A gliding dual-mode AUV and a design method thereof

Abstract

The application discloses a gliding and swimming dual-mode AUV and a design method thereof. The AUV comprises deformable gliding wings arranged on both sides of a pressure-bearing shell, capable of being unfolded to provide lift in a gliding mode and being folded to reduce fluid resistance in a swimming mode; a buoyancy adjusting system comprising an outer oil bag, front and rear buoyancy adjusting oil tanks and a buoyancy adjusting power module, used for dynamically adjusting the buoyancy and the gravity center position of the AUV through oil transfer; and a vector propulsion module arranged at the tail of the AUV, comprising a propeller capable of being adjusted at two degrees of freedom and a guide plate matched with the propeller, used for providing direction control capability in the gliding mode. The AUV simultaneously has a tail vector propulsion device, two sets of buoyancy adjusting oil tanks distributed at front and rear positions in the pressure-bearing shell and deformable gliding wings arranged on both sides of the AUV main body, so that the AUV has two operation modes of gliding by buoyancy and swimming with neutral buoyancy, and can be flexibly switched according to operation tasks.

Description

Technical Field

[0001] This invention belongs to the field of autonomous underwater vehicles (AUVs) technology, and relates to a gliding dual-mode AUV and its design method. Background Technology

[0002] Autonomous underwater vehicles (AUVs) are unmanned autonomous devices used for tasks such as ocean exploration, environmental monitoring, and marine resource exploration. Currently, AUVs are mainly divided into two categories: gliding AUVs and swimming AUVs.

[0003] Gliding AUVs rely primarily on buoyancy adjustment for gliding, offering low energy consumption and long range, but are limited in maneuverability and speed, only capable of zigzag movements underwater. Swimming AUVs, on the other hand, use propeller propulsion, providing high maneuverability but consuming more energy and having limited endurance. Therefore, developing a dual-mode AUV that combines the advantages of both gliding and swimming modes has become crucial in the field.

[0004] Existing hybrid-drive AUVs possess both gliding and swimming capabilities, but they mostly employ fixed gliders and single buoyancy adjustment modules, limiting gliding efficiency and increasing swimming drag. Furthermore, existing AUVs largely rely on tail rudders for directional control, resulting in insufficient maneuverability. In addition, due to limitations in their external structural design, existing dual-mode AUVs experience significant energy losses during mode switching, leading to low energy efficiency.

[0005] Therefore, how to design an AUV that can flexibly switch between gliding and swimming modes, has low gliding drag, high swimming efficiency, and adjustable attitude is an urgent problem to be solved in the current technology field. Summary of the Invention

[0006] The purpose of this invention is to provide a gliding-swimming dual-mode AUV that can flexibly switch between gliding and swimming modes, possessing efficient hydrodynamic characteristics and flexible attitude control capabilities. Furthermore, this invention also provides a design method for a gliding-swimming dual-mode AUV to optimize its key parameters and improve overall performance.

[0007] A first aspect of the present invention provides a dual-mode AUV for gliding, comprising:

[0008] Pressure-bearing housing, used to provide the main structure and house the internal modules;

[0009] A deformable glider is located on both sides of the pressure-bearing shell and can be deployed in gliding mode to provide lift and retracted in swimming mode to reduce fluid resistance.

[0010] The buoyancy adjustment system, including an external oil bladder, front and rear buoyancy adjustment oil tanks, and a buoyancy adjustment power module, is used to dynamically adjust the buoyancy and center of gravity of the AUV through the transfer of oil to adapt to the switching between gliding mode and swimming mode.

[0011] The vector propulsion module, located at the tail of the AUV, includes a thruster with two degrees of freedom adjustable angle and a guide plate that works with it. It provides directional control in gliding mode and enhances the flexibility of the propulsion system in swimming mode.

[0012] The main control module is used to switch the AUV's mode, adjust buoyancy, control attitude, and adjust the propulsion system based on preset tasks and sensor data.

[0013] The deformable glider is deployed and retracted by a motor, the buoyancy adjustment power module provides power for the change of oil volume through a hydraulic system, and the thruster angle adjustment of the vector propulsion module is achieved by a deep-sea servo motor.

