Vehicle lateral control method, electronic system, medium and program product

Abstract

The invention discloses a vehicle transverse control method, an electronic system, a readable storage medium and a computer program product. The control precision of vehicle transverse control can be improved. The vehicle transverse control method comprises the steps that a kinematic model of a vehicle is established, the kinematic model comprises state variables and control variables, the state variables comprise the transverse distance, the yaw angle and the actual front wheel rotation angle, and the control variables comprise the front wheel rotation angle; forming a prediction equation set based on the kinematic model, wherein the prediction equation set comprises a state quantity measurement value at the current moment, state quantity prediction of a prediction time domain and control quantity prediction of a control time domain; establishing a target function based on the prediction equation set, and introducing a constraint condition; and at least outputting an instruction value of the front wheel steering angle according to the objective function and the constraint condition.

Description

Technical Field

[0001] The present application relates to the field of unmanned driving of vehicles, and in particular to a vehicle lateral control method, an electronic system, a readable storage medium, and a computer program product. Background Art

[0002] It is known that there are currently two methods for the design of vehicle lateral control. The first design method is completely based on the upper-level action planning control of the control layer, and PID is usually used for feedback control. The advantage of the first design method is that it does not require precise knowledge of vehicle kinematics / dynamics, but only requires a vehicle model that expresses the response characteristics and a controller based on error feedback. The second design method is a control method based on the vehicle kinematics / dynamics model. As the second design method, it is necessary to build a vehicle kinematics / dynamics model, and then use different control algorithms according to needs to achieve specific goals.

[0003] The PID controller (i.e., proportional-integral-differential controller) used in the first design method is mainly composed of a proportional unit P, an integral unit I, and a differential unit D. The basis of PID control is proportional control. The integral control in PID control can eliminate steady-state errors, but there is a possibility of increasing overshoot. The differential control in PID control can speed up the response speed of large inertia systems and reduce the overshoot trend. However, PID control is difficult to be effectively applied to multivariable systems and time-varying systems. The vehicle's driving system is precisely a multivariable system and a time-varying system at the same time. In addition, the characteristics of PID control determine that it does not take into account the geometric characteristics of the road at all, and can only be applied to low-speed and small-radius curves, and is prone to oscillation. In particular, when PID control is used, the steering wheel is prone to shaking in the latter part of the curve. In addition, when driving at high speed or in a large-radius curve, there will be a large deviation, resulting in a sharp turn. As a result, the comfort is poor.

[0004] The second design method usually requires the establishment of a more accurate lateral kinematic / dynamic model of the vehicle. As a typical model, the bicycle model (also known as the single-track model) is widely used. In the bicycle model, it is usually assumed that the left and right sides of the vehicle have the same characteristics, and its control target is generally the offset between the center of the vehicle and the center of the road. At the same time, its control is also constrained by indicators such as comfort. Control based on such a vehicle kinematic / dynamic model has higher control accuracy and faster control speed, but it is more dependent on the accuracy of system modeling and is sensitive to the time-varying response characteristics of the system. In other words, if the model is not constructed accurately or the system delay is too high, it will have a greater impact on the entire control process.

[0005] On the other hand, as a typical control framework, Model Predictive Control (MPC) performs lateral control of the vehicle based on the vehicle kinematic / dynamic model. However, in conventional MPC methods, the state equation of lateral control usually only includes the lateral distance (or lateral error) and the yaw angle (also known as the heading angle, or yaw error). As a result, such kinematic / dynamic models cannot reflect the actual state of the system well, and there are problems of poor robustness and large delay. As a result, the control accuracy based on such kinematic / dynamic models is not ideal. Summary of the invention

[0006] Technical problem to be solved by the invention

[0007] This application is formed to solve the above technical problems, and its purpose is to provide a vehicle lateral control method, which can improve the control accuracy of the vehicle lateral control by constructing a kinematic model that can better reflect the actual state of the system. On this basis, this application further provides an electronic system, a readable storage medium and a computer program product corresponding to the above control method.

