Method for determining a control law for controlling at least one actuator

Abstract

The invention relates to a computer-implemented method for determining a control law (Lc) for controlling at least one actuator (20, 30) for a system, said method comprising the following steps: - providing (100) a physical model (M10) of the system; - providing (200) a trained model (M20, M30) of the dynamics of the at least one actuator (20, 30); - determining (300) a hybrid model (MH10) of the system by concatenating the physical model (M10) of the system and the model (M20, M30) of the dynamics of the at least one actuator (20, 30); - determining (400) the control law (Lc) from the hybrid model (MH10).

Description

[0001]Method for Determining a Control Law to Control at Least One Actuator. The present invention relates to the field of mechanics, and in particular to the automotive industry, and more specifically concerns a method for determining a control law to control at least one actuator for a system, for example, a vehicle. The invention aims to take into account the actual dynamics of each actuator in order to ensure, on the one hand, efficient control of the actuators and therefore of the vehicle in which they are implemented, and on the other hand, to guarantee the energy efficiency of the control system as a whole. In what follows, the invention will be described in its automotive application. However, and as will become clear from reading the description of the invention,The invention can also be applied in other technical fields where it is necessary to electronically control an actuator, as is the case, for example, in systems such as airplanes, trains, electric bicycles, motorcycles, lifting systems, and household appliances. Furthermore, the application of the invention is not limited to transportation systems. It can also be applied in the manufacturing sector, since there too, different actuators with varying dynamics must be electronically controlled to achieve a target or reference trajectory. An actuator is a component that acts on a system in such a way as to modify its state or behavior. In the automotive field, an actuator can be defined as a motor used by driver assistance software to assist the driver.The system is then the vehicle. Vehicles currently under development, and even more so future vehicles, are and will be increasingly equipped with actuators to control their mobility: front and rear steering actuators (4WD for four-wheel steering, or 4WS in English for four-wheel steering), braking actuators, various thermal and / or electric propulsion actuators, and in-wheel motor actuators (known by the abbreviation IWM for In-Wheel Motors) are cited as non-exhaustive examples. Each actuator has its own specific dynamics, which are a consequence of the technical solution implemented to perform its intended function. The dynamics of an actuator correspond to the time it takes to execute a command and its ability to reach the given setpoint. For example, for a wheel, the setpoint is the steering angle.and the dynamics consist of the time required to reach the target steering angle and the accuracy relative to the setpoint. In most of the various control laws used in automobiles, actuators are considered ideal for the sake of simplicity. Therefore, when designing a control system, it is assumed that this control will be applied instantaneously, without amplitude or phase distortion. This is not entirely accurate, but the loss of efficiency created by this simplifying assumption has not been considered significant until now. However, in the current context of the energy crisis, and even more so in the future,The vehicle control achieved through multiple actuators must be energy-efficient. This is all the more possible given the existence of control assignment techniques capable of guiding the selection of actuators used towards the most efficient ones in a vehicle (taking into account movement efficiency and energy requirements), particularly when the vehicle is equipped with more actuators than degrees of freedom to be controlled (over-actuated system). In existing control solutions, the control laws are designed without considering the actual dynamics of the actuators. These laws correct the vehicle's behavior to follow a given setpoint or trajectory by processing, through closed-loop control,the inaccuracies introduced by the dynamics of the actuators. It is therefore understandable that this correction is made at the expense of the overall electrical energy required to perform the mission. This correction, although effective, is all the more significant (and therefore energy-intensive) when the behavioral models used to design the controllers are developed without taking into account the dynamics of the actuators. The invention aims to overcome all or part of the problems mentioned above by proposing a control law design for actuators that takes into account the actual dynamics of each actuator contributing to vehicle control, right from the control law design phase. The invention thus optimally solves the vehicle control problem from an energy perspective by introducing, into the control models, the dynamic models of all the actuators onboard the vehicle. This results in personalized control,and therefore perfectly effective. To this end, the invention relates to a computer-implemented method for determining a control law to control at least one actuator for a system, said method comprising the following steps: - Providing a physical model of the system; - Providing a trained model of the dynamics of at least one actuator; - Determining a hybrid model of the system by concatenating the physical model of the system and the model of the dynamics of at least one actuator; - Determining the control law from the hybrid model. Thanks to these characteristics, the resulting control law is based on both the physical model of the system and the trained model(s) of the actuator dynamics. Taking into account the actual dynamics of the actuators avoids having to correct the inaccuracies that would be introduced by assuming perfect actuator operation. This