[0014] A second aspect of the present invention provides a design method for a dual-mode AUV for gliding, comprising the following steps:

[0015] Step 1: Establish a 3D model of the AUV and determine the position of the AUV's center of buoyancy based on the model;

[0016] Step 2: Using computational fluid dynamics, optimize the position, aspect ratio, and sweep angle of the glider through an ergonomic approach to obtain the optimal lift-to-drag ratio.

[0017] Step 3: Perform force analysis on the AUV, establish force balance and torque balance relationships, and solve for the relationship between angle of attack and glide angle, as well as the relationship between velocity and glide angle;

[0018] Step 4: Set and analyze the different capacity states of the front and rear buoyancy adjustment fuel tanks, calculate the gliding time and energy consumption in combination with gliding depth and gliding speed, and determine the optimal fuel tank capacity allocation and buoyancy gliding state.

[0019] In the design method, the shape and position optimization of the glider are based on the principle of maximizing the lift-to-drag ratio, and the fuel tank capacity allocation optimization is based on the principles of minimizing energy consumption and maximizing flight speed.

[0020] Compared with existing inventions, the present invention has the following beneficial effects:

[0021] (1) The present invention has a tail vector propulsion device, two sets of buoyancy adjustment oil tanks distributed in the front and rear positions inside the pressure shell, and deformable gliders located on both sides of the AUV body, so that the AUV has two operating modes: gliding by buoyancy and swimming by neutral buoyancy, which can be flexibly switched according to the task.

[0022] (2) The present invention adopts a deformable glider design, which allows the glider to unfold in gliding mode to improve lift and gliding efficiency; and the glider to retract in swimming mode to reduce fluid resistance and improve propulsion efficiency, thereby achieving efficient switching between gliding and swimming modes.

[0023] (3) By designing independent buoyancy-adjustable fuel tanks at the front and rear, the center of gravity of the AUV can be dynamically adjusted, making the gliding angle, gliding speed and attitude control more precise, and improving navigation efficiency and stability.

[0024] (4) The vector propulsion module is used instead of the traditional tail rudder. The propulsion unit has two degrees of freedom and adjustable angle, and is equipped with a guide plate that can swing accordingly, so that the AUV can accurately adjust its course in gliding mode, improve its directional control capability, and reduce the energy loss caused by traditional tail rudder control.

[0025] (5) Traditional AUVs have a large energy loss when switching between gliding and swimming modes. This invention optimizes the glider shape and buoyancy adjustment strategy to make the mode switching smoother, reduce energy loss, and improve operational efficiency and endurance. Attached Figure Description

[0026] Figure 1 This is a schematic diagram of the overall structure of the present invention;

[0027] Figure 2(a) is a general schematic diagram of the folding section of the glider of the present invention;

[0028] Figure 2(b) is a schematic diagram of the actuator of the folding section of the glider of the present invention;

[0029] Figure 2(c) is a cross-sectional view of the actuator of the folding section of the glider of the present invention;

[0030] Figure 3(a) is a schematic diagram of the external structure of the vector propulsion module of the present invention;

[0031] Figure 3(b) is a schematic diagram of the internal structure of the vector propulsion module of the present invention;

[0032] Figure 4(a) is a schematic diagram of the optimized position and shape of the glider of the present invention;

[0033] Figure 4(b) is a flowchart of the AUV dynamic model established using computational fluid dynamics methods in this invention;

[0034] Figure 4(c) is a schematic diagram of the relationship between the angle of attack and glide angle of the AUV predicted by the present invention;

[0035] Figure 4(d) is a schematic diagram of the relationship between the predicted AUV speed and glide angle according to the present invention. Detailed Implementation

[0036] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] This application provides a dual-mode AUV for gliding, including a pressure-bearing shell, a deformable glider, an external fuel bladder, front and rear buoyancy-adjustable fuel tanks, a buoyancy-adjustable power module, a vector propulsion module, a main control module, an underwater positioning module, a surface communication module, and a battery module.

[0038] The pressure-bearing shell is the main structure of the AUV. It is made of lightweight, high-strength materials and can withstand the high pressure of the deep-sea environment. At the same time, it provides internal space to accommodate the main control module, battery and other electronic devices, and optimizes the internal layout to improve the stability and heat dissipation performance of the equipment.

