1. Introduction
Most fish generate thrust by passing a traveling wave of increasing amplitudes from head to tail. This kind of fish is known as the Body and/or Caudal Fin (BCF) swimmer [
1,
2]. For a BCF swimmer, the posterior part of the fish body is much more important than the anterior part for swimming locomotion since it is where most of the thrust comes from. As a result, a careful design of the posterior part, especially the caudal fin, is essential for developing a high-performance biomimetic robotic fish, which is useful in some applications such as narrow space navigation, low-noise surveillance, and environment monitoring.
At present, studies about the caudal fin’s flapping pattern, stiffness, and shape are attracting researchers’ attention. Isolating effects of such parameters is difficult in live fish. As a result, robotic models are developed to provide an alternative way. For example, Xie et al. examined how tail’s flapping patterns (with different amplitudes, frequencies, asymmetry, and shape parameters) affected fish swimming performances, such as the cruising speed, the recoil, the thrust generation, and swimming efficiency [
3]. Notably, they found that the sinusoidal flapping pattern of the caudal fin, which was also adopted in Lighthill’s Elongated Body Theory (EBT) [
4,
5], had a good balance among the thrust generation, the recoil, and the swimming speed, which resulted in a high swimming efficiency. The stiffness also has a significant effect on swimming performances. Wolf et al. developed a pneumatically actuated fish-like model to study the role of stiffness on locomotor thrust generation. They showed that both the thrust and lateral force rose with the increase in frequency for the stiffer model. The stiffer the tail, the more impact the increasing frequency had on thrust generation. Moreover, flexural stiffness falls along fish’s anterior-posterior axis in nature [
6]. In order to examine the role of non-uniform bending stiffness during fish swimming, Lucas et al. fabricated foil models with discrete regions of high (5.5 × 10
−5 Nm
2) and low (1.9 × 10
−5 Nm
2) flexural stiffness of biologically relevant magnitudes. In comparison to the uniform distributions of stiffness, the combination of non-uniform stiffness distributions and 0° angle of attack pitching program better mimicked the kinematics of live fish swimming; thus, it also had better swimming performances in terms of speed, efficiency, and thrust generation [
7]. Matta et al. compared three shapes of the caudal fins, i.e., rectangular, elliptical, and swept (lunar). It was found that the lunar caudal fin, most similar to a fusiform swimmer, had the largest thrust, followed by the elliptical fin. The rectangular caudal fin generally generated the least thrust [
8,
9,
10]. Similar conclusions can also be found in [
11,
12,
13,
14,
15].
The above studies shed light on the role of caudal fin’s flapping pattern, stiffness, and shape on the swimming performances. However, the stiffness and shape of the caudal fin usually cannot be changed when the robotic fish is freely swimming. In contrast, live fish is capable of modulating the stiffness or shape during swimming in real-time to adapt to surrounding aquatic environment [
16,
17,
18,
19]. Accordingly, novel mechanisms to adjust stiffness are developed for biomimetic robotic fishes in these years. Chen et al. designed and fabricated two tensegrity robotic fishes, one of which was based on tensegrity joints by means of tension elements [
20], and the other one of which was based on antagonistic stiffness that resulted from the prestress of tension structures in a kinematically singular configuration [
21]. Park et al. proposed a novel variable-stiffness flapping (VaSF) mechanism for a biomimetic robotic dolphin. This mechanism was made up of compliant and rigid segments alternately in series, and two tendons run through it to adjust stiffness [
22]. In order to decouple the adjustable stiffness from the inherent stiffness, Li et al. proposed a stiffness decoupled mechanism based on the Mechanically Adjustable Compliance and Controllable Equilibrium Position Actuator (MACCEPA), and used it to construct a soft biomimetic robotic fish with large stiffness variation [
23]. Zhong et al. developed a variable-stiffness experimental platform and explained how and why tuning stiffness affected performances. Notably, they found that the stiffness should be scaled with swimming speed squared to maximize the swimming speed, which provided a simple stiffness tuning strategy for biomimetic robotic fish [
24]. In comparison to stiffness-variation mechanisms, studies about mechanisms to online modulate the shape of a caudal fin are far less. A caudal fin with a hole and a moving cover on it was developed. By actuating the moving cover, the area of the caudal fin could be adjusted [
25,
26]. Tangorra and Lauder [
27,
28,
29] developed several robotic fins, including the caudal fin, to study how fish produced and controlled forces, finding that subtle changes to the kinematics and mechanical properties of fin rays can significantly impact the magnitude, direction, and time course of the 3D forces used for propulsion and maneuvers. More specifically, the deformable caudal fin was made up by six individually moveable fin rays, and five kinematic patterns were examined, i.e., flat movement of the entire fin, cupping of the fin, W-shaped fin motion, fin undulation and rolling movements. Notably, the cupping motion produced the largest thrust. However, area change of the caudal fin is not investigated in their works. Yang et al. used a crank slider mechanism to design a caudal fin capable of deform slowly among circular, trapezoid, and lunar shapes [
30]. Mechanisms to modulate the area can also be found in the design of other biomimetic robots. Tang [
31] and Pandy [
32] used the dielectric elastomer actuator and a slider mechanism to change the area of webbed feet of a biomimetic robotic frog. However, among these studies, one common limitation is that how to coordinately control the deformation of caudal fin and the flapping of tail propeller within one flapping cycle has not been studied. Moreover, most of the deformation of the caudal fin is not biomimetic. In nature, there rarely exists fish with a hole on the caudal fin, or with a trapezoid/square-shaped caudal fin.
