Abstract
Fish-like robot is a special autonomous underwater vehicle with broad application prospects. Some previous studies concentrated on the hydrodynamics of free-swimming fish-like robots. But the hydrodynamic performance of fish-like robot swimming with a tilt angle in constrained space has not been well studied, and the influence of environmental wave and current on its is also still unclear. In this paper, the experiment devices, including a physical fish-like robot, a hydrodynamics measurement platform, and a six-axis force sensor, are used to study the effect of attack angle and environmental condition on the hydrodynamics of near-surface swimming fish-like robot. Nine attack angles, five oscillating amplitudes, and three environmental conditions are analyzed in the experiments. It shows that thrust force decreases when caudal fin passes above water surface, but the increased difference between gravity force and buoyancy force will compensate the decreased force generated by caudal fin when fish-like robot swims with certain dive angle. The extra reaction force generated by solid bottom boundary will promote the thrust force and vertical force. The surface water wave condition or surface water current condition also has obvious effects on hydrodynamic performance. This paper provides a new perspective to the research on the hydrodynamic performance of fish-like robot and will do favor in the development of fish-like robot.
1. Introduction
Water surface is the important boundary of swimming region for fish or fish-like robot. Fish could benefit from the wall and ground boundary of swimming region, i.e., the wall effect and ground effect [1], but the effect of water surface is still not clear. Previous research has proven that the water surface tension will affect the life of fish [2]. Fish can detect water surface conditions with their cephalic lateral line neuromasts [3] and extract energy from neighbor-induced flows [4], even the Crocodilia is highly sensitive to water surface wave [5]. The water surface is rich in oxygen and light, and most aquatic animals are frequently active near the water surface [6], which is the result of long-term natural evolution. Therefore, it is an interesting point to study the effect of environmental condition on hydrodynamics of near-surface swimming fish-like robot, especially when measuring water parameters with the sensors installed on the fish-like robot [7].
It has been proven that fish could improve by 10% or greater swimming speeds in closed surface flow than that in open surface flow [8], even the wave created by schooling swimming can provide energy to each other [9]. The swimming performance of fish near water surface is worse because of the creation of surface wave [10]. One reason is that the unsteady wave will transfer more momentum and lead to the increment of drag force [11]. The complex underwater wave-current conditions impose higher requirements for the swimming motion control law of the fish-like robot [12]. But it cannot be easily given a generalized conclusion. It has also been proven that the flexible flapping foil, imitating the motion and deformation process of fish caudal fin, can obtain better thrust performance when the motion frequency is equal to its encounter wave frequency [13]. Thus, more research should be conducted to analyze the water surface wave effect on the hydrodynamics of near-surface swimming fish or fish-like robot.
On the other hand, water current is another key factor affecting the hydrodynamics of fish or fish-like robot. It is well known that fish could capture energy from vortices when moving through turbulent flows [14], but the oncoming flow has a negative effect on the propulsion performance [15]. The flow disturbance would change the vortex shedding progress and further affect the hydrodynamics [16]. However, the problem that how the flow disturbance near water surface affects the hydrodynamics of fish or fish-like robot has not been sufficiently studied.
Besides, although the hydrodynamics of fish or fish-like robot with various horizontal swimming motion has been widely studied [17, 18], and some researchers have implemented a simple hydrodynamical model to study the behavioral swimming tilt angle of fish [19], the actual hydrodynamic performance of swimmer’s vertical swimming motion with certain attack angles is still little-known. When swimming in shallow water, fish will be affected by both the water surface and bottom boundary. Sometimes, fish dives down from water surface to deep water rapidly, e.g., the acquisition of resources and evasion of predators [20]. The slow diving motion can be realized with the swim bladder by adjusting the buoyance force [21], while the rapid diving motion needs to change the dive angle (DA) [22]. In some cases, fish pitches up from water bottom to water surface with a certain pitch angle (PA), e.g., breathing and dislodging aerial prey [23]. The bottom boundary will affect the vortex shedding progress and may increase the propulsive efficiency [24].
