ROV (Remote Operated Vehicle) soft chi-square-double-loop bit speed condition control method aiming at sea condition interference

Abstract

The invention relates to an ROV soft chi square-double loop bit speed condition control method for sea condition interference. The method comprises the steps of underwater soft chi-square test adaptive Kalman filtering and ROV model-based double-loop bit speed control; the underwater soft chi-square test adaptive Kalman filtering is used for carrying out threshold filtering processing on the three-dimensional position attitude and three-dimensional velocity and angular velocity measurement information of the ROV sensor, and ROV position information after ROV state fusion is obtained; according to the double-loop position speed control based on the ROV model, ROV position information obtained through filtering and target position information read by a sensor are used for conducting double-loop control, an outer loop is controlled to be a target course angle guide control strategy based on MPC, an inner loop is controlled to be sliding mode control speed compensation caused by water flow interference, the ROV is controlled under interference according to the updated control speed, and the control speed of the ROV is controlled. And Kalman filtering circulation is carried out on the controlled position and speed of the aircraft. According to the method, the position speed deviation caused by the ROV under the condition of water flow disturbance is compensated, and an operator can conveniently and accurately control the ROV under ocean current disturbance.

Description

Technical Field

[0001] The present invention relates to the field of underwater vehicle information fusion and control technology, and in particular to an ROV soft chi-square-dual-loop position-velocity condition control method for sea state interference, the goal of which is to enable a target vehicle to achieve precise and stable control under dynamic disturbance. Background Art

[0002] Unmanned underwater vehicles are widely used in the field of marine science and engineering to perform complex and diverse tasks, especially in special application scenarios, where the control capability of underwater vehicles has become a critical technical requirement. These scenarios include but are not limited to underwater military scientific research mapping, offshore assisted breeding in marine smart ranches, maintenance and management of sensor networks and pipeline systems, and search and recovery of black boxes from crashed aircraft.

[0003] The ocean environment is not calm. It is affected by wind, tides, vertical water flow caused by temperature difference, etc. There are often complex disturbances in the seawater, which have many impacts on the operation and control tasks of underwater vehicles. Similarly, in coastal and lake environments, the natural flow of water and its interaction with the seabed and riverbed topography also increase the irregularity of water flow.

[0004] Adaptive Kalman filtering has the sensitivity to respond to changes in external parameters when dealing with the uncertainty of noise characteristics in underwater vehicle modeling. However, when the noise variance is adaptively adjusted, the outliers of the data caused by the characteristics of the underwater sensor will increase the risk of filter divergence. The chi-square test can identify the anomalies of the measurement data, and judge and adjust the measurement anomalies according to the threshold, and then evaluate whether to make the next estimation of the measurement. Since the threshold cannot be set accurately, the binary gate function is adjusted to the soft threshold method. The threshold is weighted by the amount of new information, which can increase the use of suspicious data and greatly improve the utilization efficiency of limited underwater environment data.

[0005] The current mainstream control methods for underwater vehicles mainly focus on PID control and its variations, followed by model predictive control (MPC), fuzzy control, adaptive control, sliding mode control (SMC), neural network control, etc. The above control schemes have their own advantages and disadvantages. Although stable and accurate control can be achieved under turbulence, it is difficult to balance robustness and real-time performance. Summary of the invention

[0006] In order to overcome the defect that the existing underwater vehicle control methods are difficult to balance robustness and real-time performance, the present invention proposes a new ROV soft chi-square-dual-loop position-velocity condition control method for sea condition interference. The present invention adopts a hybrid control strategy to improve the control performance of the underwater vehicle by leveraging its strengths and avoiding its weaknesses, and can achieve stable control of offshore / lake working-level ROVs facing water flow disturbances.

