Neural network assisted vehicle adaptive autonomous navigation method

Abstract

The invention provides a neural network assisted vehicle adaptive autonomous navigation method. The method comprises the following steps: designing an improved LSTM model for multi-parameter parallel prediction; collecting data of an inertial measurement unit and executing inertial navigation calculation; when satellite navigation is effective, inertia / satellite integrated navigation calculation is executed; training a designed parallel LSTM model based on the combined navigation result; when satellite navigation is invalid, vehicle speed and attitude information are predicted based on a trained machine learning model; and when satellite navigation is invalid, carrying out adaptive integrated navigation by using variational Bayes based on a machine learning model prediction result. According to the method, the problem of insufficient error accumulation precision of vehicle navigation which only depends on inertial navigation when no reference information exists is solved, full-autonomous and high-precision navigation positioning of the vehicle can be realized, and the method has important practical application value.

Description

Technical Field

[0001] The invention belongs to the technical field of inertial navigation, and in particular relates to a vehicle adaptive autonomous navigation method assisted by a neural network. Background Art

[0002] High-precision navigation and positioning information is a prerequisite for precise vehicle control, reasonable path planning, and safe autonomous driving. At present, in-vehicle navigation and positioning mainly use inertial / satellite combined navigation. However, the accuracy and reliability of satellite navigation directly depend on the satellite signal. It cannot be used in scenes without satellite signals such as underground parking lots and tunnels, and it is not stable enough in environments such as building obstructions. At this time, the error of inertial navigation based on integral solution accumulates over time. In particular, due to volume and cost constraints in vehicle-mounted scenarios, a miniature low-cost inertial navigation system is used, and its sensor accuracy is limited, and the error accumulation characteristics are particularly obvious. Therefore, it is urgent to design a vehicle-mounted fully autonomous navigation method that does not rely on external reference information such as satellite navigation. Summary of the invention

[0003] The present invention aims to solve at least one of the technical problems existing in the prior art.

[0004] To this end, the present invention provides a vehicle adaptive autonomous navigation method assisted by a neural network.

[0005] The technical solution of the present invention is as follows:

[0006] According to one aspect, a neural network-assisted vehicle adaptive autonomous navigation method is provided, the autonomous navigation method comprising:

[0007] Step 1: Design an improved LSTM model for multi-parameter parallel prediction, including:

[0008] The improved LSTM model designed includes four sub-models:

[0009] 1) Sub-model 1: Horizontal velocity prediction model

[0010] The horizontal velocity prediction model predicts the eastward and northward velocities. The neural network framework based on it is LSTM. The model input and output are designed as follows:

[0011] Model input: gyroscope output minus harmful components such as the earth's rotation angular velocity Attitude quaternion Atti calculated by pure inertial navigation insQ , the navigation system acceleration f after deducting the gravity acceleration component n ; Among them, the navigation system acceleration f n Attitude calculation through raw accelerometer output combined with pure inertial navigation solution;

[0012] Model output: eastward and northward velocities;

[0013] 2) Sub-model 2: Celestial velocity prediction model

[0014] The model framework and model input of the celestial velocity prediction model are the same as those of sub-model 1, and the model output is the celestial velocity;

[0015] 3) Sub-model 3: Horizontal posture prediction model

[0016] The horizontal attitude prediction model predicts the pitch angle and the roll angle, the neural network framework and the model input are the same as those of sub-model 1, and the model output is the pitch angle and the roll angle;

[0017] 4) Sub-model 4: Heading prediction model

[0018] The heading prediction model predicts the heading angle in quaternion form, the neural network framework and model input are the same as sub-model 1, and the model output is the attitude in quaternion form;

[0019] Step 2: Collect inertial measurement unit data and perform inertial navigation solution;

[0020] Step 3: When GNSS is valid, obtain satellite navigation data and perform integrated navigation solution, including:

[0021] Conduct multiple GNSS-valid sports car tests, perform inertial / satellite combined navigation based on the inertial measurement unit data and GNSS data collected in step 2, and calculate the reference attitude quaternion Atti referQ and a baseline navigation system speed for training the improved LSTM model;

[0022] Step 4: Based on the inertial navigation solution result of step 2 and the combined navigation result of step 3, the improved LSTM model designed in step 1 is trained;

[0023] Step 5: Based on the improved LSTM model trained in step 4, inertial navigation data is used to predict vehicle attitude and speed information when GNSS is invalid;

[0024] Step 6: Based on the prediction results of step 5, use variational Bayesian filtering to perform adaptive integrated navigation.

[0025] Furthermore, when designing the sub-model 4, the loss function in the form of quaternion is designed as follows:

[0026]

[0027] Among them, Atti predQ =[q 0p q 1p q 2p q 3p ] Tand Atti referQ =[q 0t q 1t q 2t q 3t ] T are the quaternion forms of the predicted attitude and the reference attitude respectively; ΔQ = [Δq0Δq1Δq2Δq3] T Atti is the posture prediction result predQ With the reference pose Atti referQ The difference between them is calculated as:

[0028]

[0029] The reference attitude here is calculated by inertial / satellite combined navigation.

[0030] Furthermore, the step three specifically includes:

[0031] Collect inertial measurement unit data, perform inertial navigation solution, and obtain gyroscope output minus harmful components Attitude quaternion Atti calculated by pure inertial navigation insQ ; and based on Atti insQ The navigation system acceleration f is calculated by subtracting the gravity acceleration component from the accelerometer output n , used as input for the parallel LSTM model.

[0032] Furthermore, the step six specifically includes:

[0033] Based on the inertial measurement unit data collected in step 2, the prediction results in step 5 are used as reference information, and the variational Bayesian filter is used for integrated navigation. The execution process of the steps is as follows:

[0034] 6.1 Establish the integrated navigation state space model, including state equations and measurement equations;

[0035] 6.2 Initialize the integrated navigation algorithm parameters;

[0036] 6.3 Execution time update;

[0037] 6.4 Perform measurement update.

[0038] Furthermore, in step 6.1:

[0039] The state equation is X k =Φ k,k-1 X k-1 +w k-1 , the state quantity X includes the north sky eastward misalignment angle North sky east velocity error δv n =[δV n δV uδV e ] T , Latitude Error Altitude error δh, longitude error δλ, carrier system gyro drift ε b =[ε x ε y ε z ] T , load system accelerometer zero bias Load system arm error L out , time delay T d ;

[0040] The measurement equation is Z k =H k X k +V k , measure Z k To improve the difference between the attitude and velocity information predicted by the LSTM model and the inertial navigation solution results.

[0041] Furthermore, in step 6.2:

[0042] Initialize the parameters of the integrated navigation algorithm based on variational Bayesian filtering, including the state estimation result m k , estimated mean square error P k 、System noise variance matrix Q k , the initial value of the shape parameter of the inverse Gamma distribution α0, and the initial value of the inverse scale parameter of the inverse Gamma distribution β0.

[0043] Furthermore, in step 6.3, the time update is performed according to the following formula:

[0044]

[0045]

[0046]

[0047]

[0048] Among them, Φ k / k-1 According to the inertial navigation error equation, ρ i ∈(0.9,1],i=1,…,d is the attenuation coefficient, and They are the shape parameter and inverse scale parameter of the inverse Gamma distribution, and d represents the dimension of measurement.

[0049] Furthermore, in step 6.4, the measurement update is performed in an iterative manner:

[0050] First initialize the parameters: Then the iterative calculation is performed as follows:

[0051] for n=0:N-1

[0052]

[0053]

[0054]

[0055]

[0056] end

[0057] In the formula, N represents the number of iterations, and the output is is the resolved time-varying measurement noise variance.

