Integrated Simulation Research of Multi-natural Energy-driven Unmanned Surface Vehicle

In response to the limitations of existing unmanned surface vehicles in complex marine environments, where they often fail to meet the requirements for extended endurance, broad operational range, offshore missions, and prolonged operational durations, an autonomous Unmanned Surface Vehicle (NUSV) has been designed and developed. The NUSV is propelled by wind, solar, and wave energy sources. Concerning wind energy, a micro wind energy storage mechanism based on a spiral spring has been designed to enable power generation in low-wind conditions. A wave energy transmission device, complete with a dynamic model, has been devised for wave energy. This device converts torque generated from wave action in different directions into a unified torque, providing continuous power to drive the generator. Solar energy is harnessed using Maximum Power Point Tracking (MPPT) algorithms to ensure optimal operation of the solar panels. The electrical energy generated from these three natural sources is stored using Pulse Width Modulation (PWM) and DC-DC Boost converters. A programmable logic controller manages and allocates this stored electrical energy for the NUSV’s equipment, including underwater propulsion systems, surface cameras, laser radar, GPS, and other electronic devices. This integration of wind, solar, and wave energy sources enables the NUSV to meet power demands, allowing for long-duration operations at sea, extended offshore missions, wide operational ranges, and prolonged mission durations.


Introduction
The rapid advancement of artificial intelligence and unmanned systems is paving the way for novel perspectives in ocean-related research and maritime operations.With the emergence of numerous marine challenges, including issues such as nuclear wastewater discharge into the sea, marine research is on the verge of establishing itself as a prominent domain.Unmanned Surface Vehicles (USVs) represent surface-based robotic systems that employ buoyant structures as their carriers, accommodating diverse specialized equipment to execute one or multiple categories of maritime tasks [1][2][3].Currently, conventional means, including fuel, lithium batteries, or hybrid systems combining both, power the majority of USVs [4][5][6].During maritime operations, their inability to refuel energy limits their voyage durations, preventing long-term, wide-ranging, and offshore operations.A minority of USVs utilize natural energy sources for power supply [7], but these may fall short in low-wind conditions, relying on a single natural energy source.Renders them vulnerable to variations in environmental conditions, significantly impacting energy supply.Some USVs adopt a hybrid approach, combining natural energy sources with fuel [8].When natural energy cells outperform natural energy sources, adding natural energy cells can optimize performance.However, limitations persist due to the constrained size of battery packs and limited fuel storage in small USVs.Consequently, equipment attachment and navigation range are restricted.
In response to the challenges above, this paper has developed an autonomous unmanned vessel that integrates wind, solar, and wave energy storage.Wind, solar, and wave energy serve as the driving power sources for propulsion while also meeting the electrical power demands of onboard equipment.This innovation ensures the provision of energy and propulsion even in light wind conditions, enabling extended-duration, remote-controlled missions.

The Construction of NUSV
The NUSV comprises a twin-hull structure float, a light wind energy storage system, solar photovoltaic panels, and a wave energy conversion oscillating power generation device.Additionally, it is equipped with propulsion mechanisms, GPS antennas, cameras, and radar, as illustrated in Figure 1.Regarding hull design, the NUSV's twin-hull structure offers low-speed, high-performance capabilities and initial stability, while the wave energy conversion oscillating power generation device enhances hull stability.The multi-energy fusion system of wind, solar, and wave energy, as depicted in Figure 2, comprises a wind turbine utilizing a coiled spring as an energy storage mechanism, a solar photovoltaic power generation system, a Wave energy conversion power system, a lithium battery pack, and an energy management controller.Through a programmable logic controller, In facilitating the charging of the lithium battery, the management of these three energy sources is achieved.Furthermore, the energy management controller allocates power to the propulsion system and onboard equipment based on the stored charge level of the lithium battery.

