Sine Curve Research Articles

Modeling and Simulation of the Stepping Motor Operation Curve

To improve the open-loop control performance of stepper motors, research was conducted on their operating curves. The acceleration-velocity characteristic equations of three common operating curves were established and compared with the torque frequency characteristic curves of stepper motors. Based on this, an improved segmented correction fitting S-shaped (SCFS) curve design method based on a high torque utilization sine curve was proposed to solve the problem of rotor blockage and overshoot caused by uneven acceleration during the operation of stepper motors. In the simulation of the stepper motor load motion system, the SCFS curve was compared with common curves. The simulation results showed that the position tracking error was reduced by approximately 82% compared to the trapezoidal curve and approximately 70% compared to the exponential curve. Research has found that this method is suitable for the design of high-precision motor operating curves and has a high application value in the field of precision motion control.

A system decomposition method for region tracking control of a non‐holonomic mobile robot with dynamic parameter uncertainties

AbstractThe tracking control problem of non‐holonomic mobile robot systems has been extensively investigated in the past decades, however, most of the existing control strategies were developed specifically for the fixed‐point tracking. This technical note focuses on the region tracking control for a non‐holonomic mobile robot system with parameter uncertainties in the robot dynamics. With the system decomposition and adaptive control method, some restrictions imposed on the angular and linear velocities of the non‐holonomic mobile robot in recent literature are removed, enabling to track dynamic trajectories with any values of the angular and line velocities. The proposed adaptive control scheme can simultaneously solve both the regulation and region tracking problems of a non‐holonomic mobile robot with one passive wheel and two actuated wheels. By utilizing the designed control laws, the mobile robot system is able to globally reach inside a moving region specified by potential functions whose path can be a circular curve, a straight line, or sinusoidal curve, by using a single adaptive controller. Since the dynamic region can be specified arbitrarily small, the fixed‐point tracking can be regarded as a special case of region tracking studied in this paper. Compared with the traditional fixed‐point tracking, region tracking has more flexibility and better robustness. Numerical results are presented to show the effectiveness of the designed strategy.

Association between disruption of circadian activity rhythms and obesity

ABSTRACT This cross-sectional study aimed to elucidate the association between disruption of circadian activity rhythms and obesity-related indices. This study included 69 older participants (male, n = 36; female, n = 33), and disruption of circadian activity rhythms in daily life was assessed using the cosinor method based on physical activity data. The daily physical activity data were fitted to a cosine curve to estimate the peak phase (acrophase), and the difference in the peak phase (time) for each day was determined. The standard deviation (SD) of the mean peak phase differences over 6 days was obtained. The higher the SD value, the more disturbed the circadian rhythm of activity. Based on the calculated values, the samples were divided into tertiles (small, medium, and large). A significant positive correlation was found between Log SD and body fat percentage on the disruption of circadian activity rhythms and obesity-related indices. In addition, positive associations were observed among body mass, body mass index, and Log SD. However, these associations were not observed in women. These results suggest that disruption of circadian activity rhythms is associated with obesity-related indices and may differ according to sex.

Operating characteristics and design parameter optimization of permanent magnet linear generator applied to free-piston energy converter

A tubular permanent magnet linear generator (PMLG) with axial magnetized is proposed for the free-piston engine generator (FPEG). The structures and test rigs of the PMLG and FPEG prototypes are introduced. The working characteristics of the PMLG in FPEG system are analyzed under ignition conditions. A 2D finite element model of the PMLG is designed and verified based on initial design parameters and test results. The influences of key operating parameters on the output performance of PMLG are studied. On these basis, when considering the actual motion characteristics of the PMLG in FPEG system, the effects of different structural parameters on the power generation performance and efficiency (h) are investigated. Results show that when the working frequency of the FPEG is relatively small, the displacement profile resembles a sinusoidal curve. As the working frequency and stroke length increase, the power generation increases rapidly. As the air gap length and back iron shaft diameter decrease, and the stator slot number increases, the output voltage (U), current (I), power (Pout), and total loss power (Ploss) show an approximately linear increasing trend. As the pole arc coefficient and stator tooth width increase, the U, I, Pout, and Ploss first increase and then decrease. As the stator yoke thickness increases, the U, I, and Pout increase rapidly and then tend to stabilize. Besides, these structural parameters have little impact on power generation efficiency of this PMLG.