[0008] Technical solutions adopted to solve technical problems

[0009] The present application provides a vehicle lateral control method, comprising:

[0010] Establishing a kinematic model of the vehicle, the kinematic model including state quantities and control quantities, the state quantities including lateral distance, yaw angle and actual front wheel turning angle, the control quantities including front wheel turning angle;

[0011] Performing linearization and discretization processing on the kinematic model;

[0012] Forming a prediction equation group based on the kinematic model after linearization and discretization, the prediction equation group includes a state quantity measurement value at the current moment, a state quantity prediction in a prediction time domain, and a control quantity prediction in a control time domain;

[0013] Establishing an objective function based on the prediction equations and introducing constraints; and

[0014] At least the command value of the front wheel turning angle is output according to the objective function and the constraint condition.

[0015] According to the vehicle lateral control method described in the technical solution, compared with the existing model predictive control method that only uses the lateral distance (or lateral distance error) and the yaw angle (or yaw angle error) as the state quantity of lateral control, the actual front wheel turning angle is further added to the state quantity of lateral control, and the front wheel turning angle is set as the control quantity. More specifically, in the existing model predictive control method, the kinematic model for lateral control only includes two state equations with the lateral distance (or lateral distance error) and the yaw angle (or yaw angle error) as the state quantity and the front wheel turning angle as the control quantity. Such a kinematic model cannot well reflect the actual state of the system, and its robustness is poor and the delay is large. Different from this, by adding the actual front wheel turning angle to the state quantity of lateral control, a first-order inertia (ordinary differential) equation with the actual front wheel turning angle as the state quantity and the front wheel turning angle as the control quantity is added to the original state equation, thereby constructing a kinematic model that can more accurately reflect the actual state of the system. Therefore, by establishing a group of prediction equations based on the kinematic model, constructing an objective function and introducing constraints, an optimal control sequence can be obtained. By outputting the first value of the optimal control sequence as the command value of the front wheel steering angle, the lateral control accuracy of the vehicle can be improved.

[0016] Preferably, before forming the prediction equation group, the kinematic model is linearized and discretized.

[0017] According to the vehicle lateral control method described in the technical solution, by linearizing and discretizing the nonlinear state equation group, a linear equation group that can be used for numerical calculation can be formed.

[0018] Preferably, the constraint condition includes at least any one of a maximum front wheel turning angle and a maximum front wheel turning angle change rate.

[0019] According to the vehicle lateral control method described in the technical solution, it is possible to avoid large errors in the control at a curve with a large curvature change rate. Specifically, the applicant has found that if the maximum value of the front wheel angle (i.e., the chassis angle) is not limited and / or the maximum value of the front wheel angle change rate is not limited, then when the vehicle travels to a curve with a large curvature change rate, the direction change rate of the chassis cannot keep up with the change rate of the command issued, so the control will produce a large error at the curve. For this reason, in the technical solution, by limiting the maximum value of the front wheel angle and / or the maximum value of the front wheel angle change rate as a constraint condition, the above situation can be avoided.

[0020] Preferably, when the prediction time domain is set to n steps and the control time domain is set to m steps,

[0021] The predicted output of the state quantity prediction of the last nm steps in the prediction time domain is determined according to the control quantity prediction of the mth step in the control time domain, wherein m and n are natural numbers and satisfy n>m.

[0022] According to the vehicle lateral control method described in the technical solution, it is possible to greatly save computing costs and computing resources. Specifically, in model predictive control, after predicting the next n steps, only the current first step will be taken as the starting point for the next cycle calculation, and the remaining steps will be destroyed, and the system will approach the reference value in a very short time, and the following time will only be used for small-scale optimization. Therefore, it is obvious that a lot of resources are consumed to perform calculation optimization for the next n steps. To this end, the control time domain and the prediction time domain are separated, and the m steps in the control time domain are calculated so that the system can quickly reach the control target. Each step in the prediction time domain repeats the last step in the control time domain to predict the future nm steps. In this way, the waste of computing resources caused by unnecessary calculations can be avoided.

[0023] Preferably, an integral control compensation is performed on the command value of the front wheel steering angle to eliminate a lateral error, wherein the lateral error is a difference between a predicted value of the lateral distance and a measured value of the lateral distance.

[0024] The vehicle lateral control method according to the technical solution can eliminate the lateral distance error during vehicle driving and avoid zero deviation of the steering wheel.

[0025] Preferably, proportional control compensation and / or differential control compensation are performed on the command value of the front wheel steering angle to eliminate the yaw angle error and / or the actual steering angle error of the front wheels.