[0007] In order to make the remotely operated underwater robot (ROV) fully utilize the limited resource data of the sensor and realize stable and accurate control under 1 to 2 knots of disturbance, taking into account both robustness and real-time performance, the present invention proposes a ROV soft chi-square-dual-loop position and speed condition control scheme for sea state interference. This scheme aims at the speed control deviation caused by the low-knot ocean current interference in the ocean to the underwater vehicle, adopts adaptive soft chi-square test Kalman filtering and dual-loop position and speed control for water flow disturbance, and modifies the existing FOV line of sight guidance scheme to realize MPC-based position prediction and SMC-based speed tracking. This scheme includes underwater soft chi-square test adaptive Kalman filtering and dual-loop position and speed control based on ROV model, combined with the adaptive filtering method of soft chi-square test under new weights, as well as MPC underwater vehicle position model prediction and SMC-based underwater vehicle speed tracking, to complete the stable control of underwater vehicles under nearshore / lake disturbances.

[0008] The ROV soft chi-square-dual-loop position-velocity condition control method for sea condition interference of the present invention mainly includes two parts, namely, underwater soft chi-square test adaptive Kalman filter and dual-loop position-velocity control based on ROV model.

[0009] The underwater soft chi-square test adaptive Kalman filter performs threshold filtering processing on the three-dimensional position attitude and three-dimensional velocity and angular velocity measurement information of the ROV sensor to obtain the ROV position information after ROV state fusion, thereby achieving effective utilization of a relatively small amount of underwater data and making full use of suspicious data samples.

[0010] The dual-loop position and speed control based on the ROV model performs dual-loop control using the ROV position information obtained by filtering and the target position information read by the sensor. The outer control loop is a target heading angle guidance control strategy based on MPC, and the inner control loop is a sliding mode control speed compensation caused by water flow interference. The ROV is controlled under interference according to the updated control speed, and then the Kalman filter cycle is performed on the controlled vehicle position and speed, thereby realizing a complete control closed loop.

[0011] Underwater sensors have slow data transmission and relatively few sensors. Taking the pressure depth gauge for underwater depth information as an example, the pressure sensor converts the water pressure into an electrical signal, which is then converted into a depth reading by means of size analysis. This type of sensor generates noise due to its own physical characteristics, dynamic changes in water temperature, salinity, and turbulence in the underwater environment, as well as electro-acoustic signals and electro-mechanical signals. When processing signals, noise or even depth / position jumps will be generated. In order to extract the available information obtained by the sensor in real time as much as possible, we need to judge the data quality and filter it. Therefore, this solution adopts the Kalman filtering method based on detection judgment.

[0012] The technical solution for adaptive Kalman filtering based on soft chi-square test is:

[0013] Firstly, the underwater DVL, inertial navigation data fusion and depth meter are used to obtain the underwater vehicle's horizontal x position, y position, depth, pitch angle, roll angle, yaw angle, and the corresponding forward speed, lateral speed, depth speed, pitch angular velocity, roll angular velocity, yaw angular velocity 12-dimensional variables.

[0014] For the above 12-dimensional variables, simplify the state equation of the system x k =F k x k-1 +B k u k +Γ k ω k (ω k ~N(0,Q k )) and the observation equation z k =H k x k +v k (v k ~N(0,R k )), a pure position and attitude Kalman filter is used to perform Kalman preprocessing on the ROV's posture, initialize the state estimation and the initial estimation error covariance, and perform prediction updates.

[0015] Calculate the chi-square statistic and make a judgment based on the known chi-square threshold. Considering the state dimension of the system, set the critical chi-square threshold F α-pos =6.25, that is, when the statistic is less than the threshold, it is executed normally, and when it is greater than the threshold, it is smoothed down. The statistic λ is related to the measurement prediction error and the mean square error matrix.

[0016] To ensure the filtering effect, the equivalent filter gain innovation amount is set to ρ new :

[0017]

[0018] In the formula, the chi-square threshold is F α , the measurement innovation statistic is λ, F α-all is the full-dimensional chi-square threshold, F α-pos is the location ring chi-square threshold.

[0019] The underwater soft chi-square test adaptive Kalman filter sets the weight of new information within the threshold. After two chi-square test threshold judgments, if the new information as the judgment result is less than or equal to the threshold, the gain of the equivalent filter is set to 1; if the new information is greater than the threshold, the filter gain is set to be negatively correlated with the new information, thereby ensuring that the weight of the new information is reduced under abnormal measurement conditions, ensuring the continuity of the filter while increasing accuracy.