Pulsation curves strengthen the high gradient magnetic separation process Ⅱ: Consideration of separation performance

The use of pulsating slurry has been found to be effective in overcoming matrix blockage and improving separation selectivity in high gradient magnetic separators (HGMS). The velocity of the pulsating slurry is regulated by a sinusoidal cycle function, which causes the downward velocity to be much greater than the upward velocity due to the superposition of the sinusoidal pulsation velocity and the feeding velocity. However, the unbalanced velocity configuration in the up-downward stroke limits separation efficiency. This paper investigates the use of asymmetrical pulsation curves in a lab-scale HGMS to balance the velocity configuration and consequently improve separation performance. Magnetic field strength, feed velocity, and pulsating frequency were varied in separate experiments to determine the effect of pulsation curves on separation performance. The asymmetrical pulsation curve with a faster upward stroke and slower downward stroke was found to achieve a TiO2 concentrate grade of 23.94 %, a recovery of 66.78 %, and a separation efficiency of 50.46 % for the separation of ilmenite. When the concentrate grade is slightly higher, this new curve shows an increase of 5.68 % in recovery and 5.05 % in separation efficiency compared to the conventional sinusoidal pulsation curve. This improvement is attributed to a simultaneous strengthening of the material loose-adsorption process by separately regulating the pulsating upward and downward strokes.

Layered energy-saving speed planning and control method for electric vehicle on continuous signal lights road

Emergency start-stop in front of signal lights is one of the main reasons for additional energy consumption and ride discomfort of Electric Vehicle (EV). Existing research on this issue rarely takes into account both energy consumption and ride comfort. Therefore, the layered energy-saving speed planning and control method is proposed. The upper is the layer of energy-saving speed planning. This layer reduces energy consumption of EV by reducing the number of stops on continuous signal lights road and minimizing the range of speed change. On this basis, the sinusoidal variable speed curve is used to smooth the acceleration process to improve ride comfort. Finally, the energy-saving speed considering ride comfort is obtained. This layer makes up for the issue that existing research rarely takes into account both energy consumption and ride comfort of EV, and is an extension and innovation of existing research. The lower is the layer of Model Predictive Controller (MPC)-based speed control. Based on the longitudinal dynamics model of EV, the MPC-based speed controller is established to control EV to track the energy-saving speed. The controller is easy to understand and implement, and it is also suitable for other research on EV, which has certain application value. The simulation results show that under various working conditions, the maximum energy consumption of EV passing through continuous signal lights road without stopping is 604.29 kJ/km, and the minimum is 244.76 kJ/km. The energy consumption is lower than that of actual road test, and it can be saved by 23.18 % compared with the method in the same field. The maximum Root Mean Square of accelerations (RMSa) is 0.25 m/s2, and the minimum is 0.10 m/s2. The values of RMSa above are lower than 0.315 m/s2, which indicates that the ride comfort is good. The utilized method can reduce energy consumption of EV, improve its range and ride comfort, which has important reference significance for promoting the development of EV.

Enhancement of two-phase flow and mass transport by a two-dimensional flow channel with variable cross-sections in proton exchange membrane fuel cells

A novel two-dimensional flow channel (TDFCH) with variable cross-sections geometrically controlled by sinusoidal function is proposed for proton exchange membrane fuel cells (PEMFCs). Two-phase flow simulations and visualisation experiments are combined to reveal the mechanisms for improved water management and enhanced reactant transport. Results show that the centrifugal force generated by the vortex pushes the liquid water away from the central region of the flow channel, forming droplet and film flows to avoid blockage of the flow channel. The reactant gases accumulate on the windward side of the variable-diameter structures, leading to an increase of the local pressure and facilitating fuel diffusion into the porous electrode. The fluid inertia enhances mass transfer of reactants and removal of liquid water inside the porous electrode. The amplitude A of the flow channel based on sinusoidal curve plays a dominant role in improving the performance of the TDFCH. Under the same testing conditions, when amplitude A = 0.2 and period T = 2, the peak power density of the TDFCH-based cell reaches 517.9 mW cm−2, which is 26 % higher than the conventional straight flow channel. The newly designed TDFCH provides an efficient solution to realize performance improvement and long-term stable operation of PEMFCs.