[0026] According to the vehicle lateral control method described in the technical solution, the yaw angle and / or the actual steering angle error of the front wheels during vehicle driving can be eliminated, thereby speeding up the response of the chassis.

[0027] Preferably, the command value of the front wheel steering angle is subjected to gain scheduling control, and the gain scheduling control includes: correcting the deviation between the predicted value of the state quantity and the measured value of the state quantity to form a corrective control input; and modifying the command value of the front wheel steering angle based on the corrective control input.

[0028] The vehicle lateral control method according to the technical solution can improve the robustness of the system.

[0029] Effects of the Invention

[0030] Compared with the existing vehicle lateral control methods, the vehicle lateral control method described in the present application can increase the robustness of the system and speed up the response of the system, thereby improving the control accuracy of the vehicle lateral control. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 1 is a flowchart showing a vehicle lateral control method according to an embodiment of the present application.

[0032] Figure 2 Schematic diagram of a vehicle kinematic model used in a vehicle lateral control method according to an embodiment of the present application.

[0033] Figure 3 1 is a flowchart showing a first modified example of the vehicle lateral control method according to an embodiment of the present application.

[0034] Figure 4 1 is a flowchart showing a second modified example of the vehicle lateral control method according to the embodiment of the present application.

[0035] Figure 5 This is a flowchart showing a third modified example of the vehicle lateral control method according to the embodiment of the present application.

[0036] Figure 6 This is a framework diagram showing an example of gain scheduling control adopted in a vehicle lateral control method according to an embodiment and a modified example thereof of the present application.

[0037] Figure 7 This is a framework diagram showing another example of gain scheduling control adopted in the vehicle lateral control method according to one embodiment of the present application and its modified example. DETAILED DESCRIPTION

[0038] Below, refer to Figure 1 , the implementation steps of the vehicle lateral control method of one embodiment of the present application are described. It should be noted that the steps shown in the following embodiment are only an example, and as long as the same technical purpose or further technical purpose can be achieved, the order of these steps can be appropriately changed, and additional steps can be added.

[0039] Figure 1 A flow chart of a vehicle lateral control method according to an embodiment of the present application is shown.

[0040] Before describing the specific steps, the assumptions of the vehicle kinematic model used in this embodiment are first described. In this embodiment, for ease of understanding and technical description, a bicycle model (also known as a single-track model) is used for the lateral movement of the vehicle. Figure 2 Figure 2 shows a schematic diagram of a bicycle model. Figure 2 As shown, the bicycle model is a two-degree-of-freedom vehicle model, (X rear ,Y rear )(can be abbreviated as (x,y)) represents the coordinates of the rear axle center of the vehicle, (X front ,Yfront ) represents the coordinates of the center of the front axle of the vehicle, represents the yaw angle of the vehicle (also called heading angle), δ f represents the front wheel turning angle of the vehicle, v represents the rear axle speed of the vehicle, and l represents the (front and rear) wheelbase of the vehicle. In the inertial coordinate system OXY, the kinematic equation of the vehicle can be expressed by the following mathematical formula:

[0041]

[0042] in, It represents the longitudinal speed at the center of the rear axle of the vehicle (referred to as the longitudinal speed of the vehicle). Indicates the lateral velocity of the center of the rear axle of the vehicle (referred to as the lateral velocity of the vehicle), represents the vehicle's yaw rate, δ f represents the front wheel turning angle of the vehicle, l represents the (front and rear) wheelbase of the vehicle, and v represents the driving speed of the vehicle.

[0043] First, in step ST1, the system modeling is performed, specifically, the state space is established. In this embodiment, the state space is composed of the kinematic equations of the vehicle and the first-order inertial system equations. It should be noted that in this embodiment, since its purpose is to perform lateral control of the vehicle, the kinematic equations related to the longitudinal direction are not considered, that is, the longitudinal distance (or longitudinal distance error) is not set as the state quantity. In addition, since the response of the vehicle chassis to the command conforms to the characteristics of the first-order inertial system, the first-order inertial system equation is also included in the state space. Therefore, in this embodiment, the state quantities in the state space include the lateral distance (which can also be considered as the lateral distance error), the yaw angle (which can also be considered as the yaw angle error) and the actual turning angle of the front wheel. In addition, in this system, the control variable is the front wheel turning angle. On the basis of establishing the above-mentioned state space, on the basis of including the kinematic equations related to the lateral direction and the kinematic equations related to the yaw, the first-order inertial system equations related to the front wheel turning angle and the command are added. Therefore, in this embodiment, the state equation group of the kinematic model of the vehicle can be expressed by the following mathematical formula:

[0044]

[0045] Where y represents the lateral position of the vehicle, represents the lateral velocity of the vehicle, represents the yaw rate of the vehicle, v represents the speed of the vehicle, δ f represents the front wheel turning angle of the vehicle, l represents the (front and rear) wheelbase of the vehicle, δ real It represents the actual turning angle of the front wheels of the vehicle, and d and k are both constants.