Fish-like robot can achieve diving or pitching motion by the rotating joint of pectoral fin providing an angle of attack and the promoting effect generated by the caudal fin [25]. Ting and Yang [26] utilized stereoscopic digital particle-image velocimetry to study the inclined descent or inclined ascent behavior of a fish, and the results indicated that caudal fin-wave propagation motion could facilitate the diving or pitching stabilization. In addition, fish could shift diving model according to the change of water conditions [27], and the dive speed is adaptive to the depth of water [28]. Thus, more research should be done on the diving and pitching motion of fish-like robot to improve the kinematic flexibility in 3D space.
All in all, some interesting and useful points can be put forward. When the fish dives down with a DA at the water surface, the tail may stick out of the water. It is interesting to study the hydrodynamics as part of fish or fish-like robot tail strikes air instead of water. When the fish pitched up from the bottom boundary, the interaction between fluid and boundary may improve the propulsion force, but the boundary blocks the vortex shedding and fish could not capture energy from vortices. It is interesting to study the change of hydrodynamics under the effect of the bottom boundary. Besides, when the fish-like robot is used in the narrow shallow open channel, the motion space is constrained by the boundary, the hydrodynamics are disturbed by the near-bed flow and turbulence [29]. In order to control the motion of fish-like robot in the narrow shallow open channel, it is necessary to analyze the hydrodynamics under surface wave and water current conditions. We believe that this study will have a certain guiding significance for the improvement of its motion performance in some constrained spaces.
In this paper, the effects of attack angle and environmental condition on the hydrodynamics of near-surface swimming fish-like robot are studied by experiment. The coupled function of DA, oscillating amplitude (OA), and environmental condition to hydrodynamics is clarified innovatively. The paper is structured as follows: in Section 2, the experiment device is introduced in detail, including the fish-like robot, the hydrodynamics measurement platform, and the six-axis force sensor; in Section 3, the experiment scheme is designed; in Section 4, the experiment results are visualized and the effects of attack angle, OA, and environmental condition are discussed; in Section 6, the main conclusions of this paper are summarized and suggestions for future research are made.
2. Experiment Device
The fish-like robot is shown in Figure 1.
The shape of the fish-like robot is similar to Cyprinus carpio haematopterus. The total length is 450 mm, the height is 80 mm, and the width is 40 mm. The skin is made of soft rubber material to form a closed internal space for the installation of the communication module, the steering engine, the battery, and the controller. The mechanical transmission system of fish-like robot is constructed by the serial four-bar mechanism, which can approximately simulate the flexible oscillating trajectory of real fish. The oscillating motions of fish-like robot body and caudal fin motion are driven by three steering engines to generate the thrust force in a horizontal plane, the oscillating frequency and the OA are controllable to change the thrust force and swimming speed. Besides, the wireless communication module can transmit signals remotely to control the rotation angle of steering engine, so that the swimming speed and the swimming direction are controllable.
The hydrodynamics measurement platform is shown in Figure 2.
As shown in Figure 2, the force sensor is fixed on the longitudinal beam, and the fish-like robot is fixed to the clamping mechanism. The attack angle of fish-like robot is controlled by the adjusting nut. The force sensor and the clamping mechanism are connected by the connecting rod. The connecting rod should be very short so that the value measured by the force sensor is equal to the real hydrodynamic force on the fish-like robot. The longitudinal beam is fixed on the cross beam, and the cross beam can be fixed on the side wall of a water tank or the column that is installed on the base.
The experiment equipment and its schematic diagram is shown in Figure 3.
As shown in Figure 3, the two fish-like robots are exactly the same except for the color. The longitudinal beam is fixed on the side wall of water tank securely, and the force sensor is located directly above the water tank. The water tank has a length of 1,200 mm, a width of 600 mm, and a height of 400 mm. The water in the tank is 270 mm in depth. The control software on the computer connected to the wireless communication module can control the movement of the fish robot. The signal from the force sensor is processed by the signal amplifier and recorded by the data acquisition software in the computer. A generator making water wave or current was fixed at the end of the water tank to analyze the influence of environmental conditions.