[0039] The deformable glider wings are mounted on both sides of the AUV's outer shell. They deploy in gliding mode to provide greater lift and improve gliding efficiency, and retract in swimming mode to reduce fluid resistance and improve propulsion efficiency. The deployment and retraction of the glider wings are driven by motors and intelligently controlled by the main control module to ensure optimal gliding and swimming performance and optimize energy consumption.

[0040] The external oil bladder is installed in the wet chamber of the AUV, located at the foremost end of the outer shell. It can adjust the overall buoyancy of the AUV by increasing or decreasing the amount of oil inside, and switch between gliding and swimming states to adapt to different underwater mission requirements.

[0041] The front and rear buoyancy regulating fuel tanks are located at the bow and stern of the AUV, respectively. By controlling the change in the volume of fuel inside the tanks, the center of gravity of the AUV can be dynamically adjusted, thereby optimizing the gliding angle and speed, improving navigation stability, and providing more precise attitude control capabilities to adapt to gliding needs under different environmental conditions.

[0042] The buoyancy adjustment power module, including a hydraulic system, is used to provide the power required for changes in oil volume.

[0043] The vector propulsion module is located at the tail of the AUV and includes a vector propulsion device that can adjust the thruster angle with two degrees of freedom. A guide plate that can swing accordingly is provided on the outside of the propulsion module. This guide plate can replace the traditional tail rudder, improving the AUV's directional control capability in gliding mode and enhancing the flexibility of the propulsion system in swimming mode, enabling the AUV to adapt to complex water flow environments.

[0044] The main control module is used for the overall control of the AUV, and is responsible for realizing mode switching, buoyancy adjustment, attitude control, propulsion system adjustment, and underwater positioning functions. The main control module combines multi-sensor data to achieve adaptive navigation and optimize energy management, thereby improving the AUV's endurance and autonomous operation capabilities.

[0045] The underwater positioning module includes an inertial navigation system, sonar, etc., and is used to accurately locate the position and attitude of the vehicle.

[0046] The surface communication module is used to transmit data with the external control system when the AUV floats to the surface, enabling remote monitoring and control. It also supports the uploading of task data and the downloading of remote commands to optimize underwater operation processes.

[0047] The battery module provides the electrical energy required for AUV operation and has functions such as circuit protection.

[0048] Example 1. A dual-mode AUV for gliding

[0049] This embodiment provides a gliding dual-mode AUV, which adopts a torpedo-shaped pressure-bearing shell, and its internal structure is as follows: Figure 1 As shown. Deformable gliders 4 are arranged on both sides of the shell, an external fuel tank 1 is arranged at the bow, a battery module 3 is arranged at the bow, internal fuel tanks are arranged at the bow and stern, namely the front buoyancy adjustment fuel tank 2 and the rear buoyancy adjustment fuel tank 7, respectively, a buoyancy adjustment power module 10, a main control module 5 and an underwater positioning module 6 are arranged in the middle, a surface communication module 8 is arranged at the stern, a vector propulsion module 9 is arranged at the stern, and a guide plate is installed on the vector propulsion model.

[0050] The torpedo-shaped pressure hull is made of high-strength, lightweight materials to ensure pressure resistance and corrosion resistance, and to provide structural support for the internal modules.

[0051] As shown in Figures 2(b) and 2(c), the deformable glider is fixed by a sealed bearing housing 11, an upper fixed rotating shaft 12, a sealing ring 13, a retaining ring 14, and a lower sealing plug 15 (with the same diameter as the upper fixed rotating shaft and pressure balanced). When the deformation mechanism is in operation, the reduction motor 16 drives the turbine 17 and the worm gear 18 to rotate, which in turn drives the upper fixed rotating shaft to rotate, thereby causing the glider to fold (as shown in Figure 2(a)) or unfold (as shown in Figure 2(b)).

[0052] The outer oil tank is located in the wet compartment of the AUV and exchanges oil with the inner oil tank, thereby adjusting the buoyancy of the AUV.

[0053] The battery module is bolted to the bow of the AUV to power each module and optimize power management to extend the driving range.

[0054] The internal fuel tanks (front and rear) work in conjunction with the buoyancy adjustment power module as part of the buoyancy adjustment system. By adjusting the volume of fuel in the front and rear tanks, the center of gravity of the AUV can be changed, thereby adjusting the gliding angle and gliding speed.

