Propellant filling amount determination method and device, electronic equipment and storage medium

Abstract

The embodiment of the invention relates to the technical field of spacecraft chemical propulsion, in particular to a propellant filling amount determining method and device, electronic equipment and a storage medium. A propellant filling quantity determination method is applied to a satellite and comprises the steps that the total propellant demand quantity is determined based on the on-orbit rated consumption quantity and divergence error of a propellant; wherein the propellant comprises an oxidizing agent and a combustion agent; determining the average pressure of the oxidant storage tank and the average pressure of the incendiary agent storage tank based on the total quantity demand of the propellant, the filling pressure of the gas cylinder, the filling pressure of the oxidant storage tank and the filling pressure of the incendiary agent storage tank; determining a filling mixing ratio based on the average pressure of the oxidant storage tank and the average pressure of the combustion agent storage tank; and determining the filling amount of the oxidant and the filling amount of the combustion agent based on the total quantity demand of the propellant and the filling mixing ratio. The embodiment of the invention provides a propellant filling amount determination method and device, electronic equipment and a storage medium. The propellant filling amount can be accurately calculated.

Description

Technical Field

[0001] This invention relates to the field of spacecraft chemical propulsion technology, and in particular to a method, apparatus, electronic device, and storage medium for determining the amount of propellant to be added. Background Technology

[0002] Currently, all high-orbit satellites employ a dual-propellant unified propulsion system. In this system, the satellite's propulsion power comes from the propellant, and the amount of propellant added affects the satellite's final lifespan. Therefore, the amount of propellant added is crucial.

[0003] Therefore, in order to address the above problems, there is an urgent need for a method to determine the propellant loading amount, which can accurately calculate the propellant loading amount. Summary of the Invention

[0004] This invention provides a method, apparatus, electronic device, and storage medium for determining the propellant loading amount, which can accurately calculate the propellant loading amount.

[0005] In a first aspect, embodiments of the present invention provide a method for determining the propellant loading amount, applied to a satellite, the method comprising:

[0006] The total propellant requirement is determined based on the on-orbit rated consumption and divergence error of the propellant; wherein the propellant includes oxidizer and fuel.

[0007] Based on the total propellant demand, cylinder filling pressure, oxidizer tank filling pressure, and propellant tank filling pressure, determine the average pressure of the oxidizer tank and the average pressure of the propellant tank.

[0008] The mixing ratio is determined based on the average pressure of the oxidizer tank and the average pressure of the propellant tank;

[0009] The amount of oxidizer and the amount of propellant to be added are determined based on the total propellant requirement and the mixing ratio.

[0010] In one possible design, the divergence error includes method uncertainty, the static residual amount of the propellant, and the dynamic residual amount of the propellant.

[0011] In one possible design, the uncertainty of the method is determined by the following formula:

[0012]

[0013]

[0014] Where Δv is the velocity increment required for the satellite to be in orbit, η is the engine orbit change efficiency, and I spLet g be the engine's specific impulse, g0 be the acceleration due to gravity, and σ be the acceleration due to gravity. Mf Let σ be the uncertainty of the method. M0 δΔv represents the initial weight error of the entire satellite, and δΔv represents the error in the satellite velocity increment.

[0015] In one possible design, determining the average pressure of the oxidizer tank and the average pressure of the propellant tank based on the total propellant demand, cylinder filling pressure, oxidizer tank filling pressure, and propellant tank filling pressure includes:

[0016] Based on the total propellant demand, cylinder filling pressure, oxidizer tank filling pressure, and propellant tank filling pressure, determine the cylinder end-of-life pressure.

[0017] The average pressure of the gas cylinder is determined based on the cylinder filling pressure and the cylinder end-of-life pressure.

[0018] The average pressure of the oxidizer tank and the average pressure of the propellant tank are determined based on the average pressure of the gas cylinders.