The force sensor is the key component of hydrodynamics measurement platform and a six-axis force sensor is used in the experiment. The six-axis force sensor could decouple the force and torque in any direction of the Cartesian coordinate system and would accurately measure the hydrodynamic force on the fish-like robot. The maximum sampling frequency could be 3,000 Hz.
3. Design of Experiment
In order to study, the effects of attack angle and environmental condition on the hydrodynamics of near-surface swimming fish-like robot, the experiments were designed specially, as shown in Figure 4.
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The angle between the center line of fish-like robot and the horizontal line was defined as attack angle. In Figure 4(a), the fish-like robot was along a horizontal direction, and the attack angle was 0°. In Figure 4(b), the fish-like robot was along an obliquely downward direction with a certain DA. While in Figure 4(c), the fish-like robot was along an obliquely upward direction with a certain PA. As shown in Figures 4(d) and 4(e), the two fish-like robots were both used in the experiment based on their almost identical performance. The battery of fish-like robot was charged every half an hour to ensure that there was enough electric energy to drive the robot fish in the experiment progress. The generator could make water wave or current in the flow field. Although the wave or the current could not be controlled quantitatively, it was meaningful for the research on the function of environmental condition to the hydrodynamics qualitatively.
Besides, the fish-like robot was set to swim in the constrained environment with complex structure, for example, in the narrow channel or in the deep well. During the experiment progress, the water tank was not big enough, and the return flow and the reflected wave from the wall of water tank would affect the hydrodynamics of fish-like robot. Thus, the experiment could be conducted in a restricted space, which was more similar to the actual engineering application environment.
What is more, considering the convenience of the experiment, the oscillating frequency of fish-like robot was set as a constant value while the thrust force could be controlled by changing the OA. The oscillating frequency was set as 2 Hz. The OA was set as 50, 55, 60, 65, and 70 mm to achieve various thrust forces. So, there were five swimming speed levels, marked as A, B, C, D, and E, respectively. On the other hand, it has been proven that the attack angle of real fish could be up to 43° [30]. Considering the attitude stability of fish-like robot, the attack angle in the experiment was only in the scope of 0° to ±20°. So, the attack angle was set as 0°, ±5°, ±10°, ±15°, and ±20° to simulate various motion states. The positive value represented the DA, and the negative value represented the PA. The diving motion states were marked as Da, Db, Dc, Dd, and De, while the pitching motion states were marked as Pa, Pb, Pc, Pd, and Pe.
It should be mentioned that the caudal fin of fish-like robot was completely in the water, and the top endpoint of caudal fin was just on the water surface profile when the DA was 5°. There was about 12.3% of caudal fin area in the air and 87.7% of caudal fin area in the water when the DA was 10°. Besides, 32% of caudal fin area was in the air when the DA was 15°, and 56.6% of caudal fin area was in the air when the DA was 20°.
Totally, there could be 45 kinds of combinations for various attack angles and OAs, as shown in Table 1.
In the experiment, three environmental conditions could be realized, as follows: Condition A: there was no water wave and no water current near the water surface in flow field. Condition B: there was no water current but water wave near the water surface in flow field. Condition C: there was no water wave but water current near the water surface in flow field.
Therefore, there were 45 combinations for each environmental condition, and there were totally 135 experiment combinations. For each combination, the experiment data for the time of two oscillating periods were captured. Each experiment was repeated more than six times to calculate the average experimental error so that the experimental errors could be evaluated.
The average experimental error is denoted by .where is the measured value in each independent experiment, is the number of times for repeated experiments, and is the average value based on the repeated experiments.