results in a dual effect: on the one hand,Improved vehicle stability and performance are achieved, and energy efficiency in vehicle operation is increased since there is no longer a need to correct erroneous actuator inputs. This control law can be used by a controller in a closed loop to control the actuator based on an input setpoint. According to an optional feature of the invention,The method includes a step of determining a model of the actuator dynamics in which the trained model of the dynamics of at least one actuator is obtained by means of machine learning, which takes as input a set of actuator input data and a set of actuator output data associated with the input data. The machine learning allows real input and output data to be introduced into an initially chosen model and its parameters to be adjusted to best match the model's output data with the real actuator output data. According to an optional feature of the invention,The step of determining a model of the actuator dynamics comprises: - a first substep of choosing a model defined by initial parameters; - a second substep of feeding the model with a first input data point from the actuator to obtain a first output data point from the model; - a third substep of determining a difference between the first output data point from the model and the first output data point from the actuator associated with the first input data point from the actuator; - a fourth substep of adjusting the initial parameters and performing the second and third substeps until the difference is less than a first predefined value. By proceeding in this way, a model of the actuator dynamics is determined iteratively based on a set of real data. According to an optional feature of the invention,The actuator dynamics model determination step further includes a fifth substep for validating the actuator dynamics model. This substep is defined by performing the second substep with a second input, distinct from the first input, to obtain a second output for the model. The third substep is then performed with this second output. If the discrepancy exceeds a second predefined value, a sixth alert substep is triggered. If the discrepancy is less than this second predefined value, the actuator dynamics model is validated. This fifth substep allows for the consideration of a second set of input / output data to strengthen the actuator dynamics model. In the event of a significant discrepancy between the output data from the actuator dynamics model and the actual actuator output data,The parameters of the actuator dynamics model are adjusted. This is therefore a model validation substep to ensure the robustness of the method of the invention. The alert substep, which may be optional, draws a user's attention to the fact that the actuator dynamics model may have deficiencies. In one embodiment of the invention, the actuator dynamics model is a linear time-invariant model. In another embodiment of the invention, the actuator dynamics model is a linear model with varying parameters. In other embodiments of the invention, the control law is linear-quadratic-Gaussian or predictive. The invention also covers a vehicle comprising at least one actuator and computing means configured to implement the method described above.in which the system is the vehicle. The invention also relates to a computer program comprising instructions for executing such a method, when the program is executed by a processor. Finally, the invention also relates to a processor-readable recording medium on which is recorded a program comprising instructions for executing said method, when the program is executed by a processor. Other features and advantages of the invention will become apparent from the following description on the one hand, and from several illustrative and non-limiting examples of embodiments given by reference to the accompanying schematic drawings on the other hand, in which: - Figure 1 schematically represents the main steps of the method for determining a control law according to the invention,- Figure 2 schematically represents the substeps of the step for determining a model of the actuator dynamics according to the invention; - Figure 3 schematically represents the substeps of the step for determining a model of the actuator dynamics according to the invention, with an optional substep for validating the actuator dynamics model; - Figure 4 represents a control law that controls the yaw rate of a vehicle and the associated yaw moment, both with and without application of the method of the invention; - Figure 5 represents a control law that controls the yaw rate of a vehicle and the associated rear steering of the 4WS, both with and without application of the method of the invention. The features, variants, and different embodiments of the invention, as described or as they will be presented in the detailed description that follows,can be combined with each other in various ways, provided they are not incompatible or mutually exclusive. In particular, variants of the invention may be conceived comprising only a selection of features, described hereafter in isolation from the other described features, if this selection of features is sufficient to confer a technical advantage and / or to differentiate the invention from the prior art. For clarity, the same elements are designated by the same reference numerals in the different figures. As already mentioned, the invention is described in its automotive application for determining a control law to control an actuator for a vehicle.but is by no means limited to it and can be applied to an actuator for any type of system. Figure 1 schematically represents the main steps of the method for determining a control law according to the invention. The method for determining a control law Lc is implemented by computer. The control law Lc allows control of at least one actuator 20, 30 for a system, in particular a vehicle 10. The method of determination according to the invention includes a step 100 of providing a physical model M10 of the vehicle 10. The physical model M10 is a physical model of the