[0019] In one possible design, the average pressure of the gas cylinder is determined by the following formula:

[0020]

[0021]

[0022] Among them, P ge P is the pressure at the end of the cylinder's life. gi To pressurize the gas cylinder, V g M is the volume of the gas cylinder. p ρ represents the total propellant requirement. o ρ is the density of the oxidant. f P is the density of the propellant. toi Pressurize the oxidant storage tank, P tfi Pressurize the propellant tank, V to V is the volume of the oxidant storage tank. tf P is the volume of the propellant storage tank. toe P is the pressure at the end of the oxidant tank's life. tfe This refers to the pressure at the end of the fuel tank's lifespan. This represents the average pressure of the gas cylinder.

[0023] In one possible design, determining the mixing ratio based on the average pressure of the oxidizer tank and the average pressure of the propellant tank includes:

[0024] The propellant consumption mixing ratio of the engine is determined based on the average pressure of the oxidizer tank and the average pressure of the propellant tank.

[0025] The fueling mixture ratio is determined based on the engine's propellant consumption mixture ratio and the engine's propellant consumption amount.

[0026] In one possible design, the amount of oxidizer and the amount of propellant added are determined by the following formula:

[0027]

[0028]

[0029] Among them, M po M is the amount of oxidant added. pf γ is the amount of propellant added, γ is the mixing ratio, and M is the amount of propellant added. p This represents the total propellant requirement.

[0030] Secondly, embodiments of the present invention also provide a propellant loading amount determination device, applied to a satellite, the determination device comprising:

[0031] The first calculation unit is used to determine the total propellant requirement based on the on-orbit rated consumption and divergence error of the propellant; wherein the propellant includes an oxidizer and a fuel.

[0032] The second calculation unit is used to determine the average pressure of the oxidizer tank and the average pressure of the propellant tank based on the total propellant demand, the cylinder filling pressure, the oxidizer tank filling pressure and the propellant tank filling pressure.

[0033] The third calculation unit is used to determine the mixing ratio based on the average pressure of the oxidizer tank and the average pressure of the propellant tank;

[0034] The fourth calculation unit is used to determine the amount of oxidizer and fuel to be added based on the total propellant demand and the mixing ratio.

[0035] Thirdly, embodiments of the present invention also provide an electronic device, including a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, it implements the method described in any embodiment of this specification.

[0036] Fourthly, embodiments of the present invention also provide a computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to perform the methods described in any embodiment of this specification.

[0037] This invention provides a method, apparatus, electronic device, and storage medium for determining propellant loading amount. In this embodiment, addressing the need for refined propellant budgeting for on-orbit satellites, the propellant budget is subdivided, and multiple divergence errors are statistically calculated separately to improve the accuracy of total propellant loading amount calculation. This allows for accurate prediction of propellant loading amount, avoiding insufficient or excessive budgeting. Simultaneously, by considering on-orbit usage, the on-orbit propellant mixing ratio is estimated, determining the loading amounts of oxidizer and propellant to reduce satellite idle weight, increase propellant reserves, and extend satellite lifespan. This technical method is easy to implement, fully utilizes existing ground test data from propulsion systems, improves the accuracy of propellant loading amount prediction, achieves adequate propellant matching, effectively increases the satellite's payload-to-dryness ratio, and extends satellite lifespan, demonstrating significant economic benefits and promising application prospects. Attached Figure Description

[0038] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0039] Figure 1 This is a flowchart of a method for determining the propellant loading amount according to an embodiment of the present invention;

[0040] Figure 2 This is a hardware architecture diagram of an electronic device provided in an embodiment of the present invention;

[0041] Figure 3 This is a structural diagram of a propellant loading determination device provided in an embodiment of the present invention. Detailed Implementation

[0042] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0043] Please refer to Figure 1 This invention provides a method for determining the propellant loading amount, applied to satellites. The method includes:

[0044] Step 100: Determine the total propellant requirement based on the on-orbit rated consumption and divergence error of the propellant; wherein the propellant includes oxidizer and fuel.