4. Results and Discussion
4.1. Experiment Results
The force on fish-like robot measured by the six-axis force sensor is denoted by the following symbol. The force along x-axis direction is denoted by , the force along y-axis direction is denoted by , and the force along z-axis direction is denoted by . In terms of the function of each force, is the resultant force including thrust force and resistance force, is the lateral force to change the swimming direction, is the vertical force to change the swimming depth. Those three forces are time-varying parameters. It will be effective to enlarge to realize high propulsive efficiency [31] and to narrow to realize good stability [32]. When the attack angle is 0°, is equal to 0.
Taking the experiments of attack angle being 0° under Condition A as examples, the time history curves of and are shown in Figure 5.
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The negative value indicates that the force direction is opposite to the positive direction of the coordinate axis in Figure 4. Considering the oscillating frequency of fish-like robot was set as 2 Hz, the experiment data in two oscillating periods (i.e., 1 s) were taken out for each speed level with corresponding OA, as illustrated in Figure 5. There were two peak-valley cycles in one oscillating period of the time history curves of , which meant the changing frequency of was twice as much as the oscillating frequency of the fish-like robot. In consideration of only one peak-valley cycle being in one oscillating period of the time history curves of , the changing frequency of was the same with the oscillating frequency of the fish-like robot. These results have been verified by the previous research [33].
However, the time history curves of measured in the experiment were not as smooth as the calculated curves in the simulation, such as the curves calculated by Chowdhury et al. [34]. The two peak values in one oscillating period were not equally large, and there was an obvious fluctuation at the trough of each curve. The reason was that the mechanical transmission system of fish-like robot was not able to fit the desired oscillating law curve precisely, the rubber skin of fish-like robot was not able to deform flexibly enough and there was mechanical tolerance in the experiment device. The simulation process did not consider the mechanical tolerance, and the result was under idealized conditions.
Although each experiment has been repeated more than six times, the measurement error was not able to be eliminated completely or expressed quantitatively. In these circumstances, the average values were relatively more representative indicators, which have been widely used to process the experiment results in the previous research [35]. Therefore, the average value of the measured force was used to evaluate the hydrodynamic performance in this work.
In order to reduce the signal noise of measured force, the Rloess method was taken into utilization, which was a widely used data smoothing method [36]. The residuals of the measured forces were calculated, marked as r. Then the robust weight of each data point within the window width was calculated according to the Bisquare function, as shown in Equation (3)where is the residual of the ith measured data in each experiment, M is the median absolute residual, as shown in Equation (4).
The median absolute residual is a measure of the extent of the residual distribution. The average value of , and are denoted by , and , respectively, as follows:
4.2. Effect of Attack Angle
In order to analyze the effect of attack angle on hydrodynamic performance of fish-like robot, the experiment under Condition A was taken as an example. The DA increased from 0° to 20° with an interval of 5°. The curves of , and over DA are shown in Figure 6.
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Considering the resistance force was almost equal to 0 under the condition of no water wave and no water current, the resultant force along x-axis direction could be regarded to as the thrust force. In terms of average force along x-axis direction, as shown in Figure 6(a), decreased as the DA increased. It was obvious that the larger OA would obtain a larger thrust force. When OA was equal to 50 mm, decreased from 0.50 to 0.22 N as DA increased from 0° to 20°, with a decline rate of 56.7%. It should be noticed that the caudal fin area in water had a decline rate of 56.6% as DA increased from 0° to 20°. When OA was equal to 70 mm, the decline value of was about 0.43 N and the decline rate was 41.1% as DA increased from 0° to 20°. When the DA increased, the larger OA would lead to a larger decline value of but not a larger decline rate.
The average force along y-axis direction should be 0 in an ideal situation, but the experiment showed another result. As shown in Figure 6(b), when OA was 50 mm, was almost always 0 regardless of the change of DA. The absolute value of was mostly increased as the DA increased. When OA was 70 mm and DA was 15°, could be −0.27 N, which meant poor swimming stability.