[0020] A 12-dimensional full-state Kalman filter of posture and angular velocity is used to pre-process the posture and velocity of the ROV. After calculating the high-dimensional chi-square statistic, the chi-square threshold is used for judgment. Set the critical chi-square threshold F α-all =10.65, follow the same steps as above.

[0021] The filtered results of position measurement and full-dimensional measurement are used as input and substituted into the dual-loop position and speed control.

[0022] Specifically, the present invention provides an ROV soft chi-square-dual-loop position-speed condition control method for sea condition interference. The method uses the ROV position information obtained by the soft chi-square test adaptive filtering and the target position information read by the sensor to perform dual-loop control for the dual-loop MPC position-SMC speed control of water flow disturbance. The outer control loop is a target heading angle guidance control strategy based on MPC, and the inner control loop is a sliding mode control speed compensation caused by water flow interference. The ROV is controlled under interference according to the updated control speed.

[0023] The dual-loop position-speed control scheme based on the ROV model for sea disturbance (water flow disturbance) of the present invention relies on the MPC and SMC to jointly control the vehicle in a position-speed combination manner. The MPC-based ROV target heading angle guidance control strategy is used as the coarse adjustment of the dual-loop position-speed control. The line of sight angle guidance strategy is adopted, and the MPC model is used to predict the control input FOV guidance controller. The ROV's own state information obtained by fusing the target information and the Kalman information is used as the known information to perform full-dimensional posture guidance under the target state, and the speed control amount of the guidance controller is calculated.

[0024] The present invention aims at the dual-loop MPC position-SMC speed control of water flow disturbance. The sliding mode control speed compensation caused by water flow disturbance is adjusted by making a difference between the speed information read by the sensor and the speed control amount adjusted by the MPC position. A smooth sliding surface is designed and the sigmoid function and the boundary layer method are combined to eliminate the vibration. The obtained inner loop speed is superimposed with the FOV guided outer loop control to obtain the spacecraft command control amount and act on the thrusters in turn.

[0025] The present invention is directed to the dual-loop MPC position-SMC speed control of water flow disturbance, and the steps of the dual-loop control are as follows:

[0026] Step 1: First, establish the system's target guidance control mathematical model. Compare the position and attitude of the target point to be tracked with the vehicle's own posture information obtained by Kalman filtering to obtain the difference based on the line of sight angle guidance.

[0027] Step 2: Based on the multi-step estimation of the Kalman filter, obtain the multi-step prediction of the target and the MPC prediction of the future state. The loss function should be related to the future output and the expected output, and the future output is related to the model state, the current state and the future control amount. Set Q as the state weight matrix to penalize the state error, set R as the control input weight matrix to penalize the size of the control input, set x as the system state, u as the control input, the final state weight matrix used to penalize the prediction time domain terminal error is F, and the number of prediction time domain steps is N; the design cost function is:

[0028]

[0029] To explain step 2, according to the motion state of the target, the relative motion relationship between the ROV platform and the target can be used to model and predict, and then derived based on the Kalman filter.

[0030] Step 3: According to the control amount of the interval, after obtaining the optimal input, take the current input as the first control input and output it as the desired speed.

[0031] Step 4: Apply SMC speed control correction to the desired speed magnitude to adapt the system to underwater uncertainties and external disturbances. SMC speed tracking can be used to design an internal controller to ensure that the system output tracks the given speed trajectory.

[0032] For step 4, the specific implementation process of sliding mode variable structure control is as follows:

[0033] Step 4-1: After determining the system model and control objectives, first define the error dynamic function, i.e., the sliding surface, so that the system state reaches a low-dimensional subspace. Set the difference between the expected speed and the actual speed to e v , k e , τ is the control gain coefficient, and the sliding surface formula is:

[0034]

[0035] Step 4-2: Update the control gain by dynamically adjusting the error through the adaptive control law and set k e0 , τ 0 is the basic control gain, γ e and γ τ is the adaptive control law parameter, and the adaptive control law is:

[0036]

[0037] Step 4-3: Use the hyperbolic tangent function tanh(s) to process the discontinuous part of the control, replacing the sign function of the traditional sliding mode control to reduce chattering. The formulas for each acceleration control law are:

[0038]

[0039] Step 4-4: Perform Lyapunov analysis to prove the stability of the system, and track the force required for the desired speed, apply it to the spacecraft, and obtain the final control law for the speed of each propeller of the spacecraft through thrust distribution.