[0045] Step 102: Based on the total propellant demand, cylinder filling pressure, oxidizer tank filling pressure, and propellant tank filling pressure, determine the average pressure of the oxidizer tank and the average pressure of the propellant tank.

[0046] Step 104: Determine the mixing ratio based on the average pressure of the oxidizer tank and the average pressure of the propellant tank;

[0047] Step 106: Determine the amount of oxidizer and fuel to be added based on the total propellant demand and the mixing ratio.

[0048] In this embodiment, to address the need for refined propellant budgeting for on-orbit satellites, the propellant budget is subdivided, and multiple divergence errors are statistically calculated separately to improve the accuracy of the total propellant loading calculation. This allows for accurate prediction of the propellant loading amount, avoiding insufficient or excessive budgeting. Simultaneously, by combining on-orbit usage data, the on-orbit propellant mixing ratio is estimated, determining the loading amounts of oxidizer and propellant to reduce satellite idle weight, increase propellant reserves, and extend satellite lifespan. This technical method is easy to implement, fully utilizes existing ground test data from propulsion systems, improves the accuracy of propellant loading prediction, achieves adequate propellant matching, effectively increases the satellite's payload-to-dryness ratio, and extends satellite lifespan, demonstrating significant economic benefits and promising application prospects.

[0049] In this embodiment, the oxidizer and propellant of the satellite are stored in an oxidizer tank and a propellant tank, respectively. The oxidizer in the oxidizer tank and the propellant in the propellant tank are powered by gas cylinders and supplied to the engine and thruster through pipelines.

[0050] For step 100;

[0051] On-orbit rated consumption is determined as follows:

[0052]

[0053] Among them, M c η is the rated on-orbit consumption, Δv is the velocity increment required for the satellite in orbit (including transfer orbit velocity increment, position acquisition velocity increment, north-south position-keeping velocity increment, east-west position-keeping velocity increment, on-orbit test velocity increment, and deorbit velocity increment), η is the engine orbit change efficiency, and I is the velocity increment required for the satellite in orbit. sp Where is the engine specific impulse, g0 is the gravitational acceleration, and M0 is the satellite launch weight.

[0054] In some embodiments of the present invention, the divergence error includes method uncertainty, static residual amount of propellant, and dynamic residual amount of propellant.

[0055] In some embodiments of the present invention, the method uncertainty is determined by the following formula:

[0056]

[0057]

[0058] Where Δv is the velocity increment required for the satellite to be in orbit, η is the engine orbit change efficiency, and I sp Let g be the engine's specific impulse, g0 be the acceleration due to gravity, and σ be the acceleration due to gravity. Mf Let σ be the method uncertainty. M0 δΔv represents the initial weight error of the entire satellite, and δΔv represents the error in the satellite velocity increment.

[0059] It should be noted that ε is an intermediate variable and has no practical meaning.

[0060] In this embodiment, the static residual amount Δm r Determined by the following formula:

[0061] Δm r1 =μ(ρ o V to +ρ f V tf )

[0062] Δm r2 =ρ o V lo +ρ f V lf

[0063]

[0064] Δm r =Δm r1 +Δm r2 +Δm r3

[0065] Where, Δm r1 V represents the amount of propellant that cannot be expelled due to the tank extrusion efficiency, where μ is the tank extrusion efficiency. to ρ is the volume of the oxidant storage tank. o V is the density of the oxidant. tf ρ is the volume of the propellant storage tank. f Δm represents the density of the propellant. r2 To reduce the amount of propellant remaining in the propulsion system piping, V lo V lf Δm represents the volume of the oxidizer and fuel lines, respectively. r3 The static residual amount of the propellant is the saturated vapor pressure, where R is the gas constant and P is the static residual amount of the propellant. vo P vfThe saturated vapor pressures of the oxidizer and propellant are respectively, T is the on-orbit temperature of the storage tank, and M is the pressure of the propellant. g denoted as the molar mass of the gas.