When it came to the average force along z-axis direction, as shown in Figure 6(c), the absolute value of increased as the DA increased. When the DA was <10°, the change of was not obvious, especially in the cases of OA being less than 60 mm. When OA was 70 mm and DA was 20°, could be −0.60 N, whose absolute value was close to under the same conditions.
On the other hand, the PA was controlled to change from 0° to 20° with an interval of 5° in the experiment under Condition A. The curves of , and over PA are shown in Figure 7.
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Compared with in Figure 6(a), the decline rate of was much smaller when the PA increased. When OA was 50 mm, the decline rate was 31.0% as PA increased from 0° to 20°, When OA was 70 mm, that decline rate was 30.1%.
The average forces along y-axis direction in the experiments with various PAs in Figure 7(b) were similar to those with various DAs in Figure 6(b).
On the importance of average force along z-axis direction, in Figure 7(c) was direct proportion to the PA, but the growth rate was small. When OA was 70 mm, increased from 0 to 0.34 N as PA increased from 0° to 20°, but the absolute value of in Figure 6(c) increased from 0 to 0.60 N. That meant the water surface and the bottom boundary had very different effects on the vertical force.
4.3. Effect of Oscillating Amplitude
The experiment under Condition A was also taken as an example to analyze the effect of OA on hydrodynamic performance of fish-like robot. The OA increased from 50 to 70 mm with an interval of 5 mm. The curves of , and over OA are shown in Figure 8.
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As shown in Figure 8(a), increased as the OA increased with a relatively large growth rate. When DA was 0°, increased from 0.50 to 1.05 N with a growth rate of 109.1% as OA increased from 50 to 70 mm with the growth rate of 40%. On the other hand, when DA was 20°, obtained the growth value of 0.40 N with a growth rate of 184.2% as OA increased from 50 to 70 mm. It showed that the larger DA would cause a larger growth rate but not a larger growth value when the OA increased.
In terms of , as shown in Figure 8(b), the absolute value increased as the OA increased, which meant poor swimming stability at the state of large OA.
When coming to the absolute value of , as shown in Figure 8(c), the value was always 0 when DA was 0°. As OA increased from 50 to 70 mm, the total growth value was 0.08 N with a growth rate of 122.7% when DA was 5°, and the total growth value was 0.29 N with a growth rate of 97.3% when DA was 20°. It showed that the effect of changing OA was more significant when the DA was small.
Besides, the OA was controlled to change from 50 to 70 mm with an interval of 5 mm in the experiment under Condition A. The curves of , and over PA are shown in Figure 9.
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As shown in Figure 9(a), increased as the OA increased, and the variation curves were closer to each other compared with the curves in Figure 8(a). When PA was 20°, increased from 0.35 to 0.73 N with a growth rate of 111.8% as OA increased from 50 to 70 mm. It showed that was in direct proportion to the OA.
The change of over OA as shown in Figure 9(b) was almost the same with that in Figure 8(b).
On the importance of in Figure 9(c), the growth rate of average force along z-axis direction was much smaller than that in Figure 8(c). As OA increased from 50 to 70 mm, the total growth value was 0.01 N with a growth rate of 18.1% when PA was 5°, and the total growth value was 0.10 N with a growth rate of 40.8% when DA was 20°. It showed that the effect of changing OA was more significant when the PA was large.
4.4. Effect of Environmental Condition
In order to analyze the effect of environmental condition on hydrodynamic performance of fish-like robot, the experiments under various water surface conditions (i.e., water wave and water current) have been conducted. The histograms of , and with various DAs over environmental conditions are shown in Figure 10.
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As shown in Figure 10(a), compared with the average force along x-axis direction under hydrostatic condition that there was no water wave or water current, underwater wave condition was overall smaller, but had no obvious change underwater current condition. For example, when OA was 65 mm and DA was 15°, under hydrostatic condition was 0.66 N, underwater wave condition was 0.59 N, underwater current condition was 0.64 N.