[0040] The thrust distribution matrix takes into account three-dimensional velocity and three attitude angular velocities. According to the structural layout of the ROV, there are 8 thrusters (4 lateral thrusters and 4 vertical thrusters). The thrust and torque in the x, y, and z directions are generated according to the acceleration, and the thrust rotation speed of the 8 thrusters is obtained according to the distribution relationship.

[0041] The effect advantage of the present invention is:

[0042] (1) The utilization efficiency of the sensor data resources of each sensor of the underwater vehicle is improved, and the effective data is used to the maximum extent for Kalman filter reasoning without discarding suspicious data.

[0043] (2) It combines the advantages of MPC in position tracking and guidance control and SMC in rapid speed tracking control, enabling the vehicle to perform stable and rapid control while resisting low-speed turbulence. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments of the present invention. Obviously, the following drawings are only some embodiments recorded in the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0045] Figure 1 The present invention is a functional flow chart of the ROV soft chi-square-dual-loop position-velocity condition control method for sea condition interference.

[0046] Figure 2 This is a diagram showing the tracking trajectory of the dual-loop simulation control of the present invention.

[0047] Figure 3 This is a diagram showing the effect of the soft chi-square adaptive filtering of the present invention, wherein: Figure 3 (a) is the result of the position and speed chi-square test. Figure 3 (b) is the weight distribution of measurement abnormal results.

[0048] Figure 4 It is a schematic diagram of the GUI operation interface of the present invention. DETAILED DESCRIPTION

[0049] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. The present invention can also be implemented or applied through other different specific implementation methods. The details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention.

[0050] At the same time, it should be understood that the protection scope of the present invention is not limited to the specific embodiments described below; it should also be understood that the terms used in the embodiments of the present invention are for describing specific embodiments rather than for limiting the protection scope of the present invention.

[0051] Embodiment: A ROV soft chi-square-dual-loop position-velocity condition control method for sea condition interference

[0052] like Figure 1 As shown, the method is generally divided into two parts, and the technical characteristics and specific use of each part include the following steps:

[0053] Step 1: The inertial navigation system and depth gauge measure the state of the aircraft platform to obtain the measurement information of three-dimensional position and speed. The aircraft platform first reads the data and pre-processes the Kalman filter based on the information fused by its own inertial navigation and DVL, combined with equipment such as pressure depth gauge. Data pre-processing includes full-dimensional residual covariance processing.

[0054] Step 2: Use the pure position and attitude Kalman filter to perform Kalman preprocessing on the ROV's posture, calculate the chi-square statistic, and make a judgment based on the known chi-square threshold to set the critical chi-square threshold F α-pos =6.25.

[0055] Step 3: Set the weight of the new information within the threshold. After two chi-square test threshold judgments, if the new information as the judgment result is less than or equal to the threshold, set the gain of the equivalent filter to 1; if the new information is greater than the threshold, set the filter gain to be negatively correlated with the new information, so as to ensure that the weight of the new information is reduced under abnormal measurement conditions, ensure the continuity of the filter and increase the accuracy. To ensure the filtering effect, set the equivalent filter gain new information amount ρ new .

[0056] Step 4: Use the 12-dimensional full-state Kalman filter of posture and angular velocity to perform Kalman filter preprocessing on the posture and velocity of the ROV, calculate the high-dimensional chi-square statistic, and use the chi-square threshold to make a judgment. Set the critical chi-square threshold F α-all =10.65.

[0057] Step 5: Setting the threshold innovation weight is similar to step 3.

[0058] Step 6: Based on the control output results, establish a dual-loop MPC position-SMC speed control for water flow disturbances.

[0059] Step 7: First, establish the system's target guidance control mathematical model, compare the position and attitude of the target point to be tracked with the vehicle's own posture information obtained by Kalman filtering, and obtain the difference based on the line of sight angle guidance.