[0046] According to the above kinematic model, the autonomous driving vehicle system can be regarded as a control quantity u = δ f and the state quantity is The general form of the control system is:

[0047]

[0048] In addition, for a given reference trajectory, it can be described by the motion trajectory of the reference vehicle. Each point on the ride satisfies at least the first two equations in the above kinematic model. The subscript ref represents the reference quantity, and its general form is:

[0049]

[0050] Thus, the kinematic model of the vehicle is constructed, and the operation of step ST1 is completed. Then, the process proceeds to step ST2.

[0051] In step ST2, considering that the vehicle kinematics model is a nonlinear system, it is linearized. First, only the first two kinematics equations of the state equations are linearized. Specifically, assuming that the vector value function X is at the reference point If there is a second-order continuous partial derivative near the reference point, a first-order Taylor expansion can be performed at the reference point and high-order terms can be ignored to obtain the following mathematical formula:

[0052]

[0053] in,

[0054]

[0055] Therefore, mathematical formula (5) can be further expressed as:

[0056]

[0057] Next, Set as XX ref Let ΔX, and let uu ref Assuming Δu, mathematical formula (8) can be further expressed as:

[0058]

[0059] in:

[0060]

[0061] After completing the linearization processing of the above two kinematic equations, enter step ST3.

[0062] In step ST3, the linear equations formed by the two kinematic equations after the linearization process are discretized. For example, in this embodiment, the forward Euler method is used for discretization. Specifically, the sampling time is set to T, then It can be discretized into the following form:

[0063]

[0064] Here, ΔX(k) represents the error of the state quantity at time k, and ΔX(k+1) represents the error of the state quantity at time k+1.

[0065] At the same time, the third equation in the above state equation, namely the first-order inertial system equation, is discretized using the forward Euler method to obtain the following mathematical formula:

[0066] δ real (k+1)=(1-Td)·δ real (k)+Tk·δ f (k) (13)

[0067] By combining the above two discretized kinematic equations with the discretized first-order inertial system equation, the following discretized equation group can be obtained:

[0068]

[0069] in:

[0070]

[0071] In addition, for the convenience of the following description, W and u ref (k) Combined form, It is expressed by the following mathematical formula:

[0072]

[0073] After the discretization process of the state equation is completed, enter step ST4.

[0074] In step ST4, a prediction equation group is formed based on the above discretized state equation, that is, mathematical formula (14). The prediction equation group can be expressed by the following mathematical formula:

[0075]

[0076] in, represents the measured value of the state quantity at the current k moment, represents the prediction of the i-th state quantity at time k, u(k+i|k) represents the prediction of the i-th control quantity at time k, Np Indicates the number of steps in the prediction time domain, N c Indicates the number of steps in the control time domain.

[0077] Considering that the expression of the above mathematical formula (20) is relatively complicated, here, for the sake of ease of understanding, the above mathematical formula (20) is simplified as follows:

[0078]

[0079] After completing the construction of the prediction equation group, proceed to step ST5.

[0080] In step ST5, an objective function (also called a cost function) is established based on the prediction equations constructed in step ST4. Specifically, the objective function is represented by the following mathematical formula:

[0081]

[0082] Among them, Q represents the weight matrix corresponding to the state quantity, and R represents the weight matrix corresponding to the control quantity.