[0066] In this embodiment, the dynamic residual σm d Determined by the following formula:

[0067]

[0068] Where K is the nominal mixing ratio of the propellant, taken as 1.65, δK is the on-orbit deviation of the mixing ratio, typically taken as 0.03, and M... c This is the rated consumption in orbit.

[0069] In summary, M p The total propellant requirement is obtained using the following formula:

[0070] M p =M c +Δm r +σ Mf +σm d

[0071] Regarding step 102:

[0072] In some embodiments of the present invention, step 102 includes:

[0073] Determine the end-of-life pressure of the gas cylinders based on the total propellant demand, cylinder filling pressure, oxidizer tank filling pressure, and propellant tank filling pressure.

[0074] The average pressure of the gas cylinder is determined based on the cylinder filling pressure and the pressure at the end of the cylinder's lifespan.

[0075] The average pressure of the oxidizer tank and the average pressure of the propellant tank are determined based on the average pressure of the gas cylinders.

[0076] In some embodiments of the present invention, the average pressure of the gas cylinder is determined by the following formula:

[0077]

[0078]

[0079] Among them, P ge P is the pressure at the end of the cylinder's life. gi To pressurize the gas cylinder, V g M is the volume of the gas cylinder. p For the total propellant requirement, ρ o ρ is the density of the oxidant. f P is the density of the propellant. toi Pressurize the oxidant storage tank, P tfiPressurize the propellant tank, V to V is the volume of the oxidant storage tank. tf P is the volume of the propellant storage tank. toe P is the pressure at the end of the oxidant tank's life. tfe This refers to the pressure at the end of the fuel tank's lifespan. This represents the average pressure of the gas cylinder.

[0080] In this embodiment, determining the average pressure of the oxidizer tank and the average pressure of the propellant tank based on the average pressure of the gas cylinder includes:

[0081] By fitting the ground gas pipeline test data, the first mapping relationship f(P) between the average pressure of the gas cylinder and the average pressure of the oxidizer tank, and the second mapping relationship g(P) between the average pressure of the gas cylinder and the average pressure of the propellant tank were obtained respectively.

[0082] The average pressure of the oxidant tank is obtained through the first and second mapping relationships. and average pressure of fuel tank

[0083] Regarding step 104:

[0084] Step 104 includes:

[0085] The propellant consumption mixing ratio of the engine is determined based on the average pressure of the oxidizer tank and the average pressure of the propellant tank.

[0086] The fueling mixture ratio is determined based on the engine's propellant consumption mixture ratio and the engine's propellant consumption.

[0087] Specifically, the mixing ratio is obtained using the following formula:

[0088] γ e =aP eo +bP ef +cT o +dT f +e

[0089] Where, γ e The propellant consumption mixture ratios of the engine, and the coefficients a, b, c, d, and e, were all obtained through ground tests of the orbital control engine. eo T is the oxidizer inlet pressure of the engine. o P is the oxidant inlet temperature of the engine. ef T is the engine's propellant inlet pressure. f This refers to the engine's fuel inlet temperature.

[0090]

[0091]

[0092] in, The average pressure of the oxidant storage tank. ΔP is the average pressure of the propellant tank. lo ΔP lf These are the flow resistances for the oxygen path and the combustion path, respectively.

[0093]

[0094] γ=γ c

[0095] Where, γ c γ represents the total propellant consumption over the entire service life, and γ represents the mixing ratio during refueling.

[0096] In one possible design, the amounts of oxidizer and propellant added are determined by the following formula:

[0097]

[0098]

[0099] Among them, M po M represents the amount of oxidant added. pf γ is the amount of propellant added, γ is the mixing ratio, and M is the amount of propellant added. p This represents the total propellant demand.