[0055] The buoyancy adjustment power module is connected to the front and rear fuel tanks and the outer fuel tank via hydraulic lines to realize the exchange of oil inside the AUV, so as to precisely adjust the buoyancy and center of gravity of the AUV, and improve gliding performance and attitude control capabilities.

[0056] The surface communication module is externally encased in a guide vane, and the communication antenna is connected to the internal main control module, which can reduce navigation resistance while enabling communication with the outside world.

[0057] The vector propulsion module, such as Figure 3(a) , 3(b) As shown, the output shaft of the deep-sea servo motor 9-1 is connected to its respective rotating frame (horizontal rotating frame 9-2 or vertical rotating frame 9-3) by bolts. The rotating frame is connected to the stern hull 9-6 by rotating shaft 9-4. The tail of the deep-sea thruster 9-5 is connected to the rotating frame by bolts.

[0058] Guide plates 9-8 are arranged on the thruster shield 9-7. At this time, activating the deep-sea servo motor can drive the swivel frame to rotate around the axis, thereby driving the thruster to rotate, thus realizing the adjustment of the two degrees of freedom of the thruster. In addition, the guide plates on the thruster shield will rotate with the thruster to achieve precise directional control in gliding mode.

[0059] The AUV in this embodiment can flexibly switch between two operating modes: buoyancy gliding mode and neutral buoyancy swimming mode, to meet different operational needs. Specifically, it is implemented as follows:

[0060] (1) Buoyancy gliding mode

[0061] The buoyancy gliding mode is divided into ascending gliding and descending gliding. Before entering gliding mode, the deformable glider unfolds to increase the lift-to-drag ratio and reduce energy consumption during ascent or descent.

[0062] During descent and gliding, the buoyancy adjustment power module fills the two internal fuel tanks from the external fuel bladder. At this point, the overall weight of the AUV is greater than the buoyancy, and the descent begins. Simultaneously, the main control module adjusts the fuel ratio between the two internal fuel tanks according to the AUV's attitude requirements, increasing the fuel level in the forward tank and decreasing or keeping the fuel level in the aft tank. At this time, the AUV's center of gravity shifts forward, the bow tilts downward, and it begins to glide at a certain angle.

[0063] During ascent and gliding, the buoyancy adjustment power module drains fuel from the two internal fuel tanks into the external fuel tank. At this point, the overall buoyancy of the AUV exceeds its weight, and it begins to ascend. Simultaneously, the main control module adjusts the fuel ratio between the two internal fuel tanks according to the AUV's attitude requirements, reducing the fuel level in the forward tank and increasing or maintaining the level in the aft tank. This shifts the AUV's center of gravity aft, causing the bow to tilt upward, and initiating an ascent at a specific angle. This allows for precise control of the gliding angle.

[0064] In addition, the guide vanes of the vector propulsion system are dynamically adjusted according to the gliding direction to optimize the gliding path and maintain stability.

[0065] (2) Neutral buoyancy swimming mode

[0066] Before entering swimming mode, the deformable glider folds up to reduce fluid resistance and improve propulsion efficiency. At this time, the buoyancy adjustment power module adjusts the overall buoyancy of the AUV to neutral according to the instructions of the main control module. The vector propulsion system is then activated, and by adjusting the thruster angle, the AUV achieves efficient swimming. This enables the AUV to achieve highly maneuverable swimming to adapt to complex water flow environments.

[0067] (3) Mode switching

[0068] AUVs can seamlessly switch between buoyancy gliding mode and neutral buoyancy swimming mode according to mission requirements.

[0069] When switching from gliding mode to swimming mode, the main control module adjusts the buoyancy regulation system to bring the AUV's buoyancy close to neutral, retracts the glider, and then activates the thrusters to enter swimming mode.

[0070] When switching from swimming mode to gliding mode, the main control module shuts down the thrusters, deploys the glider, and adjusts the buoyancy control system to put the AUV into gliding mode.

[0071] Example 2. A design method for a dual-mode gliding AUV.

[0072] The design method in this embodiment mainly improves the gliding performance and energy efficiency of the AUV by optimizing the shape and position of the glider and the fuel tank capacity.