In this paper, a novel deformable caudal fin platform is proposed to improve the thrust generation of biomimetic robotic fish. The contributions of this paper are twofold. On one hand, the design and control strategy of the deformable caudal fin are firstly proposed. The design offers a quick deformation ability for the caudal fin, and an improved Central Pattern Generator (CPG) model provides coordinate control between 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. On the other hand, by using this novel deformable caudal fin, the thrust sees a 27.5% improvement compared with conventional nondeformable caudal fin with proper deformation control strategy. Since measuring the real-time thrust when the robotic fish is freely swimming is very difficult, in this paper, we use ‘stationary thrust’ to estimate the ‘real thrust’. The stationary thrust is obtained when the robotic fish is fixed to a load cell.
The rest of this paper is organized as follows.
Section 2 introduces materials and methods, including the design and CPG control strategy.
Section 3 gives experiments of three deformation patterns, i.e., conventional nondeformable mode, sinusoidal-based mode, and instant mode.
Section 4 provides a detailed discussion of the experimental results. Finally,
Section 5 concludes this article and gives an outlook on the future research direction.
4. Discussion
This paper presents a novel deformable caudal fin platform for a biomimetic robotic fish. An improved CPG model is proposed, and three deformation patterns, i.e., conventional nondeformable mode, sinusoidal-based mode, instant mode, are formulated. Comparisons of the mean thrust of the three deformation patterns are made, which is as shown in
Figure 7. Each point is the mean thrust of five tests, and each test contains four periods. Please note that the largest mean thrust of sinusoidal-based mode is adopted in the comparison, which means the phase difference is 1/8. From
Figure 7, two conclusions can be drawn. (1) The instant mode has the largest mean thrust, followed by the sinusoidal-based mode. The conventional nondeformable mode has the smallest mean thrust. Actually, when the flapping amplitude is small (
A = 35°), thrust of the three deformation patterns is close. However, thrust of the instant mode augments more rapidly than the other two modes. (2) For all the three deformation patterns, the mean thrust grows with the increase of the flapping amplitude and the flapping frequency.
Table 5 and
Table 6 shows the mean thrust of the sinusoidal-based mode and instant mode in comparison to the conventional nondeformable mode, which is most widely employed in current biomimetic robotic fish. It is found that both the sinusoidal-based and the instant mode have a significant improvement. Notably, when the flapping frequency is 0.2 Hz and the flapping amplitude is 45°, the sinusoidal-based mode sees a 18.2% improvement and the instant mode sees a 27.5% improvement, which is a big promotion to the thrust generation of a biomimetic robotic fish.
A further analysis is given to explain why these three deformation patterns have different thrust generation.
Figure 8 shows the instantaneous thrust at the frequency of 0.2 Hz and amplitude of 45°. It is found that even though the peak-to-peak amplitudes of these deformation patterns are close, the positive thrust and negative thrust generated in one flapping cycle are significantly different. The conventional nondeformable mode generates the most negative thrust in one cycle, followed by the sinusoidal-based mode. The instant mode has the least negative thrust. As a result, the instant mode has the largest mean thrust and the conventional nondeformable mode has the least mean thrust. Moreover, it is also found that the instant mode fluctuates more intensively than the other two. The reason may be that this mode contains sudden deformation of the caudal fin, and only the deformation speed (the speed of the assistant servo motor) of the instant mode is discontinuous. Please note that a careful choice of the control parameters is needed to make the deformable caudal fin have better performances. A counter example is that for the sinusoidal-based mode, the caudal fin may generate negative thrust when the phase difference is 4/8.
5. Conclusions and Future Work
In this paper, a novel deformable caudal fin platform is presented to improve thrust generation of biomimetic robotic fish. The design and control are detailed. An improved CPG model is developed and three deformation patterns, i.e., conventional nondeformable mode, sinusoidal-based mode, instant mode, are formulated to verify the performance of it. Extensive experiments are carried out. More specifically, diversified combinations of the flapping frequencies (0.20 Hz, 0.25 Hz, and 0.3 Hz), the flapping amplitudes (35°, 40°, 45°, 50°) and the phase differences (0, 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8) are examined. Overall, it is found that the instant mode of the caudal fin is proven to have 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. In addition, it is also seen that even though the peak-to-peak amplitudes of these deformation patterns are close when the same flapping frequency and flapping amplitude are given, the positive thrust and negative thrust generated in one flapping cycle are significantly different. The conventional nondeformable mode generates the most negative thrust in one cycle, followed by the sinusoidal-based mode. The instant mode has the least negative thrust, and this is why it has the best thrust performance. This work provides a new way to design and control the caudal fin of biomimetic robotic fish in fulfillment of large thrust generation.
In the future, more explorations will be conducted to study the deformation of the caudal fin, such as Computational Fluid Dynamics (CFD), real-time closed-loop control, and pragmatic optimization of the design.