vehicle, based on the laws of physics, such as those used in current solutions for controlling a vehicle. In what follows, the invention is illustrated by considering the actuators of the vehicle's lateral control, i.e., the wheel and differential braking actuators. Of course, the invention applies equally to any type of actuator,by adapting the models used. For example, for longitudinal control, the actuators involved are the engine or braking actuators. For vertical control, the actuators involved are the active or semi-active suspension actuators. Lateral or yaw control of the vehicle usually employs a linear dynamic model, commonly called the bicycle model of the vehicle. The bicycle model is the most widely used for trajectory generation and the development of control laws for vehicle control. This model results from Newton's first two laws, which allow us to derive the equations of vehicle dynamics.referenced below (6) and (9). The table below presents the physical parameters and signals characterizing this physical model. Symbol Description^^ Distance from center of gravity to front axle^^ Distance from center of gravity to rear axle^^ Front axle drift stiffness^^ Rear axle drift stiffness^ Road friction coefficient^^ Longitudinal speed^ Vehicle mass^^ Vehicle drift angle^^ Front axle drift angle^^ Rear axle drift angle^^ Yaw rate^^ Front wheel steering angle^^ Rear wheel steering angle (4WS)^^ Yaw moment^^ Transverse force on front axle^^ Transverse force on rear axle. According to Newton's first law: the sum of external forces is equal to mass multiplied by acceleration (equation (1)) and we obtain:, According to Newton's second law, the sum of the moments of the external forces is equivalent to the derivative of the angular momentum at the center of gravity of the vehicle (equation (7)). We then obtain: Starting from equations (6) and (9), we obtain the mathematical description of the bicycle model of the vehicle in the form of a referenced state representation (10): (abbreviation for Electric Power Steering), δ ^ rear-wheel steering, 4WS or 4 Wheels Steering, and M ! the overall yaw moment to be allocated to the braking actuators or to the IWM (In Wheel Motor) or to any other actuator capable of producing this yaw moment. is the output of the model. The determination method according to the invention includes a step 200 of providing a driven model M20, M30 of the dynamics of at least one actuator 20, 30. If the vehicle implements a single actuator 20, the method includes providing the driven model M20. If the vehicle implements a single actuator 30, the method includes providing the driven model M30. If the vehicle implements both actuators 20 and 30, the method includes providing the driven models M20 and M30. Of course, one can proceed similarly with a plurality of actuators, for example 10, 50, or 100.For each actuator 20 (respectively 30), the trained model of the actuator dynamics is obtained using machine learning. This model receives as input a set of input data E20 (respectively E30) for actuator 20 (respectively 30) and a set of output data S20 (respectively S30) for actuator 20 (respectively 30), associated with the input data E20 (respectively E30). For each actuator 20, 30, the input data E20, E30 and the output data S20, S30 are collected. Based on this data, a machine learning technique is used to generate a model of the dynamics of the actuators involved in vehicle control. The determination of the trained model (step 205) will be detailed below.Next, the method of the invention includes a step 300 of determining a hybrid model MH10 of the vehicle 10 by concatenating the physical model M10 of the vehicle 10 and the models M20, M30 of the dynamics of at least one actuator 20, 30. The hybrid model is a concatenation of the previously provided physical model of the vehicle and the actuator dynamics model obtained previously by machine learning. Finally, the method of the invention includes a step 400 of determining the control law Lc from the hybrid model MH10. Instead of using the physical model of the vehicle, as is done in the prior art, the method of the invention allows the control law to be designed based on the hybrid model, which includes the physical model of the vehicle and the actuator dynamics model. The determination of the control law Lc is performed in a conventional manner.A control law is easily determined based on knowledge of all the system states. Since the model is a function that understands the vehicle's dynamics, it calculates an output adapted to an actuator based on the inputs. For example, for a longitudinal speed actuator, the model links a speed setpoint to the torque to be applied by the motor. The control law can be, for example, linear-quadratic-Gaussian or predictive. It is thus understood that, thanks to the invention, the known vehicle control model based on the laws of physics (called the vehicle's physical model) remains unchanged. It is supplemented or augmented, for each actuator used by the vehicle, by a model of the actuator's dynamics. This results in the hybrid model. The method of the invention contributes to improved vehicle stability, thereby increasing the safety of the vehicle's occupants.Furthermore, the method of the invention reduces the energy required to control the vehicle. According to the invention, the method for determining the control law Lc is implemented on the vehicle. The step of determining a model of the actuator dynamics, however, is performed offline, prior to determining the control law and before operating the vehicle. Figure 2 schematically represents the substeps of the step of determining a model of the actuator dynamics according to the invention. As described previously, the trained model of the dynamics of at least one actuator is obtained by means of machine learning, which takes as input a set of input data E20, E30 from actuator 20, 30 and a set of output data S20, S30 from actuator 20, 30 associated with the input data E20, E30 (step 205).Step 205 is a dynamic model determination step that is implemented offline, prior to determining the control law Lc. This