Borehole TV Imaging Technology for Horizontal Directional Drilling Based on an Optimization Algorithm for Structural Planes

The horizontal directional drilling technology combined with the borehole TV imaging technology can be used to obtain most of the geological information in conventional adit exploration. This combination has little impact on the environment and is free from topographic constraints, thus contributing to green exploration. However, conventional algorithms for structural planes fail to accurately extract information on the attitudes of incomplete structural planes in boreholes of any azimuth. Moreover, existing borehole TV devices are mostly cable-based and, thus, difficult to put in place in horizontal drilling. They are prone to get stuck in the collapse section of boreholes, thus damaging the devices. Given these challenges, this study develops an optimization algorithm for structural planes: (1) first, information on multiple points in the 2D unfolded view is fitted using a sinusoidal function curve, three arbitrary points are constructed using the fitted curve, and the normal vector of the plane determined by the three points is calculated; (2) the normal vector in the geodetic coordinate system is obtained after two rotations of the spatial coordinate system based on the theory of transformation of Cartesian coordinate system; (3) finally, the dip angle and dip direction of a structural plane are calculated using the normal vector in the geodetic coordinate system. By making the best use of the information on multiple points in the 2D unfolded view, the optimization algorithm can overcome the defect that is difficult for conventional two-point methods to locate the highest and lowest points of discontinuous structural planes. Therefore, the optimization algorithm applies to calculating the attitudes of structural planes in boreholes of any azimuth. Based on this optimization algorithm, this study successfully develops a cable-free, storage-based TV device for boreholes of any azimuth. This device was employed for laboratory experiments on 20 complete structural planes and 32 incomplete structural planes. As indicated by the experiment results, the optimization algorithm proposed in this study is applicable to many types of structural planes, with a dip direction error of less than 10° and a dip angle error of less than 5°, thus meeting the production requirements.

Visual similarity simulation of slub denim based on image processing

The slub denim has various appearance styles that attract consumers due to the irregular distribution and long cycle of the slubs in the slub yarn. This characteristic of the slub yarn makes the slub denim proofing that relies on artificial visual contrast time-consuming with a long design cycle. A visual similarity simulation method was proposed for slub denim based on slub yarn images to solve this problem. At first, the yarn images were pre-processed by grey-level transformation, image threshold segmentation, and morphological operations to obtain the yarn core images. Secondly, according to the elastic change of yarn in fabric structure, the elliptic and sine curve models were established to treat the string to obtain the actual yarn shape in the fabric. Then, a light intensity curve function, which consists of a radial curve model and an interlacing point curve model, was established to simulate the light intensity distribution on the yarn surface. Finally, the cover relation of warp and weft yarns was controlled by Boolean matrix, and mean filtering was used to adjust the fuzzy denim fabric images. The experimental results show that the slub denims simulated by the method proposed in this article have a high visual similarity with the actual slub denims. Meanwhile, multiple parameters of the simulation model established in this article can be adjusted to enhance the adaptability of the model and the accuracy of the simulation results.

Normal variation in pelvic roll motion pattern during straight-line trot in hand in warmblood horses

In horses, hip hike asymmetry, i.e. left–right difference in hip upwards movement during hind limb protraction in trot, is a crucial lameness sign. Vertical hip movements are complex, influenced by both pelvic roll and pelvic vertical motion. Veterinarians find it challenging to identify low-grade lameness, and knowledge of normal variation is a prerequisite for discerning abnormalities. This study, which included 100 clinically sound Warmblood horses, aimed to describe normal variation in pelvic roll stride patterns. Data were collected during straight-line trot in hand using optical motion capture. Stride-segmented pelvic roll data, normalised with respect to time (0–100% of the stride) and amplitude (± 0.5 of horse average stride range of motion), were modelled as a linear combination of sine and cosine curves. A sine curve with one period per stride and a cosine curve with three periods per stride explained the largest proportions of roll motion: model estimate 0.335 (p < 0.01) and 0.138 (p < 0.01), respectively. Using finite mixture models, the horses could be separated into three groups sharing common pelvic roll characteristics. In conclusion, pelvic roll motion in trot follows a similar basic pattern in most horses, yet there is significant individual variation in the relative prominence of the most characteristic features.