[0100] like Figure 2 , Figure 3 As shown, this embodiment of the invention provides a device for determining the propellant loading amount. The device embodiment can be implemented by software, hardware, or a combination of both. From a hardware perspective, such as... Figure 2 The diagram shown is a hardware architecture diagram of an electronic device for determining propellant loading amount according to an embodiment of the present invention. (Except for...) Figure 2 In addition to the processor, memory, network interface, and non-volatile memory shown, the electronic device in the embodiment may also include other hardware, such as a forwarding chip responsible for processing packets. Taking software implementation as an example, such as... Figure 3 As shown, a device in a logical sense is formed by the CPU of its electronic device reading the corresponding computer program from the non-volatile memory into memory and running it. This invention also provides a propellant loading amount determination device, applied to a satellite, which includes:

[0101] The first calculation unit is used to determine the total propellant requirement based on the on-orbit rated consumption and divergence error of the propellant; wherein the propellant includes oxidizer and fuel.

[0102] The second calculation unit is used to determine the average pressure of the oxidizer tank and the average pressure of the propellant tank based on the total propellant demand, the cylinder filling pressure, the oxidizer tank filling pressure and the propellant tank filling pressure.

[0103] The third calculation unit is used to determine the mixing ratio based on the average pressure of the oxidizer tank and the average pressure of the propellant tank;

[0104] The fourth calculation unit is used to determine the amount of oxidizer and propellant to be added based on the total propellant demand and the mixing ratio.

[0105] It should be noted that the embodiments of the determining device provided in this invention are based on the same inventive concept as the embodiments of the determining method described above. Therefore, they can achieve the same technical effects. For specific effects, please refer to the embodiments of the determining method described above, which will not be repeated here.

[0106] It is understood that the structures illustrated in the embodiments of the present invention do not constitute a specific limitation on a propellant loading determination device. In other embodiments of the present invention, a propellant loading determination device may include more or fewer components than illustrated, or combine some components, or split some components, or have different component arrangements. The illustrated components may be implemented in hardware, software, or a combination of software and hardware.

[0107] The information interaction and execution process between the modules in the above-mentioned device are based on the same concept as the method embodiment of the present invention, and the specific details can be found in the description of the method embodiment of the present invention, and will not be repeated here.

[0108] This invention also provides an electronic device, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements a method for determining the propellant loading amount according to any embodiment of this invention.

[0109] This invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform a method for determining the propellant loading amount according to any embodiment of this invention.

[0110] Specifically, a system or apparatus equipped with a storage medium may be provided, on which software program code implementing the functions of any of the embodiments described above is stored, and the computer (or CPU or MPU) of the system or apparatus may read and execute the program code stored in the storage medium.

[0111] In this case, the program code read from the storage medium can itself implement the function of any of the above embodiments, and therefore the program code and the storage medium storing the program code constitute part of the present invention.

[0112] Examples of storage media used to provide program code include floppy disks, hard disks, magneto-optical disks, optical disks (such as CD-ROM, CD-R, CD-RW, DVD-ROM, DVD-RAM, DVD-RW, DVD+RW), magnetic tapes, non-volatile memory cards, and ROMs. Alternatively, program code can be downloaded from a server computer via a communication network.

[0113] Furthermore, it should be clear that not only can the program code read by the computer be executed, but also the operating system or other components operating on the computer can be instructed based on the program code to perform some or all of the actual operations, thereby realizing the function of any of the embodiments described above.

[0114] Furthermore, it is understood that the program code read from the storage medium is written to the memory set in the expansion board inserted into the computer or to the memory set in the expansion module connected to the computer. Then, based on the instructions of the program code, the CPU or other components installed on the expansion board or expansion module execute some and all of the actual operations, thereby realizing the function of any of the above embodiments.

[0115] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0116] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media that can store program code, such as ROM, RAM, magnetic disk, or optical disk.