model is obtained using machine learning techniques based on the input and output data of each actuator. The model is obtained solely from data, hence the name Data Driven Model, as opposed to a physical model obtained through the laws of physics. Within the scope of the invention, the Data Driven Model approach is identical to the supervised machine learning approach or to System Identification. It consists of estimating the parameters of the actuator dynamics model from the input and output signals. Step 205, which determines a model M20, M30 of the actuator dynamics 20, 30, includes a first substep 210 of selecting a model Mi defined by initial parameters Pi.To limit the complexity of the calculations, a reduced-order model can be used, but the invention applies equally to higher-order models. For actuators, a reduced-order LTI (Linear Time Invariant) model is suitable, but other types of models can be used, for example, the LPV (Linear Variable Parameters) model. The inputs should preferably cover the entire amplitude of the actuator to obtain a model that is reliable over the entire operating range of the actuator. Step 205, for determining a model M20, M30 of the dynamics of actuator 20, M30, includes a second substep 220 of feeding the model Mi with a first input data E1 from the actuator to obtain a first output data SM1 from the model Mi.This second substep 220 is performed after each actuator has been activated in predefined configurations (with varying amplitudes and frequencies) to obtain corresponding input and output data sequences. This data is processed according to modeling assumptions: frequency filtering, bias elimination, data sequence weighting, etc. For example, for a wheel steering actuator, the input is the steering setpoint, and the output is the actuator's response (i.e., the actual steering angle applied). After obtaining the input / output data pairs, the model Mi is successively fed an input data E1 to produce an output data for the model SM1.Step 205 of determining a model M20, M30 of the actuator dynamics 20, 30 includes a third substep 230 of determining a difference 40 between the first output data SM1 of the model and the first output data S1 of the actuator associated with the first input data E1 of the actuator. In other words, the output data SM1 of the model is compared with the actual output data S1 of the actuator to determine a difference between the output signal measured on the actuator and the output signal of the model subjected to the same input signal. If the difference is greater than a predefined value, it is then necessary to adjust the characteristics of the model to minimize the difference.Step 205, for determining a model M20, M30 of the actuator dynamics 20, 30, includes a fourth substep 240 for adjusting the initial parameters Pi and performing the second and third substeps 220, 230 until the deviation 40 is less than a first predefined value 50. For convex optimization, the identified model parameters are those that minimize the L2 norm (least squares norm) of the deviation between the model and reality. This means that the model parameters Pi are modified, and then the substeps of feeding the model with the input data and determining the deviation between the model output data and the actual data are repeated until the resulting deviation is less than the predefined value 50. The learning part, i.e. step 205 of determining a model of the actuator dynamics, is done "offline", upstream of the use of the vehicle.It is performed once for the entire range of vehicles. Figure 3 schematically represents the substeps of the actuator dynamics model determination step according to the invention, with an optional actuator dynamics model validation substep. In addition to the steps presented previously, the actuator dynamics model determination step 205 further includes a fifth substep 250 for validating the actuator dynamics model, defined by performing the second substep 220 with a second input data E2, distinct from the first input data E1, to obtain a second output data SM2 of the model, and performing the third substep 230 with the second output data SM2, S2, and if the deviation 40 is greater than a second predefined value 51, a sixth alert substep 260.This substep allows for the identification and validation of the obtained model by verifying its predictive nature, that is, its ability to account for the actuator's output for input sequences different from those used for identification. This step is optional and ensures the model's quality. The hybrid model determination step will now be explained. As an example, an actuator dynamics model determined in step 205 might have an LTI-type structure. Such a model is first-order and allows for approximating actuator dynamics. Such a model for the 4WS (four-wheel steering) application might have the following structure: with $ %_'() , the actuator gain; * %_'(), its response time constant, and + the Laplacian. As an example, the actuator gain can take the value 1 and the time constant can take the value 0.05. Previously, the method for identifying actuator dynamics was illustrated with the example of the 4WS actuator. The hybrid model used for designing the control law is a concatenation of the vehicle's physical model and the dynamic model of the different actuators in the vehicle. Therefore, to construct this hybrid model, the physical model of the vehicle and the dynamic model of each actuator implemented in the vehicle are required. The vehicle's physical model was presented previously (see referenced equation (10)). Regarding the actuator dynamic model, based on the 4WS actuator example, the corresponding state representation is: ^ ,_'()is the actuator's excitation input (i.e., the setpoint), and the actuator's output ,_'() =^ ,_'() The Data Driven approach applied to braking actuators that perform the overall yaw moment gives the following state representation: ^ ,_-^,. / is the excitation input of the braking actuator, and the output of the actuator ,_-^,. / =^ ,_-^,. / The Data Driven approach applied to DAE yields the following state representation: ^ ,_012 