Direction Estimates for Short-Period P-Waves on Three-Component Stations and Arrays

Abstract P-arrival backazimuth estimates can be crucial in locating poorly constrained seismic events. Correlating short windows of the vertical waveform with corresponding windows of the radial rotation for different backazimuths can provide estimates, but these are often uncertain and biased due to skewness in the Z–R correlation functions. Assessing how well cosine curves centered on different backazimuths match the Z–R correlation functions provides more reliable estimates that depend less upon the time-window used. Stacking best-fit-cosine curves from neighboring three-component stations improves stability further in a form of array-processing that does not require coherence between the waveforms themselves. We demonstrate for recordings of North Korean nuclear tests at the Pilbara 3C array in Australia that the biases in the Z–R correlation functions vary greatly between adjacent stations. This bias is reduced both by the cosine curve fitting and stacking operations. We advocate obtaining backazimuth estimates for all P arrivals at three-component stations globally. This could improve phase association and event location, identify sensor orientation problems, and provide baseline backazimuth corrections and uncertainty estimates. We propose two benchmark datasets for developing, documenting, and comparing backazimuth estimation algorithms and codes. All the data and code used to generate the results presented here are open.

Algorithm for simulating melting polar ice, Earth internal movement and volcano eruption with 3-dimensional inertia tensor

This paper reports the result of an investigation of a hypothesis that the melting polar ice of Earth flowing down to the equatorial region causes volcano eruptions. We assumed a cube inside the spherical body of Earth, formulated a 3-dimensional inertia tensor of the cube, and then simulated the redistribution of the mass that is to be caused by the movement of melted ice on the Earth’s surface. Such mass distribution changes the inertia tensor of the cube. Then, the cube’s rotation inside Earth was simulated by multiplying the Euler angle matrix by the inertia tensor. Then, changes in the energy intensity and the angular momentum of the cube were calculated as coefficients of Hamiltonian equations of motion, which are made of the inertia tensor and sine and cosine curves of the rotation angles. The calculations show that the melted ice increases Earth’s internal energy intensity and angular momentum, possibly increasing volcano eruptions.

Experimental validation of a 4D dynamic dose calculation model for proton pencil beam scanning without spot time stamp considering free-breathing motion.

We developed a 4-dimensional dynamic dose (4DDD) calculation model for proton pencil beam scanning (PBS). This model incorporates the spill start time for all energies and uses the remaining irradiated spot time model instead of irradiated spot time logs. This study aimed to validate the calculation accuracy of a log file-based 4DDD model by comparing it with dose measurements performed under free-breathing conditions, thereby serving as an alternative approach to the conventional log file-based system. Three cubic verification plans were created using a heterogeneous block phantom; these plans were created using 10 phase 4D-CT datasets of the phantom. The CIRS dynamic platform was used to simulate motion with amplitudes of 2.5, 3.75, and 5.0mm. These plans consisted of eight- and two-layered rescanning techniques. The lateral profiles were measured using a 2D ionization chamber array (2D-array) and EBT3 Gafchromic films at four starting phases, including three sinusoidal curves (periods of 3, 4, and 6s) and a representative patient curve during actual treatment. 4DDDs were calculated using in-house scripting that assigned a time stamp to each spot and performed dose accumulation using deformable image registration. Furthermore, to evaluate the impact of parameter selection on our 4DDD model calculations, simulations were performed assuming a ±10% change in irradiation time stamp (0.8±0.08s) and spot scan speed. We evaluated the 2D gamma index and the absolute point doses between the calculated values and the measurements. The 2D-array measurements revealed that the gamma scores for the static plans (no motion) and 4DDD plans exceeded 97.5% and 93.9% at 3%/3mm, respectively. The average gamma score of the 4DDD plans was at least 96.1%. When using EBT3 films, the gamma scores of the 4DDD model exceeded 92.4% and 98.7% at 2%/2mm and 3%/3mm, respectively. Regarding the 4DDD point dose differences, more than 95% of the dose regions exhibited discrepancies within ±5.0% for 97.7% of the total points across all plans. The spot time assignment accuracy of our 4DDD model was acceptable even with ±10% sensitivity. However, the accuracy of the scan speed, when varied within ±10%sensitivity, was not acceptable (minimum gamma scores of 82.6% and maximum dose difference of 12.9%). Our 4DDD calculations under free-breathing conditions using amplitudes of less than 5.0mm were in good agreement with the measurements regardless of the starting phases, breathing curve patterns (between 3 and 6s periods), and varying numbers of layered rescanning. The proposed system allows us to evaluate actual irradiated doses in various breathing periods, amplitudes, and starting phases, even on PBS machines without the ability to record spot logs.