The Design of the Light Wind Energy Storage and Generation System
The designed light wind energy storage system consists of wind turbine blades, a coiled spring energy storage device, a planetary gear reducer, a cylindrical cam, an extendable pushrod, an energy storage disc, retaining blocks, a reduction shaft, and a generator, as illustrated in Figure 3.The planetary gear reducer reduces the rotational speed generated by the wind turbine blades under the influence of wind, simultaneously increasing the input torque.Under the influence of the cylindrical cam, extendable pushrod, and retaining blocks, the coiled spring within the energy storage disc undergoes cyclic compression.When the energy storage reaches its maximum capacity, it rapidly releases energy to drive the generator, generating electricity.This device can produce significant torque in light wind conditions, thus compressing the coiled spring to achieve energy storage objectives.It effectively resolves the issue of wind turbine blades being unable to drive the generator due to generator damping in low-wind conditions.

Design and Calculation of the Energy Storage Spring Model
Based on whether the spring coils are in contact, we categorize planar coiled springs into contact-type and non-contact-type planar coiled springs.Contact-type planar coiled springs are typically chosen for energy storage applications [9], as depicted in Figure 4. Contact-type planar coiled springs are commonly manufactured from materials such as spring steel, tool steel, cold-rolled steel strips, heat-treated spring steel strips, and special-shaped steel wire materials used in automotive body components.The thickness of these coiled springs typically ranges from 0.5 to 4.0mm, while the width varies from 5 to 80mm.The strength of coiled spring steel strips can be classified into three levels based on the hardness and tensile strength of the steel strips.Contact-type planar coiled springs, in terms of their outer end fixation, can be categorized into hinge-type fixation, pin-type fixation, V-type fixation, and liner fixation.The fixation coefficient, denoted as K₁, is presented in Table 1.In this study, we have adopted the method of liner fixation for designing energy storage coiled springs [10].
Table 1.Fixation forms of contact-type coiled springs.

Fixation forms
Fixation coefficient K₁ Hinge-type fixation 0.65~0.70Pin-type fixation 0.72~0.78V-type fixation 0.80~0.85Liner fixation 0.90~0.95 In order to meet the power generation requirements and accommodate the overall structural design of the vessel, a contact-type flat coiled spring for energy storage has been designed.It must have a maximum output torque of 15,000 . and a minimum output torque of 7,000 ..The coiled spring is made of a secondary heat-treated spring steel strip, with the outer end fixed using liner fixation.The fixation coefficient, denoted as  1 , is 0.95.The ultimate tensile strength (  ) is 1,600 /  2 , and the hardness ranges from 48 to 55 HRC.This design complies with the National Standard of the People's Republic of China GB/T 23935-2009.The elastic modulus () is 206 × 10 3 .
Based on the Mechanical Industry Standard of the People's Republic of China JB/T 7366-94, it is determined that the minimum output torque  1 is: The maximum output torque  2 is: The limit torque   is: Where  represents the spring width, ℎ denotes the thickness of the spring leaf, and   indicates the tensile strength of the spring material.The width, , is designed to be 30, and with the associated parameters, the calculated spring leaf thickness, ℎ, is determined to be 1.404 .Consequently, the designed spring thickness for energy storage is ℎ = 1.4 , as depicted in Figure 5 (a).
The core shaft diameter of the spring is: The outer diameter at which the spring is wound onto the core shaft is: The inner diameter of the spring, when wound loosely inside the spring box, is: The inner diameter of the spring box is: Where  represents the working length of the spring, the inner diameter of the spring box affects the storage and release of energy in the coiled spring.When the ratio of the spring box diameter to the core shaft diameter is 3, the spring achieves its maximum adequate energy [11].Taking the adequate number of turns of the spring as  = 7 and  1 /ℎ = 30, according to the characteristic curve of the contact-type coiled spring's effective coefficient shown in Figure 6, we obtain  2 = 0.85.Therefore, the working length of the spring is: With the spring core shaft diameter  1 = 30ℎ = 42 , the inner diameter of the spring box is therefore selected as  2 = 138 , as illustrated in Figure 5 (c).The number of coils in the coiled spring in its free state is: represents the elastic modulus,  = 2(1 + ),  is the shear modulus, and  is the Poisson's ratio [12].
The number of coils in the coiled spring when loosely wound inside the spring box is: The number of coils in the spring when tightly wound on the core shaft is: Therefore, the effective working number of coils for the spring inside the spring box is  =  2 ( 2 −  1 ) ≈ 7.28, meeting the design criteria.The design parameters for the coiled spring are as shown in Table 2.