is the excitation input of the DAE actuator, and the output of the actuator " ,_012 =^ ,_012 The hybrid model is obtained by concatenating ^ ^ ^^^^ ^, ",_'()=^,_'()," ,_-^,. / =^ ,_-^,. / And " ,_012 =^ ,_012 Denoting by h the index pertaining to the hybrid model, the new state variable is: We obtain the state representation of the hybrid model: The control law design is based on the hybrid model. Although the power steering (PSE), four-wheel drive (4WS), and braking systems are used in the hybrid model, the method for obtaining this hybrid model will apply analogously to other actuators. Figure 4 shows a control law that controls the yaw rate of a vehicle (top graph) and the associated yaw moment, both with and without application of the method of the invention (bottom graph). Figure 5 shows a control law that controls the yaw rate of a vehicle (top graph) and the rear steering of the associated 4WS, both with and without application of the method of the invention (bottom graph).Figures 4 and 5 illustrate three configurations: - Yaw rate obtained without a control law (No Controller, denoted NC) - Yaw rate obtained with a control law designed on the physical model (Controller based on Vehicle model, denoted CB − MV) - Yaw rate obtained with a control law designed on the hybrid model (Controller based on Vehicle Hybrid model, denoted CB − MHV) The application illustrated in Figures 4 and 5 corresponds to an overtaking maneuver, with an initial lane change to pass, followed by a second lane change to return to the original lane. The "reference" control law represents the control law resulting in the ideal trajectory. The NC ("no controller") control law is quite far from the reference trajectory because driver errors are not compensated for by the trajectory aids.The CB-MV (controller based on vehicle model) control law, based on the physical model alone, offers an improvement over driver-only control, but it exhibits peaks relative to the reference. These peaks are overshoots of the setpoint, linked, for example, to actuator amplitude errors. For instance, if the desired setpoint is a 3.5° front wheel steering angle, and the actuator only applies 3°, the setpoint compensates by increasing the requested steering angle, resulting in increased energy consumption. The CB-MHV control law, designed for the hybrid model, offers better performance than the control law designed for the physical model in terms of stability and control of the setpoint or reference. Indeed, the CB-MHV control law, designed for the hybrid model, eliminates the peaks introduced by the physical model's failure to account for actuator dynamics.Furthermore, the control required for this performance is reduced by approximately 20% in the CB-MHV control law using the hybrid model developed within the framework of this invention, which gives it the characteristic of energy efficiency. The lower graph of Figures 4 and 5 illustrates this reduction with a low yaw moment (^. ^ ) and a low steering angle of the 4WS (^ ^) for the control law designed based on the vehicle's hybrid model. In Figures 4 and 5, the yaw moment and 4WS rear steering are used independently. For improved performance with the control law using the hybrid model (upper graph of Figure 4), the control energy (yaw moment) is reduced by approximately 20% for the control law using the hybrid model (lower graph of Figure 4). For improved performance with the control law using the hybrid model (upper graph of Figure 5), the control energy (the 4WS rear steering setpoint) is also reduced by approximately 20% for the control law using the hybrid model (lower graph of Figure 5). Thanks to the method of the invention, more stable vehicle behavior is obtained, ensuring increased passenger safety.This stability is of particularly crucial importance in emergency obstacle avoidance situations where the vehicle (i.e., the vehicle and all the actuators involved in the avoidance maneuver) must be perfectly controlled. The method of the invention also ensures, through the use of the hybrid model for determining the control law, lower energy consumption for the control system, resulting in increased battery range. The invention also relates to a vehicle comprising at least one actuator and computing means configured to implement the method for determining a control law Lc to control at least one actuator 20, 30 for the vehicle. The invention also covers a computer program comprising instructions for executing the method according to the invention as described above, when the program is executed by a processor.The invention also relates to a processor-readable storage medium on which is stored a program containing instructions for executing the method for determining a control law Lc to control at least one actuator for a system, when the program is executed by a processor. Although not limited to such applications, embodiments of the invention are particularly advantageous for implementation in a vehicle, and especially an autonomous vehicle. A person skilled in the art understands that the system or subsystems according to embodiments of the invention can be implemented in various ways in the form of hardware, software, or a combination of hardware and software, particularly in the form of program code that can be distributed as a program product in various forms.In particular, program code can be distributed using computer-readable media, which may include computer-readable storage media and communication media. The processes or methods described herein can, in particular, be implemented in the form of computer program instructions that can be executed by one or more processors in a computer processing device. These computer program instructions can also be stored on computer-readable media. Of course, the invention is not limited to the examples just described, and numerous modifications can be made to these examples without departing from the scope of the invention. In particular, the features of different embodiments of the invention can be combined to carry out the invention, provided that these embodiments are not mutually incompatible.