[0073] Step 1: Establish a 3D model of the AUV and determine its center of buoyancy based on the model. Use an ergonomic method to set different wing position parameters before and after the center of buoyancy, and use computational fluid dynamics to numerically calculate the lift-to-drag ratio of the wing under different positions.

[0074] Using the wing position with the highest lift-to-drag ratio as a fixed value, different aspect ratios were set at that position using an ergonomic method, and the lift-to-drag ratio of the wing under different aspect ratios was numerically calculated using computational fluid dynamics.

[0075] Again, using the aspect ratio that maximizes the lift-to-drag ratio as a fixed value, different wing sweep angles were set under this aspect ratio condition using an ergonomic method, and the lift-to-drag ratio of the wing under different sweep angles was numerically calculated using computational fluid dynamics. Thus, as shown in Figure 4(a), the optimal wing shape and position parameters can be obtained.

[0076] Step 2: Perform a force analysis on the AUV. By analyzing the horizontal force balance, vertical force balance, and moment balance relationships, the following equation can be obtained:

[0077]

[0078] B

[0079]

[0080] in, For the angle of attack, For gliding angle, For lift, Where M is the drag force, B is the pitching moment, and C is the buoyancy force. , For longitudinal velocity and vertical velocity, , For added mass, This represents the difference in weight between the front and rear fuel tanks. This refers to the position of the front fuel tank from the center of buoyancy. This refers to the distance between the rear fuel tank and the center of buoyancy.

[0081] Furthermore, lift, drag, and pitching moment can be calculated using the following formula:

[0082] Where V is , The resultant velocity constituted , , , , , All of these are hydrodynamic coefficients, which can be obtained by fluid dynamics simulation calculations. The specific flowchart is shown in Figure 4(b).

[0083] Furthermore, in Figure 4(b), after obtaining the three-dimensional model, the three-dimensional model is meshed, then simulation parameters are set, a series of gliding angles are selected for oblique flight simulation, and finally the least squares method is used to solve the simulation results to obtain the above hydrodynamic coefficients.

[0084] Solving the above equation yields the following equation:

[0085]

[0086] in, Let be the gliding angle. Given that the above equation has a solution, the range of the gliding angle can be obtained as follows:

[0087]

[0088] By taking any value within the above range, the formulas for calculating the angle of attack and velocity can be obtained as follows:

[0089]

[0090]

[0091] in This is the net buoyancy. From this, we can obtain the relationship between angle of attack and angle of glide, and the relationship between velocity and angle of glide, as follows: Figure 4(c) , 4(d) As shown in the diagram, increasing the amount of fuel in the internal tank, i.e., increasing the net buoyancy, will lead to a greater vertical velocity. At this point, the horizontal velocity will first increase and then decrease. This allows us to obtain the optimal attitude angle for the horizontal velocity.

[0092] Step 3: Set different capacity states for the front and rear fuel tanks and arrange them into various combinations. Then, input these combinations into the relationship diagram established in Step 2 to calculate the horizontal and vertical navigation speeds under each fuel tank capacity state.

[0093] The required gliding time can be obtained by combining the preset gliding depth with the calculated gliding speed. Then, by combining the power consumption of the buoyancy adjustment power module, the energy consumption of the gliding mode can be calculated. Finally, by comparing different energy consumption conditions and flight speeds, the optimal front and rear internal fuel tank capacity distribution and the optimal buoyancy gliding state can be obtained.

[0094] As described above, the present invention can be well implemented. The above embodiments are only preferred embodiments of the present invention and are not intended to limit the scope of implementation of the present invention; that is, all equivalent changes and modifications made in accordance with the content of the present invention are covered by the scope of protection claimed in the claims of the present invention.