The Design of Wave Energy Conversion and Power Generation Devices
In using wave energy, a different approach is taken, where the reciprocating motion of the waves is converted into stable mechanical energy using energy absorption devices [13][14][15].The designed wave energy conversion device primarily consists of a buoy, a swinging arm, a bearing seat, a transmission mechanism, a coupling, a speed increaser, and a generator, as shown in Figure 7.The left and right buoys oscillate up and down under the influence of the waves, with a designed maximum oscillation angle of  ⁄ 9.The swinging arm drives the central driving shaft to rotate periodically in both clockwise and counterclockwise directions, and the driving shaft, through the transmission mechanism, ensures that the generator rotates in the same manner.

Linear Wave Theory
Linear wave theory, known as small-amplitude wave theory, simplifies the wave by approximating it as a cosine function.It assumes the fluid to be an ideal, incompressible, inviscid [15].Under these assumptions, the wave equation can be simplified to:  = ( − ) (12) In this context, the amplitude  equals 1/2 times the significant wave height (), and  is the phase of the linear wave expressed as  =  − .Linear waves exhibit periodicity in both time and space, and it can be observed that the wavelength () is equal to 2/ (where  is the wave number), and the period () is equal to 2/ (where  is the angular frequency).
In the marine environment, the wave-induced loads on engineering structures can be broadly categorized into three types: drag force, inertia force, and diffraction force.The drag force is typically the resistance encountered by an object moving through a fluid due to fluid flow.The inertia force results from pressure variations on the object's surface due to acceleration generated by fluid motion.The diffraction force occurs when waves encounter an object, causing it to diffract around the object and generate a force in its vicinity.When calculating the wave forces on an object, different methods can be employed, such as diffraction theory (Mac et al., 1954) [17], Froude-Krylov theory, and the Morison equation.The choice of the appropriate method depends on the scale of the target object, whether it is a large-scale or small-scale structure.Large-scale structures, typically characterized by a diameter-to-wavelength ratio (/) greater than 0.25, are often analyzed using diffraction theory and Froude-Krylov theory to compute their wave loads, primarily considering the inertia and diffraction forces.In contrast, for small-scale structures (/ < 0.2), the wave-induced loads are predominantly composed of inertia and drag forces, making the Morison equation a suitable approach for calculation.
The Morison equation, proposed in 1950 by Morison and colleagues at the University of California, Berkeley, USA [18], is a semi-empirical theoretical approach primarily based on diffraction theory for calculating wave forces on structures in a fluid medium.This theory assumes that structural objects in a fluid have a negligible impact on fluid motion, and the interaction between the structural object and the fluid is mainly influenced by the fluid's viscous effects and added mass.For the calculation of vertical wave forces, based on the Morison equation, Fan Yunlin provided relevant explanations in 1983 for calculating wave forces on submarine pipelines [19].The fluid flow velocity above and below the pipeline varies, resulting in a pressure difference.The pressure is influenced by the lift coefficient (  ) in conjunction with the inertia force from the Morison equation, yielding the vertical wave force on the submarine pipeline.Graham Dixon and others modified the vertical force equation by removing the resistance term, introducing buoyancy and variable volume, and using the least squares method to calculate the inertia coefficient (  ).They demonstrated that the calculation of wave forces is most accurate when   is set to 2.0 [20].Hu and colleagues used the Cartesian cut-cell method to provide boundary-fitted networks and performed numerical simulations for the vertical wave forces on non-submerged cylinders [21].Easson and others introduced a static buoyancy removal term in calculating vertical wave forces, which removed the static buoyancy by the difference in object displacement volume between dynamic and static water surface states.Building on Easson's work, Bijin Liu and colleagues presented a modified Morison equation for calculating vertical wave forces on freely floating cylindrical bodies of varying degrees of submergence [22].In the design of the wave energy conversion and power generation devices in this paper, the left and right buoys are relatively small in size.Therefore, a modified Morison equation calculates wave loads on the energy absorption system.Calculating the vertical wave force on an individual buoy includes the removal of the static buoyancy term.