Claims

CLAIMS 1- A computer-implemented method for determining a control law (Lc) to control at least one actuator (20, 30) for a system (10), said method comprising the following steps: - Provision (100) of a physical model (M10) of the system (10); - Provision (200) of a driven model (M20, M30) of the dynamics of at least one actuator (20, 30); - Determination (300) of a hybrid model (MH10) of the system (10) by concatenation of the physical model (M10) of the system (10) and the model (M20, M30) of the dynamics of at least one actuator (20, 30); - Determination (400) of the control law (Lc) from the hybrid model (MH10).2- Method according to claim 1, comprising a step (205) of determining a model of the dynamics of the actuator (20,30) in which the trained model of the dynamics of at least one actuator is obtained by means of machine learning receiving as input a set of input data (E20, E30) of the actuator (20, 30) and a set of output data (S20, S30) of the actuator (20, 30) associated with the input data (E20, E30) (step 205).3- Method according to claim 2, wherein the step (205) of determining a model (M20, M30) of the dynamics of the actuator (20, 30) comprises: - a first substep (210) of choosing a model (Mi) defined by initial parameters (Pi); - a second substep (220) of supplying the model (Mi) with a first input data (E1) of the actuator to obtain a first output data (SM1) of the model (Mi); - a third substep (230) of determining a gap (40) between the first output data (SM1) of the model and the first output data (S1) of the actuator associated with the first input data (E1) of the actuator;. - a fourth substep (240) of adjusting the initial parameters (Pi) and carrying out the second and third substeps (220, 230) until the deviation (40) is less than a first predefined value (50). 4- Method according to claim 3, wherein the step (205) of determining a model of the actuator dynamics further comprises a fifth substep (250) of validating the model of the actuator dynamics defined by carrying out the second substep (220) with a second input data (E2), distinct from the first input data (E1), to obtain a second output data (SM2) of the model and carrying out the third substep (230) with the second output data (SM2, S2), and if the deviation (40) is greater than a second predefined value (51), a sixth substep (260) of alerting.

5. A method according to any one of claims 2 to 4, wherein the actuator dynamics model is a time-invariant linear model.

6. A method according to any one of claims 2 to 4, wherein the actuator dynamics model is a linear model with varying parameters.

7. A method according to any one of claims 1 to 6, wherein the control law is linear-quadratic-Gaussian or predictive.

8. A vehicle comprising at least one actuator and computing means configured to implement the method according to claim 1, wherein the system (10) is the vehicle.

9. A computer program comprising instructions for executing the method according to any one of claims 1 to 7, when the program is executed by a processor.10- Processor-readable recording medium on which is recorded a program containing instructions for executing the method according to any one of claims 1 to 7, when the program is executed by a processor.

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