[0117] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for determining the amount of propellant to be added, characterized in that, When applied to satellites, the determination method includes: The total propellant requirement is determined based on the on-orbit rated consumption and divergence error of the propellant; wherein the propellant includes oxidizer and fuel. Based on the total propellant demand, cylinder filling pressure, oxidizer tank filling pressure, and propellant tank filling pressure, determine the average pressure of the oxidizer tank and the average pressure of the propellant tank. The mixing ratio is determined based on the average pressure of the oxidizer tank and the average pressure of the propellant tank; The amount of oxidizer and the amount of propellant to be added are determined based on the total propellant requirement and the mixing ratio.

2. The method for determining the propellant loading amount according to claim 1, characterized in that, The divergence error includes method uncertainty, the static residual amount of the propellant, and the dynamic residual amount of the propellant.

3. The method for determining the propellant loading amount according to claim 1, characterized in that, The uncertainty of the method is determined by the following formula: where Δv is the velocity increment required for the satellite in orbit, η is the orbit transfer efficiency of the engine, I sp is the specific impulse of the engine, g0 is the acceleration of gravity, σ Mf is the uncertainty of the method, σ M0 is the initial weight error of the whole satellite, and δΔv is the error of the satellite velocity increment.

4. The method for determining the propellant loading amount according to claim 1, characterized in that, The determination of the average pressure of the oxidizer tank and the average pressure of the propellant tank based on the total propellant demand, cylinder filling pressure, oxidizer tank filling pressure, and propellant tank filling pressure includes: Based on the total propellant demand, cylinder filling pressure, oxidizer tank filling pressure, and propellant tank filling pressure, determine the cylinder end-of-life pressure. The average pressure of the gas cylinder is determined based on the cylinder filling pressure and the cylinder end-of-life pressure. The average pressure of the oxidizer tank and the average pressure of the propellant tank are determined based on the average pressure of the gas cylinders.

5. The method for determining the propellant loading amount according to claim 4, characterized in that, The average pressure of the gas cylinder is determined by the following formula: Among them, P ge P is the pressure at the end of the cylinder's life. gi To pressurize the gas cylinder, V g M is the volume of the gas cylinder. p ρ represents the total propellant requirement. o ρ is the density of the oxidant. f P is the density of the propellant. toi Pressurize the oxidant storage tank, P tfi Pressurize the propellant tank, V to V is the volume of the oxidant storage tank. tf P is the volume of the propellant storage tank. toe P is the pressure at the end of the oxidant tank's life. tfe This refers to the pressure at the end of the fuel tank's lifespan. This represents the average pressure of the gas cylinder.

6. The method for determining the propellant loading amount according to claim 1, characterized in that, The determination of the mixing ratio based on the average pressure of the oxidizer tank and the average pressure of the propellant tank includes: The propellant consumption mixing ratio of the engine is determined based on the average pressure of the oxidizer tank and the average pressure of the propellant tank. The fueling mixture ratio is determined based on the engine's propellant consumption mixture ratio and the engine's propellant consumption amount.

7. The method for determining the propellant loading amount according to claim 1, characterized in that, The amount of oxidizer and the amount of propellant added are determined by the following formula: Among them, M po M is the amount of oxidant added. pf γ is the amount of propellant added, γ is the mixing ratio, and M is the amount of propellant added. p This represents the total demand for the propellant.

8. A device for determining the amount of propellant to be added, characterized in that, Applied to satellites, the determining device includes: The first calculation unit is used to determine the total propellant requirement based on the on-orbit rated consumption and divergence error of the propellant; wherein the propellant includes an oxidizer and a fuel. The second calculation unit is used to determine the average pressure of the oxidizer tank and the average pressure of the propellant tank based on the total propellant demand, the cylinder filling pressure, the oxidizer tank filling pressure and the propellant tank filling pressure. The third calculation unit is used to determine the mixing ratio based on the average pressure of the oxidizer tank and the average pressure of the propellant tank; The fourth calculation unit is used to determine the amount of oxidizer and fuel to be added based on the total propellant demand and the mixing ratio.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, and the processor, when executing the computer program, implements the method as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to perform the method of any one of claims 1-7.

Images