[0060] Step 8: Based on the multi-step estimation of the Kalman filter, the multi-step prediction of the target is obtained, and the MPC prediction of the future state is obtained. The loss function should be related to the future output and the expected output, and the future output and the model state, the current state and the future control quantity. The design cost function J(x,u) is a function of the state quantity and the input control quantity.

[0061] Step 9: According to the motion state of the target, the relative motion relationship between the ROV platform and the target can be used to model and predict, and then derived based on the Kalman filter.

[0062] Step 10: According to the control quantity of the interval, after obtaining the optimal input, take the current input as the first control input and output it as the desired speed. SMC speed control correction is performed on the desired speed to adapt to the system of underwater uncertainty and external disturbances. SMC speed tracking can be used to design an internal controller to ensure that the system output tracks the given speed trajectory.

[0063] Step 11: After determining the system model and control target, first define the error dynamic function, i.e., the sliding surface, so that the system state reaches a low-dimensional subspace. Track the expected speed and set the difference between the expected speed and the actual speed to e v , and design the sliding surface formula.

[0064] Step 12: Update the control gain by designing an adaptive control law to dynamically adjust the error.

[0065] Step 13: Use the hyperbolic tangent function tanh(s) to process the discontinuous part of the control, and combine the boundary layer method to replace the sign function of the traditional sliding mode control to reduce the vibration, and obtain the formulas of various acceleration control laws.

[0066] Step 14: Perform Lyapunov analysis to prove the stability of the sliding mode control speed tracking system.

[0067] Step 15: Track the force required for the desired speed and apply it to the vehicle. After the thrust is distributed, the final control law for the speed of each propeller of the vehicle is obtained, and full drive control of the propeller is performed under water flow interference.

[0068] Step 16: Perform data fusion measurement of the inertial navigation unit, DVL, depth meter and other equipment, update the system input of the Kalman filter, and perform the next round of control until the established control target is achieved.

[0069] Figure 2-Figure 4 Shown are the implementation effect of the method of the present invention and the GUI operation interface of the method of the present invention.

[0070] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Any technician familiar with the profession can make some changes or modifications to the technical contents disclosed above without departing from the scope of the technical solution of the present invention to obtain equivalent embodiments of equivalent changes. However, any simple modification, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention should be included in the scope of protection of the claims of the present invention.

Claims

1. A ROV soft chi-square-dual-loop position-velocity condition control method for sea condition interference, characterized in that: The method adopts adaptive soft chi-square test Kalman filter and dual-loop MPC position-SMC speed control for disturbance to correct the FOV sight guidance scheme in order to solve the speed control deviation caused by ocean current disturbance in the ocean to the underwater vehicle. The method comprises: underwater soft chi-square test adaptive Kalman filtering and double-loop MPC position-SMC speed control based on ROV model.

2. The ROV soft chi-square-dual-loop position-velocity condition control method for sea state interference according to claim 1, characterized in that: The underwater soft chi-square test adaptive Kalman filter adopts a secondary multidimensional threshold test, and the specific implementation steps include: 1) First, a pure position and attitude Kalman filter is used to perform Kalman preprocessing on the ROV’s posture, calculate the chi-square statistic, and make a judgment based on the preset chi-square threshold. The critical chi-square threshold F is pre-set. α-pos =6.25; 2) Then, a 12-dimensional full-state Kalman filter of posture and angular velocity is used to preprocess the posture and velocity of the ROV. After calculating the high-dimensional chi-square statistic, a judgment is made based on the preset chi-square threshold, and the critical chi-square threshold F is pre-set. α-all =10.

65.

3. The ROV soft chi-square-dual-loop position-velocity condition control method for sea state interference according to claim 2 is characterized in that: The 12-dimensional full-state Kalman filter of the position, attitude, velocity and angular velocity filters the following 12-dimensional variables of the underwater vehicle: Horizontal x-position, y-position, depth, pitch angle, roll angle, yaw angle, and corresponding forward velocity, lateral velocity, depth velocity, pitch velocity, roll velocity, yaw velocity.