In terms of in Figure 10(b), the absolute value of underwater current condition was overall larger than that underwater wave condition, which meant the water current would weaken the swimming stability.
When it came to the average vertical force along z-axis direction, compared with the absolute value of under hydrostatic condition, the absolute value of underwater wave condition was overall larger, but the absolute value of changed little underwater current condition. For example, when OA was 60 mm and DA was 20°, the absolute value of under hydrostatic condition was 0.39 N, the absolute value of underwater wave condition was 0.51 N, the absolute value of underwater current condition was 0.35 N.
On the whole, as shown in Figure 11(a), compared with under hydrostatic condition, underwater wave condition was a little smaller, and underwater current condition was a little larger. For example, when OA was 55 mm and DA was 10°, under hydrostatic condition was 0.53 N, underwater wave condition was 0.39 N, underwater current condition was 0.62 N.
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In Figure 11(b), the absolute values of underwater wave condition and underwater current condition were overall larger than that under hydrostatic condition, which meant the two environmental conditions would weaken the swimming stability.
When coming to , compared with under hydrostatic condition, underwater wave condition and underwater current condition were overall larger, and the change of underwater wave condition was more obvious. For example, when OA was 70 mm and DA was 15°, under hydrostatic condition was 0.31 N, underwater wave condition was 0.45 N, underwater current condition was 0.39 N.
5. Discussion
In the experiment progress, although the experimental facilities were not absolutely perfect, the experiment results have shown something interesting, which was worth further discussing.
When the attack angle increased, regardless of whether it was DA or PA, the thrust force would decrease and the absolute value of vertical force would increase. However, the changes of and over DA were larger than these over PA. That phenomenon could be attributed to different flow field boundaries.
When the fish-like robot swam with certain DA near the water surface, part of the caudal fin would pass above water surface. Then the force generated by caudal fin would decrease, and the thrust force would have a large decline. Besides, part of the caudal fin was not in the water, so the displacement water volume of fish-like robot would decrease. But the gravity force on fish-like robot reminded unchanged. The increased difference between gravity force and buoyancy force would make up the decreased force generated by caudal fin, and the absolute value of vertical force would have a large growth.
When the fish-like robot swam with certain PA near the bottom boundary, the solid boundary would disturb the evolution of the wake vortex to decrease the force generated by the caudal fin, but the reaction force generated by the solid boundary would be applied to the fish-like robot to increase the thrust force and vertical force. Totally, and had a small growth.
It was obvious that the gravity force and the buoyancy force were unbalanced or not collinear when the attack angle increased, the swimming stability would be poor.
No matter whether the attack angle was DA or PA, the thrust force and the absolute value of vertical force would increase as the OA increased. That was because the larger OA of caudal fin would lead to a larger force. The growth rate of and with various DAs were more obvious than those with various PAs, which can be attributed to the two same reasons of the boundary effect and the difference between gravity force and buoyancy force.
Considering the effect of environmental condition, water wave or water current near water surface had different effects on the hydrodynamic performance with different attack angles.
Under the water wave condition, had a decline and the absolute value of had a growth, regardless of whether the attack angle was DA or PA. That phenomenon could be explained from two aspects, one was that the water wave further decreased the caudal fin area in water, and another one was that the water wave increased the resistance force. With the effect of water wave, the water surface would rise and fall, the caudal fin area in water would decrease, and the force generated by the caudal fin would decrease either, then decreased in the swimming model with certain DA. Besides, the displacement water volume of fish-like robot would decrease because of the undulating water surface, the difference between gravity force and buoyancy force would increase, then the absolute value of increased in the swimming model with certain DA. On the other hand, the water wave propagation would generate resistance force on the head part of fish-like robot, the component force along x-axis direction would decrease and the component force along z-axis direction would increase in the swimming model with certain PA.