[0083] The first term on the right side of the equal sign in the above mathematical formula (22) reflects the system's ability to follow the reference trajectory, and the second term on the right side reflects the constraint on the change of the control quantity. Further, the above mathematical formula (22) can be expressed as:

[0084]

[0085] Among them, N p Represents the prediction time domain, set to n steps, N c Represents the control time domain, which is set to m steps. Preferably, n>m. On this basis, the constraint condition is introduced. In vehicle control, there are a variety of constraint conditions (including equality constraint conditions and inequality constraint conditions), which can be selected according to actual needs. In this embodiment, in order to better perform lateral control of the vehicle, the following four constraint conditions are introduced:

[0086]

[0087] u(k+i|k)≤u max (25)

[0088]

[0089] Among them, mathematical formula (24) is the discretized state equation, mathematical formula (25) shows that the control input value of the front wheel angle shall not be greater than the maximum input value of the angle, mathematical formula (26) shows that the control input value of the front wheel angular velocity shall not be greater than the maximum input value of the angular velocity, and mathematical formula (27) represents the initial condition of the control quantity. It should be noted that the constraints related to the control input value of the front wheel angle and the constraints related to the control input value of the front wheel angular velocity can be adopted at the same time, or any one of them can be adopted. In addition, other constraints can be added on the basis of the above constraints.

[0090] After the establishment of the objective function and the introduction of the constraint conditions are completed, step ST5 ends and the process proceeds to step ST6.

[0091] In step ST6, based on the above-mentioned objective function and the multiple constraints introduced, the optimal control sequence of the control variable, i.e., the front wheel steering angle, is solved, for example, through various quadratic programming algorithms (for example, the operator splitting quadratic programming algorithm, i.e., OSQP algorithm), and the first value of the optimal control sequence, i.e., u(k|k), is used as the instruction value (also called the control input value) output.

[0092] On the other hand, after the optimal control sequence of the front wheel steering angle is obtained through step ST6, the predicted value of the state quantity in the prediction time domain can be obtained according to the above mathematical formula (14). In particular, in the case of n>m, the predicted value of the state quantity of the last nm steps in the prediction time domain can be determined based on the predicted value of the control quantity of the last step in the optimal control sequence, that is, the mth step.

[0093] According to the vehicle lateral control method described in this embodiment, when the vehicle is lateral controlled, compared with the conventional MPC method that only considers the lateral distance (or lateral error) and the yaw angle (or yaw angle error) as the state quantity, the actual front wheel turning angle is further selected as the state quantity, and the first-order inertia system equation containing the actual front wheel turning angle as the state quantity and the front wheel turning angle as the control quantity is added to the conventional state equation, thereby constructing a new state equation. In this way, compared with the conventional MPC method, the newly constructed state equation can more accurately reflect the actual driving state of the vehicle. On this basis, by linearizing and discretizing the newly constructed state equation and establishing the corresponding prediction equation group based on it, and further constructing the objective function and introducing the constraint conditions, the optimal control sequence that is more in line with the actual driving situation can be calculated, so that the vehicle can be laterally controlled based on the optimal control sequence. As a result, compared with the prior art, the control accuracy of the vehicle lateral control is improved.

[0094] Next, refer to Figure 3 to Figure 6, the first to third modified examples of the vehicle lateral control method of the above embodiment are described. For ease of understanding and to avoid repeated description, only the differences between the first to third modified examples and the above embodiment are described below.

[0095] Figure 3 FIG. 4 is a flow chart showing a first variation of the vehicle lateral control method of the above embodiment. Figure 3 As shown, compared with the above-mentioned embodiment, the first variant also includes step ST7A. In step ST7A, the control quantity solved in step ST6, i.e., the command value of the front wheel steering angle, is integrally controlled. During the actual driving of the vehicle, when the system has no external input, due to the imperfect characteristics of the internal components, there is a deviation between the system output and the expected value, which is called the zero bias of the steering wheel. In vehicle control, the zero bias of the steering wheel may cause the vehicle to deviate from the predetermined trajectory. In order to avoid this situation, it is necessary to compensate the command value solved in step ST6. Specifically, it is assumed that the command value of the front wheel steering angle is set to Uo. At this time, the PID controller uses the command value Uo as the set point. In this case, the integral link KI of the PID controller compensates for the difference between the actual output of the system (i.e., the actual steering angle of the front wheel) and the set point to eliminate the lateral error caused by the zero bias of the steering wheel.

[0096] Figure 4 FIG. 4 is a flow chart showing a second variation of the vehicle lateral control method of the above embodiment. Figure 4 As shown, compared with the above embodiment and the first variation, the second variation includes step ST7B. Specifically, considering that external variables such as side slip and delay may cause the chassis to fail to respond well to the above command. Therefore, in step ST7B, the command value of the front wheel steering angle is compensated by using the proportional link KP and / or the differential link KD. In this way, the error caused by the poor response of the chassis to the command due to the above factors can be avoided.