[0058] Furthermore, the autonomous navigation method further comprises:

[0059] When there is auxiliary information such as satellite navigation, execute steps 2 to 4 to update the machine learning model online. When there is no auxiliary information such as satellite navigation, execute steps 2, 3, 5, and 6.3 and 6.4 in step 6 until the test is completed and navigation is completed.

[0060] According to another aspect, a computer device is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above method when executing the computer program.

[0061] The above technical solution aims to solve the problem that inertial navigation alone cannot meet the high-precision navigation and positioning requirements of vehicles when reference information such as satellite navigation is invalid. A neural network-assisted vehicle adaptive autonomous navigation method is proposed. When satellite navigation is valid, an improved LSTM model with multi-parameter parallel prediction is trained to achieve high-precision prediction of motion parameters of different magnitudes. When satellite navigation is invalid, the trained model is used to predict vehicle speed and attitude, and variational Bayesian filtering is used to assist inertial navigation for adaptive combined navigation.

[0062] The solution proposed in the present invention does not rely on reference information other than inertial navigation, and can realize fully autonomous navigation of the vehicle. That is, the vehicle can realize fully autonomous and high-precision navigation without any reference information, only using the inertial measurement unit installed on itself, and significantly reduce the time accumulation error of inertial navigation. It can be applied to satellite navigation failure scenarios such as tunnels and building obstructions, and has important practical application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] The included drawings are used to provide a further understanding of the embodiments of the present invention, which constitute a part of the specification, are used to illustrate the embodiments of the present invention, and together with the text description, explain the principles of the present invention. Obviously, the drawings in the following description are only some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0064] Figure 1 It is a flow chart of an embodiment of the method of the present invention. DETAILED DESCRIPTION

[0065] It should be noted that, in the absence of conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is by no means intended to limit the present invention and its application or use. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0066] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0067] Unless otherwise specifically stated, the relative arrangement of the parts and steps described in these embodiments, numerical expressions and numerical values ​​do not limit the scope of the present invention. At the same time, it should be understood that, for ease of description, the sizes of the various parts shown in the accompanying drawings are not drawn according to the actual proportional relationship. The technology, method and equipment known to ordinary technicians in the relevant field may not be discussed in detail, but in appropriate cases, the technology, method and equipment should be regarded as a part of the authorization specification. In all examples shown and discussed here, any specific value should be interpreted as being merely exemplary, rather than as a limitation. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once a certain item is defined in an accompanying drawing, it does not need to be further discussed in subsequent drawings.

[0068] refer to Figure 1This embodiment provides a neural network-assisted vehicle adaptive autonomous navigation method according to the present invention, which specifically includes the following steps:

[0069] Step 1: Design an improved LSTM model for multi-parameter parallel prediction, including:

[0070] Designing an improved LSTM model for multi-parameter parallel prediction includes four sub-models, the specific information is as follows:

[0071] 1) Sub-model 1: Horizontal velocity prediction model

[0072] The horizontal velocity prediction model predicts the eastward and northward velocities. The neural network framework based on it is LSTM. The model input and output are as follows:

[0073] Model input: gyroscope output minus harmful components such as the earth's rotation angular velocity Attitude quaternion Atti calculated by pure inertial navigation insQ , the navigation system acceleration f after deducting the gravity acceleration component n Among them, the navigation system acceleration f n Attitude calculation through raw accelerometer output combined with pure inertial navigation solution;

[0074] Model output: eastward and northward velocities;

[0075] 2) Sub-model 2: Celestial velocity prediction model

[0076] The model framework and model input are the same as sub-model 1, and the model output is the celestial velocity;

[0077] 3) Sub-model 3: Horizontal posture prediction model

[0078] The horizontal attitude prediction model predicts the pitch angle and roll angle. The neural network framework and model input are the same as sub-model 1, and the model output is the pitch angle and roll angle;