Feasibility of 8-Shaped Motion Test for Five-Axis Machining Center

ISO 10791-7, which specifies the machining accuracy test standard for machining centers, and ISO 10791-6, which specifies the interpolation motion test standard, were revised in 2014 to include five-axis machining centers (5-axis MCs). In addition, cone frustum test, which has been used as the National Aerospace Standard (NAS), was revised and introduced in these ISO standards. However, prior to the establishment of these standards, an aircraft manufacturing company in China proposed S-shaped machining test to measure the accuracy of the test piece of an aircraft. This was adopted as an informative annex of ISO 10791-7 in 2020. Furthermore, in 2019, China proposed a method related to S-shaped machining test and a method of 8-shaped interpolation motion test. Since the S-shaped test requires high acceleration and deceleration in some sections, the test results depend on the performance of the computer-aided manufacturing (CAM) software; therefore, it is not efficient in determining the accuracy of the machine tools. In contrast, in the 8-shaped motion test, the tip of the spindle moves based on a sine curve; consequently, high acceleration/deceleration does not occur. Since the tip of the cutting tool is fixed, a device called R-test is used to measure the position of the center of reference ball using three displacement sensors. In this study, we have discussed the feasibility and problems of the 8-shaped motion test. First, the motion of the machine in the figure “8” motion test is clarified. Next, the definition of the parameters necessary to create the NC programs is outlined. In addition, we have proposed a method in which suitable conditions are set for simultaneous 5-axis feed on a 5-axis MC. Finally, the results of an actual test are applied to the 5-axis MC to confirm that no major problems exist.

Mechanical Fourier transform for programmable metamaterials

Proactively programming materials toward target nonlinear mechanical behaviors is crucial to realize customizable functions for advanced devices and systems, which arouses persistent explorations for rapid and efficient inverse design strategies. Herein, we propose a "mechanical Fourier transform" strategy to program mechanical behaviors of materials by mimicking the concept of Fourier transform. In this strategy, an arbitrary target force-displacement curve is decomposed into multiple cosine curves and a constant curve, each of which is realized by a rationally designed multistable module in an array-structured metamaterial. Various target curves with distinct shapes can be rapidly programmed and reprogrammed through only amplitude modulation on the modules. Two exemplary metamaterials are demonstrated to validate the strategy with a macroscale prototype based on magnet lattice and a microscale prototype based on an etched silicon wafer. This strategy applies to a variety of scales, constituents, and structures, and paves a way for the property programming of materials.

A Comparative Analysis of Force Fields of Drug-Like Molecules: Omeprazole, Favipiravir and Amoxicillin by using Bonded and Non-Bonded Potential Distributions

This research aims to compare and analyze the force field parameters of drug-like compounds generated by the online servers CGenFF, SwissParam, and LigParGen. CHARMM27, OPLS-AA, and CHARMM36 force fields of amoxicillin, favipiravir, and omeprazole have been examined by bonded and non-bonded energy distributions of the potential function. The local terms of the force field function are bond length, bond angle, and dihedral potentials, while the non-local terms are van der Waals and pairwise electrostatic interactions. The parabolic curves of bond length potential appear to internally bend because of the larger values of force constants. The bond length and angle energies are lowest at reference values for each of the corresponding atom pairs in the molecules. The higher values of the bending force constant positively deflect the sinusoidal curve from the equilibrium position according to the dihedral angle energy distribution. The Lennard-Jones interaction exhibits the same repellent nature at closer ranges and the same attracting nature at farther ranges whereas a mildly differentiated interaction is seen at the intermediate state as a result of changing well-depth parameters. Depending on the size of the optimized partial charges, it is discovered in electrostatic interaction that the distributions of end-to-end lengths of identical atom pairs are more exponentially skewed from one another. The main cause of inconsistency in the results of MD simulations for the same protein-ligand system is due to the shifted topology and parameters.