Under the water current condition, and had little changes in the swimming model with certain DA, that was because the wave current would not change the water surface and would not change the caudal fin area in water. However, and had a growth in the swimming model with certain PA, which could be attributed to the pressure decline due to the increased flow rate of surface water. The water current would speed up the flow rate of surface water, and the pressure in fluid area before fish-like robot which swam with certain PA would decrease. With the action of differential pressure, the force along the direction from the caudal fin to the head part of the fish-like robot was generated. The reaction force from the bottom boundary mentioned earlier and the differential pressure force would increase and .
In general, the experiment results had been reasonably explained.
6. Conclusion
In this work, the experiment to measure hydrodynamic force is conducted to study the effect of attack angle, OA, and environmental condition on the hydrodynamics of near-surface swimming fish-like robot. The experiment devices, including fish-like robot, hydrodynamics measurement platform, and six-axis force sensor, are introduced in detail. The experiments cover nine attack angle factors, five oscillating frequency factors, and three environmental conditions, 135 experiments are designed and carried out. Each experiment is repeated more than six times to reduce the experimental error. The resultant force along x-direction, the lateral force along y-direction, and the vertical force along z-direction are measured in the experiments. The average values of the experimental data are used to evaluate the hydrodynamic performance of fish-like robot. Based on the experiment results, some unique and interesting conclusions can be generalized.(1)When fish-like robot swam with certain attack angle, the effects of reduced buoyancy force or extra reaction force should be considered. The thrust force will decrease if the caudal fin passes above water surface at the state of fish-like robot with certain DA, but the difference between gravity force and buoyancy force will compensate the force generated by caudal fin, and the vertical force may increase. If fish-like robot swims with certain PA, the extra reaction force generated by solid bottom boundary will promote the thrust force and vertical force.(2)It has been proven that the larger OA of caudal fin will lead to a larger force. The large thrust force and vertical force will promote the motion of fish-like robot, but the large lateral force will reduce the swimming stability. It is suggested that the influence of OA on swimming stability should be taken into consideration when increasing the swimming speed by increasing the OA.(3)The surface water wave condition will affect the displacement water volume of fish-like robot when swimming with certain DA to further decrease the thrust force and increase the difference between gravity force and buoyancy force, but the surface water current has no such effect. Besides, the surface water wave will increase the resistance force on fish-like robot in the swimming model with certain PA. However, water current may decrease the water pressure before the head part of fish-like robot, and the differential pressure force will further increase thrust force and vertical force when swimming with certain PA.
On the whole, this paper provides a new perspective to study the hydrodynamic performance of the fish-like robot, and the relevant conclusions will provide a basis for research on the fish-like robot swimming in the narrow shallow open channel or other constrained space. In the future, more research should be done to study the effect of attack angle and environmental condition on the hydrodynamics of near-surface swimming fish-like robot. The flow field should be visualized to reveal the functional mechanism of various attack angles and environmental conditions. The water wave and water current should be quantitatively controlled in the experiment. The optimal combination of attack angle and OA should be found to obtain good hydrodynamic performance under certain environmental condition.
Data Availability
The authors declare that the data supporting the findings of this study are available within the article.
Consent
All authors have read and agreed to the version of the manuscript.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Authors’ Contributions
Conceptualization, G. X. and F. B.; methodology, G. X.; software, G. X.; validation, G. X.; formal analysis, G. X.; investigation, F. B.; resources, F. B.; data curation, Z. L.; writing-original draft preparation, G. X. and F. B.; writing-review and editing, Z. L.; visualization, Z. L.; supervision, Z. Li.; project administration, Y. L.; funding acquisition, Y. L.
Acknowledgments
The research was supported by the National Natural Science Foundation of China (No. 52001186), the Natural Science Foundation of Shandong Province (No. ZR2020QE292), the Open Fund Project of Key Laboratory of Ocean Observation Technology (No. 2021klootA01), and the Science and Technology Innovation Project of Laoshan Laboratory (No. LSKJ202203505), hereby thanks. Thanks to Shenzhen Lezhi Robot Company for the fish-like robot especially.