4. The ROV soft chi-square-dual-loop position-velocity condition control method for sea state interference according to claim 1, characterized in that: The underwater soft chi-square test adaptive Kalman filter sets the weight of the new information within the threshold. After two chi-square test threshold judgments, if the new information as the judgment result is less than or equal to the threshold, the gain of the equivalent filter is set to 1; if the new information as the judgment result is greater than the threshold, the filter gain is set to be negatively correlated with the new information; To ensure the filtering effect, set the chi-square threshold F α , the measurement innovation statistic is λ, then the equivalent filter gain innovation is ρ new : In the formula, F α-all is the full-dimensional chi-square threshold, F α-pos is the location ring chi-square threshold.

5. The ROV soft chi-square-dual-loop position-velocity condition control method for sea state interference according to claim 1, characterized in that: The dual-loop MPC position-SMC speed control for disturbances uses the ROV position information obtained by underwater soft chi-square test adaptive Kalman filtering and the target position information read by the sensor to perform dual-loop control. The outer control loop is a target heading angle guidance control strategy based on MPC, and the inner control loop is a sliding mode control speed compensation caused by water flow interference. The ROV is controlled under interference according to the updated control speed.

6. The ROV soft chi-square-dual-loop position-velocity condition control method for sea state interference according to claim 5 is characterized in that: The MPC-based target heading angle guidance control strategy is used as a coarse adjustment of the dual-loop MPC position-SMC speed control, adopts a line of sight angle guidance strategy, applies the MPC model predictive control input FOV guidance controller, uses the ROV's own state information obtained by fusing the target information with the Kalman information as the known information amount to perform target three-dimensional posture guidance, and calculates the speed control amount of the guidance controller.

7. The ROV soft chi-square-dual-loop position-velocity condition control method for sea state interference according to claim 5 is characterized in that: The sliding mode control speed compensation caused by the water flow interference is adjusted by making a difference between the speed information read by the sensor and the speed control amount adjusted by the MPC position. A smooth sliding surface is designed and the sigmoid function and the boundary layer method are combined to eliminate the vibration. The obtained inner loop speed is superimposed with the FOV guided outer loop control to obtain the vehicle command control amount and act on the thrusters in turn.

8. The ROV soft chi-square-dual-loop position-velocity condition control method for sea state interference according to claim 5 is characterized in that: The dual-loop MPC position-SMC speed control comprises the following steps: Step 1: First, establish the mathematical model of the system, compare the read target point position and attitude with the vehicle's own attitude information obtained by Kalman filtering, and obtain the difference based on the line of sight guidance; Step 2: Based on the multi-step estimation of the Kalman filter, obtain the multi-step prediction of the target and the MPC prediction of the future state; set Q as the state weight matrix to penalize the state error, set R as the control input weight matrix to penalize the size of the control input, set x as the system state, u as the control input, the final state weight matrix used to penalize the prediction time domain terminal error is F, and the number of prediction time domain steps is N; design the cost function as: Step 3: According to the control amount of the interval, after obtaining the optimal input, take the current input as the first control input and output it as the desired speed; Step 4: Make SMC speed control corrections to the desired speed magnitude to adapt the system to underwater uncertainties and external disturbances.

9. The ROV soft chi-square-dual-loop position-velocity condition control method for sea state interference according to claim 8, characterized in that: Step 4 includes: Step 4-1: After determining the system model and control objectives, first define the error dynamic function, i.e., the sliding surface, so that the system state reaches a low-dimensional subspace and set the difference between the expected speed and the actual speed to e v , k e , τ is the control gain coefficient, and the sliding surface formula is: Step 4-2: Dynamically adjust the error through the adaptive control law to update the control gain and set k e0 ,τ0 is the basic control gain,γ e and γ τ is the adaptive control law parameter, and the adaptive control law is: Step 4-3: Use the hyperbolic tangent function tanh(s) to process the discontinuous part of the control, replacing the sign function of the traditional sliding mode control to reduce chattering: Step 4-4: Perform Lyapunov analysis to prove the stability of the system, and track the force required for the desired speed, apply it to the spacecraft, and obtain the final control law for the speed of each propeller of the spacecraft through thrust distribution.

10. An ROV soft card-square-dual-loop position-velocity condition control system for sea condition interference, characterized in that: When the system is running, the steps of the ROV soft chi-square-dual-loop position-velocity condition control method for sea condition interference described in any one of claims 1 to 9 are implemented.

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