GJ 9404 b: A Confirmed Eccentric Planet, and not a Candidate

Eccentric orbits can be decomposed into a series of sine curves which affects how the false alarm probability is computed when using traditional periodograms on radial-velocity data. Here we show that a candidate exoplanet orbiting the M dwarf GJ 9404, identified by the HADES survey using data from the HARPS-N spectrograph, is in fact a bona fide planet on a highly eccentric orbit. Far from a candidate, GJ 9404b is detected with a high confidence. We reach our conclusion using two methods that assume Keplerian functions rather than sines to compute a detection probability, a Bayes Factor, and the false-inclusion probability periodogram. We compute these using nested sampling with kima.

Characteristics of Chaotic Weak Reflection in Carbonate Fracture-Cavity Reservoirs: A Case Study of Ordovician Reservoirs in Block 10 of the Tahe Oilfield, Tarim Basin, China.

The identification of carbonate reservoirs is a critical task in oil and gas exploration. Chaotic weak reflection is an important type of reflection characteristic in carbonate reservoirs. Widespread distribution of chaotic weak reflection has been observed in the Ordovician Yijianfang Formation in the Tahe area. However, there is still a lack of systematic research on the distribution, characteristics, reservoir space, and reservoir types of chaotic weak reflection in the Tahe area. To address this issue, this study conducted a comprehensive analysis of multiscale data and found that chaotic weak reflections are distributed within 100 ms below the top interface of the Middle Ordovician. Seismic profiles exhibit a "string of pearls" with a "tail" or "pearl-like" widening feature. On well logs, all three porosity curves exhibit localized peaks, with increases in acoustic (AC) and compensated neutron (CNL) and decreases in density (DEN), while the deep and shallow lateral resistivity (RD, RS) curves show positive amplitude differences. In the FMI, they are represented by dark sinusoidal curves and dark small patches. Based on these response characteristics, two types of reservoir spaces are identified for chaotic weak reflections: high-angle vertical fractures and caves with heights less than 7 m, which can form independent reservoirs or fracture-cavity complexes. Three types of reservoirs are distinguished: fracture, cavity, and cavity-fracture types.

A parallel heterogeneous policy deep reinforcement learning algorithm for bipedal walking motion design.

Considering the dynamics and non-linear characteristics of biped robots, gait optimization is an extremely challenging task. To tackle this issue, a parallel heterogeneous policy Deep Reinforcement Learning (DRL) algorithm for gait optimization is proposed. Firstly, the Deep Deterministic Policy Gradient (DDPG) algorithm is used as the main architecture to run multiple biped robots in parallel to interact with the environment. And the network is shared to improve the training efficiency. Furthermore, heterogeneous experience replay is employed instead of the traditional experience replay mechanism to optimize the utilization of experience. Secondly, according to the walking characteristics of biped robots, a biped robot periodic gait is designed with reference to sinusoidal curves. The periodic gait takes into account the effects of foot lift height, walking period, foot lift speed and ground contact force of the biped robot. Finally, different environments and different biped robot models pose challenges for different optimization algorithms. Thus, a unified gait optimization framework for biped robots based on the RoboCup3D platform is established. Comparative experiments were conducted using the unified gait optimization framework, and the experimental results show that the method outlined in this paper can make the biped robot walk faster and more stably.

A free-swimming tadpole model based on immersed boundary-lattice Boltzmann method and its application

A two-dimensional (2D) free-swimming tadpole model is built in this study using the immersed boundary-lattice Boltzmann method. The tadpole is developed by connecting a passive elliptical head with a beating tail. This developed tadpole is capable of controlling the tail swing amplitude to change the swimming speed and achieve the desired swimming direction by attaching an angle offset on the tail axis. The hydrodynamics of the proposed tadpole model in swimming is investigated by regulating the width of the confined space. To be specific, three points are summarized below. First, a lower swimming speed will be produced in a narrower channel under the identical swimming pattern. Second, under the effect of a slight swing strength, a small-scale disturbance is triggered to the surrounding fluid, and a small swimming speed will be generated. Third, a relatively small or excessive swimming speed adversely affects the stability of its swimming. Moreover, a perception-response strategy for the tadpole is further formulated to achieve its autonomous locomotion control. A virtual perceptive field is proposed as the visual range, which is conducive to implementing tadpole motion control based on a set of mechanical response rules. With the above-mentioned improvements, the tadpole can effectively achieve obstacle avoidance in sophisticated obstacle array environments and tracking sine curve routines. Accordingly, this study can provide a valuable reference for the theoretical design of underwater bionic tadpole-like robots.