[0097] Figure 5 FIG. 4 is a flow chart showing a third variation of the vehicle lateral control method of the above embodiment. Figure 5 As shown, compared with the above-mentioned embodiment and the first and second variants, the third variant includes step ST8. In step ST8, gain scheduling control is performed on the command value of the front wheel steering angle solved in step ST6 so that the actual driving trajectory of the vehicle follows the ideal output trajectory. It should be noted that the ideal output trajectory can be obtained by a model predictive control method similar to the above, and the description is omitted here. Figure 6The framework diagram of gain scheduling control is shown. Here, the command value of the front wheel steering angle (at time k) and the predicted value of the state quantity (at time k+1) obtained by the above steps ST1 to ST6 are set as Ud and xd respectively. At this time, the measured value of the state quantity of the system is obtained and filtered to form the actual value x. Considering that the model predictive control itself linearizes and discretizes the actual system, there is a deviation between the predicted value xd and the actual value x. In order to eliminate this deviation, the deviation between xd and x (set as e) is input to the LQR controller, and the deviation e is multiplied by the gain parameter K to form a corrective control input V. Then, the command value Ud of the front wheel steering angle is added to the corrective control input V to form a new command value U. In this way, by using LQR to design a gain coefficient at each working point, the actual system can reach the target state faster, so that the robustness of the system is improved.

[0098] It should be noted that, although the first modification example, the second modification example and the third modification example are described in separate forms, these modifications can be combined in any manner. Figure 7 A framework diagram of gain scheduling control including the above-mentioned step ST7A and / or step ST7B and step ST8 is shown.

[0099] It should be understood that the present invention is not limited to the exact construction that has been described above and shown in the drawings and that various modifications and changes may be made without departing from the scope thereof. The scope of the present invention is limited only by the appended claims.

Claims

1. A vehicle lateral control method, It is characterized in that include: Establishing a kinematic model of the vehicle, the kinematic model including state quantities and control quantities, the state quantities including lateral distance, yaw angle and actual front wheel turning angle, the control quantities including front wheel turning angle; Forming a prediction equation group based on the kinematic model, the prediction equation group includes a state quantity measurement value at the current moment, a state quantity prediction in a prediction time domain, and a control quantity prediction in a control time domain; Establishing an objective function based on the prediction equations and introducing constraints; as well as At least the command value of the front wheel turning angle is output according to the objective function and the constraint condition.

2. The vehicle lateral control method according to claim 1, It is characterized in that Before forming the prediction equation group, the kinematic model is linearized and discretized.

3. The vehicle lateral control method according to claim 1, It is characterized in that The constraint condition includes at least any one of a maximum front wheel turning angle and a maximum front wheel turning angle change rate.

4. The vehicle lateral control method according to claim 1, It is characterized in that When the prediction time domain is set to n steps and the control time domain is set to m steps, The predicted output of the state quantity prediction of the last nm steps in the prediction time domain is determined according to the control quantity prediction of the mth step in the control time domain, wherein m and n are natural numbers and satisfy n>m.

5. The vehicle lateral control method according to claim 1, It is characterized in that Integral control compensation is performed on the command value of the front wheel steering angle to eliminate a lateral error, which is a difference between a predicted value of the lateral distance and a measured value of the lateral distance.

6. The vehicle lateral control method according to claim 1, It is characterized in that Proportional control compensation and / or differential control compensation are performed on the command value of the front wheel steering angle to eliminate the yaw angle error and / or the actual steering angle error of the front wheel.

7. The vehicle lateral control method according to claim 1, It is characterized in that Performing gain scheduling control on the command value of the front wheel steering angle, the gain scheduling control comprising: Correcting the deviation between the predicted value of the state quantity and the measured value of the state quantity to form a corrective control input; and The command value of the front wheel steering angle is corrected based on the correction control input.

8. An electronic system comprising a memory, a processor, and a computer program stored in the memory, It is characterized in that The processor executes the computer program to implement the method of any one of claims 1 to 7.

9. A computer-readable storage medium storing a computer program. It is characterized in that When the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

10. A computer program product, the computer program product comprising a computer program, It is characterized in that When the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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