Claims

1. A design method for a dual-mode gliding AUV, wherein the dual-mode gliding AUV comprises: Pressure-bearing housing, used to provide the main structure and house the internal modules; A deformable glider is located on both sides of the pressure-bearing shell and can be deployed in gliding mode to provide lift and retracted in swimming mode to reduce fluid resistance. The buoyancy adjustment system, including an external oil bladder, front and rear buoyancy adjustment oil tanks, and a buoyancy adjustment power module, is used to dynamically adjust the buoyancy and center of gravity of the AUV through the transfer of oil to adapt to the switching between gliding mode and swimming mode. The vector propulsion module, located at the tail of the AUV, includes a thruster with two degrees of freedom adjustable angle and a guide plate that works with it. It provides directional control in gliding mode and enhances the flexibility of the propulsion system in swimming mode. The main control module is used to switch the AUV's mode, adjust its buoyancy, control its attitude, and adjust its propulsion system based on preset tasks and sensor data. The deformable glider is deployed and retracted by an electric motor, the buoyancy adjustment power module provides power for the change of oil volume through a hydraulic system, and the thruster angle adjustment of the vector propulsion module is achieved by a deep-sea servo motor. Its characteristic is that it includes the following steps: Step 1: Establish a 3D model of the AUV and determine the position of the AUV's center of buoyancy based on the model; Step 2: Using computational fluid dynamics, optimize the glider's position, aspect ratio, and sweep angle through an ergonomic approach to obtain the optimal lift-to-drag ratio; specifically: The ergonomic method was used to set different wing position parameters before and after the center of buoyancy, and computational fluid dynamics was used to numerically calculate the lift-to-drag ratio of the wing under different positions. Using the wing position with the highest lift-to-drag ratio as a fixed value, different aspect ratios were set at that position using an ergonomic method, and the lift-to-drag ratio of the wing under different aspect ratios was numerically calculated using computational fluid dynamics. Again, using the aspect ratio with the highest lift-to-drag ratio as a fixed value, different wing sweep angles are set under this aspect ratio condition using the ergonomic method, and the lift-to-drag ratio of the wing under different sweep angles is numerically calculated using computational fluid dynamics methods, thereby obtaining the optimal wing shape and position parameters; Step 3: Perform force analysis on the AUV, establish force balance and torque balance relationships, and solve for the relationship between angle of attack and glide angle, as well as the relationship between velocity and glide angle; B in, For the angle of attack, For gliding angle, For lift, Where M is the drag force, B is the pitching moment, and C is the buoyancy force. , For longitudinal velocity and vertical velocity, , For added mass, This represents the difference in weight between the front and rear fuel tanks. The position of the front fuel tank from the center of buoyancy. This refers to the distance between the rear fuel tank and the center of buoyancy. Lift, drag, and pitching moment are calculated using the following formula: Where V is , The resultant velocity constituted , , , , , All are hydrodynamic coefficients, obtained from fluid mechanics simulation calculations; After obtaining the 3D model, the 3D model is meshed, then the simulation parameters are set, a series of gliding angles are selected for oblique flight simulation, and finally the least squares method is used to solve the simulation results to obtain the above hydrodynamic coefficients. Solving the above equation yields the following equation: in, Let be the gliding angle. Given that the above equation has a solution, the range of the gliding angle is: Taking any value from the above range, the formulas for calculating the angle of attack and velocity are as follows: in Net buoyancy; Thus, the relationship between angle of attack and glide angle, and between velocity and glide angle, is obtained, thereby obtaining the attitude angle for the optimal horizontal velocity; Step 4: Set and analyze the different capacity states of the front and rear buoyancy adjustment fuel tanks, calculate the gliding time and energy consumption in combination with gliding depth and gliding speed, and determine the optimal fuel tank capacity allocation and buoyancy gliding state. In the design method, the shape and position optimization of the glider are based on the principle of maximizing the lift-to-drag ratio, and the fuel tank capacity allocation optimization is based on the principles of minimizing energy consumption and maximizing flight speed.

2. The design method of the dual-mode AUV for gliding as described in claim 1, characterized in that, In step 4, by comparing the energy consumption and speed under different fuel tank capacities, the fuel tank capacity allocation scheme with the lowest energy consumption and the highest horizontal speed is selected to improve the gliding efficiency and endurance of the AUV.

3. The design method of the dual-mode AUV for gliding as described in claim 1, characterized in that, Step 2 also includes meshing the three-dimensional model of the AUV and setting simulation parameters, and using the least squares method to fit the simulation results to obtain accurate hydrodynamic coefficients.

4. The design method of the dual-mode AUV for gliding as described in claim 2, characterized in that, The design method also includes a comprehensive evaluation of the AUV's gliding depth, gliding time, and energy consumption to determine the optimal buoyancy gliding state and ensure the AUV's efficient operation under different mission requirements.

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