In this study, a long snake-like shape is chosen instead of a lump shape for compatibility with tendon-drive characteristics. The snake-like shape is likely to cause buckling under the tendon force as the length increases, making the system extremely unstable. Implanting skeletal disk nodes in the structure is our solution to the buckling phenomenon by maintaining the tendon path in the desired position and for distributing the force evenly, thereby achieving stable stiffness transition capabilities for long free-curved shapes. As a proof of concept, a soft wearable device for wrist support is presented using the proposed variable stiffness mechanism. The weight of the device is 184 g, including the actuators, and it can support 2 kgf. Furthermore, the stiffness transition is completed within 2 s, thus achieving quick responses.

Numerical study on the hydrodynamics of thunniform bio-inspired swimming under self-propulsion

Numerical simulations are employed to study the hydrodynamics of self-propelled thunniform swimming. The swimmer is modeled as a tuna-like flexible body undulating with kinematics of thunniform type. The wake evolution follows the vortex structures arranged nearly vertical to the forward direction, vortex dipole formation resulting in the propulsion motion, and finally a reverse Kármán vortex street. We also carry out a systematic parametric study of various aspects of the fluid dynamics behind the freely swimming behavior, including the swimming speed, hydrodynamic forces, power requirement and wake vortices. The present results show that the fin thrust as well as swimming velocity is an increasing function of both tail undulating amplitude Ap and oscillating amplitude of the caudal fin θm. Whereas change on the propulsive performance with Ap is associated with the strength of wake vortices and the area of suction region on the fin, the swimming performance improves with θm due to the favorable tilting of the fin that make the pressure difference force more oriented toward the thrust direction. Moreover, the energy loss in the transverse direction and the power requirement increase with Ap but decrease with θm, and this indicates that for achieving a desired swimming speed increasing θm seems more efficiently than increasing Ap. Furthermore, we have compared the current simulations with the published experimental studies on undulatory swimming. Comparisons show that our work tackles the flow regime of natural thunniform swimmers and follows the principal scaling law of undulatory locomotion reported. Finally, this study enables a detailed quantitative analysis, which is difficult to obtain by experiments, of the force production of the thunniform mode as well as its connection to the self-propelled swimming kinematics and vortex wake structure. The current findings help provide insights into the swimming performance and mechanisms of self-propelled thunniform locomotion.

Fluid Dynamics of Biomimetic Pectoral Fin Propulsion Using Immersed Boundary Method

Numerical simulations are carried out to study the fluid dynamics of a complex-shaped low-aspect-ratio pectoral fin that performs the labriform swimming. Simulations of flow around the fin are achieved by a developed immersed boundary (IB) method, in which we have proposed an efficient local flow reconstruction algorithm with enough robustness and a new numerical strategy with excellent adaptability to deal with complex moving boundaries involved in bionic flow simulations. The prescribed fin kinematics in each period consists of the power stroke and the recovery stroke, and the simulations indicate that the former is mainly used to provide the thrust while the latter is mainly used to provide the lift. The fin wake is dominated by a three-dimensional dual-ring vortex wake structure where the partial power-stroke vortex ring is linked to the recovery-stroke ring vertically. Moreover, the connection of force production with the fin kinematics and vortex dynamics is discussed in detail to explore the propulsion mechanism. We also conduct a parametric study to understand how the vortex topology and hydrodynamic characteristics change with key parameters. The results show that there is an optimal phase angle and Strouhal number for this complicated fin. Furthermore, the implications for the design of a bioinspired pectoral fin are discussed based on the quantitative hydrodynamic analysis.