Model Calculations
In linear wave theory, water particles undergo harmonic oscillations with a fixed angular frequency.When the water depth, denoted as "," is less than half of the wavelength "," the trajectories of water particles assume an elliptical shape.Conversely, when "" exceeds half of "," the trajectories of water particles become circular.As the water depth increases, the motion radius of water particles gradually decreases [23].Consequently, for wave energy conversion oscillating power generation devices, it is considered when the buoy's motion trajectory follows a circular arc or elliptical arc [24], as illustrated in Figure 9.In this depiction, the buoy takes on a hollow elliptical shape.According to the linear wave theory, the vertical velocity and vertical acceleration of the water particle at the center axis of the buoy 1 are as follows: Where  is the wave number,  is the wave height,  is the water depth,  0 is the distance from the buoy's center position to the seabed,  is the acceleration due to gravity.
Due to the periodic nature of linear waves in both time and space, the oscillation angle  of the upand-down motion of the left and right buoys falls within the range of (−/9, /9).In the case of the dual-buoy system, the horizontal coordinates  corresponding to the left and right buoys can be considered as fixed points in space.Therefore, the wave equation for linear waves can be expressed as follows: Where  is the phase velocity of the wave: Based on the wave's propagation velocity, the time it takes for the wave to propagate between the buoys is given by: By the same logic, the vertical velocity and vertical acceleration of the water particle at the center axis of the buoy 2 are as follows: To calculate the wave forces acting on the buoy in the ocean, based on the Morison equation and its modified formulations, it is assumed that the buoy has a submerged volume of  when subjected to wave action and a submerged volume of  0 when at rest on the still sea surface, the projected area perpendicular to the direction of wave propagation is denoted as   .
Hence, the wave force experienced by Buoy 1 is: Assuming that both buoys displace an equal volume of water during the wave action, the wave force experienced by Buoy 2 is: For an individual buoy, during the wave motion, it experiences the effects of wave forces, as well as gravitational and buoyant forces.In the entire system, both buoys are of equal mass and size, and without considering friction in the rotational movement with the rotating axis, the two buoys alternately oscillate up and down, with their gravitational and buoyant forces effectively canceling each other out.Therefore, when analyzing the force on the entire system, it is only necessary to consider the total wave force.
Considering all the factors discussed above, the total wave force acting on the entire system is as follows: According to the relevant theoretical calculations of torque based on moments, the generated torque under the influence of waves can be expressed as:

Simulation Analysis
Based on the on-site investigation conducted in October and considering the integration of multiple renewable energy sources, the deployment location for the unmanned boat prototype was identified at the coast of Dongshan County, Zhangzhou City, Fujian Province.The local hydrological resources, as reported by the China Oceanic Administration, indicate wave heights ranging from 0.4 to 0.7 meters, an average sea temperature of 25°C, an average current velocity of 0.206 /, a wave period of 16 seconds, an average tidal height of 0.89 meters, and an average water depth of 15 meters.The average horizontal solar radiation was recorded as 1628 ℎ/ 2 , with sea winds ranging from 1 to 6 /.For the simulation experiments, the on-site data was used as a basis for simulating the three natural energy conversion devices (wind, solar, and wave) using MATLAB's Simulink.The simulation environment employed a 2nd Gen Intel(R) Core(TM) i9-12900H processor with a clock speed of 2.50 GHz and an NVIDIA GeForce RTX 3060 Laptop for graphics.The MATLAB version used for these simulations was 2022b.
In wind energy conversion, the analysis and testing revealed that the maximum torque released by the micro-wind energy storage and generation device could reach 14.9 ..It utilizes a 120, 24 permanent magnet DC generator for power generation, with an average generator output power of 95.87 and an average battery charging power of 114.4, as shown in Figure 10.In the wave energy conversion and power generation simulation tests, a sea depth of 15m, seawater density of 1030 / 3 , acceleration due to gravity of 9.81 / 2 , wave height of 0.616 , wavelength of 3.383 , wave period of 16.422 , and wave velocity of 0.206/ were set as parameters.In the designed wave energy conversion and power generation device, the pendulum length was 1.8, the long semi-axis of the elliptical buoy was 0.24, and both short semi-axes were 0.08.Regarding the determination of the hydrodynamic coefficients   and   , their influencing factors primarily include the Reynolds number (), the wave period parameter (), the surface roughness of the column (/), and the wave phase [25][26][27].In this paper,   is set to 2, and   is set to 1.2.
The simulation results for wave energy conversion and power generation, as shown in Figure 11, reveal that the maximum wave forces absorbed by the two end buoys of the wave energy conversion and power generation device can reach up to 6.103 .The total wave force experienced by the energy absorption system reaches a maximum of 10.640 .After passing through the transmission device and the speed increaser, the maximum torque input to the generator is 599.7 ..Power generation is performed using a 300 generator with a rated voltage of 24.The data indicates an average charging power of 281.8 for the battery and an average output power of 316.7 for the generator.In the utilization of solar power generation, two solar panels with a power of 20, a peak voltage of 17.5, and a peak current of 1.27 are used, and they are connected in parallel.The average power generated by the batteries is 38.06, while the photovoltaic panels output an average power of 39.37, as shown in Figure 12.

Conclusion
This paper addresses the energy challenges of oceanic unmanned vessels, selecting a contact-type planar torsion spring to meet micro-wind energy storage requirements.Considering factors such as the spring's maximum and minimum output torques and the material of the torsion spring, a secondary heat-treated spring steel strip is employed.The design utilizes the liner-fixed method with a fixed coefficient of 0.95.Experimental validation demonstrates that the device can generate wind power in a 1.2m/s gentle breeze, providing a novel approach to oceanic wind power generation, especially in lowwind conditions.Additionally, the paper determines the float's motion trajectory through the harmonic oscillation trajectory of water particles, introducing terms to eliminate static buoyancy and account for wave propagation time between floats.By employing the modified Morison equation, a dynamic model for the wave energy conversion device is constructed, which is applicable to the analysis of dynamic forces in linear waves for similar double-float oscillating systems.This device introduces new perspectives to the design of wave energy conversion devices, as well as hydrodynamics and mechanism dynamics, contributing innovative ideas to harnessing natural oceanic energy resources.While limited optimization has been applied to NUSV energy distribution management in this study, future work aims to enhance information and intelligence in energy distribution management based on different operational scenarios.

Figure 2 .
Figure 2. The multi-energy fusion system of the NUSV.

Figure 3 .
Figure 3.The light wind energy storage device.

Figure 4 .
Figure 4. Solid model of a contact-type planar coiled spring.
(a) Cross-Sectional Diagram.(b) The Loosely Wound State.(c) The Tightly Wound State.

Figure 6 .
Figure 6.The effective coefficient of the contact-type flat coiled spring.

Figure 7 .Figure 8 .
Figure 7. Wave energy conversion and power generation devices.The transmission mechanism, as shown in Figure 8 (a), connects input gear 1 and input gear 2 to the driving shaft via two opposing unidirectional clutches.The idler gear is connected to the intermediate shaft, and the output gear is linked to the output shaft.As depicted in Figure 8 (b), when the swinging arm oscillates clockwise, input gear 1 rotates counterclockwise, directly driving the output gear to rotate clockwise.Conversely, when the swinging arm oscillates counterclockwise, input gear 2 rotates clockwise, driving the idler gear, thereby causing the output gear to rotate clockwise.

Figure 10 .
Figure 10.Simulation results for the light wind energy storage and generation.

Figure 11 .
Figure 11.Simulation results of the wave energy conversion and power generation device.
(a) Battery current, voltage, and SOC (b) Battery and photovoltaic panel power

Figure 12 .
Figure 12.Simulation results of solar energy.

Table 2 .
Design parameters for torsion springs.