[0079] 4) Sub-model 4: Heading prediction model

[0080] In order to overcome the problem that the heading angle is not differentiable when switching between 0° and 360°, the heading angle is estimated in quaternion form. The neural network framework and model input are the same as sub-model 1, and the model output is the attitude in quaternion form. The loss function in quaternion form is designed as follows:

[0081]

[0082] Among them, Atti predQ =[q 0p q 1p q 2p q 3p ]T and Atti referQ =[q 0t q 1t q 2t q 3t ] T are the quaternion forms of the predicted attitude and the reference attitude respectively; ΔQ = [Δq0Δq1Δq2Δq3] T Atti is the posture prediction result predQ With the reference pose Atti referQ The difference between them is calculated as:

[0083]

[0084] The reference attitude here is calculated by inertial / satellite combined navigation;

[0085] Since the pitch angle and roll angle have small changes, the accuracy is limited when they are jointly predicted with the heading angle. Therefore, the pitch angle and roll angle use the prediction results of sub-model 3, and sub-model 4 only uses the prediction results of the heading angle.

[0086] Step 2: Collect IMU data and perform inertial navigation solution

[0087] Collect inertial measurement unit data, perform inertial navigation solution, and obtain gyroscope output minus harmful components Attitude quaternion Atti calculated by pure inertial navigation insQ , and based on Atti insQ The navigation system acceleration f is calculated by subtracting the gravity acceleration component from the accelerometer output n , used as input for the parallel LSTM model;

[0088] Step 3: When GNSS is valid, obtain satellite navigation data and perform integrated navigation solution

[0089] Conduct multiple GNSS-valid sports car tests, perform inertial / satellite combined navigation based on the collected inertial measurement unit data and GNSS data, and calculate the reference attitude quaternion Atti referQ =[q 0t q 1t q 2t q 3t ] T and baseline navigation system speed for training parallel LSTM models;

[0090] Step 4: Train the parallel LSTM model designed in step 1 based on the inertial navigation results of step 2 and the combined navigation results of step 3;

[0091] Step 5: Based on the parallel LSTM model trained in step 4, inertial navigation data is used to predict vehicle attitude and speed information when GNSS is invalid;

[0092] Step 6: Based on the prediction results of step 5, use variational Bayesian filtering to perform adaptive integrated navigation.

[0093] Based on the inertial measurement unit data collected in step 2, the prediction results in step 5 are used as reference information, and the variational Bayesian filter is used for integrated navigation. The specific steps are as follows:

[0094] 6.1 Establishing the integrated navigation state space model

[0095] Establish the state space model used by the integrated navigation algorithm, including the state equation and measurement equation:

[0096] The state equation is X k =Φ k,k-1 X k-1 +w k-1 . State quantity X, including the north sky east misalignment angle North sky east velocity error δv n =[δV n δV u δV e ] T , Latitude Error Altitude error δh, longitude error δλ, carrier system gyro drift ε b =[ε x ε y ε z ] T , load system accelerometer zero bias Load system arm error L out , time delay T d wait;

[0097] The measurement equation is Z k =H k X k +V k , measure Z k It is the difference between the attitude and velocity information predicted by the parallel LSTM model and the inertial navigation solution result;

[0098] 6.2 Initializing integrated navigation algorithm parameters

[0099] Initialize the parameters of the integrated navigation algorithm based on variational Bayesian filtering, including the state estimation result m k , estimated mean square error P k 、System noise variance matrix Q k , the initial value of the shape parameter of the inverse Gamma distribution α0, the initial value of the inverse scale parameter of the inverse Gamma distribution β0;

[0100] 6.3 Execution time update

[0101] Time update is performed according to the following formula:

[0102]

[0103]

[0104]

[0105]

[0106] Among them, Φ k / k-1 According to the inertial navigation error equation, ρ i ∈(0.9,1],i=1,…,d is the attenuation coefficient, and are the shape parameter and inverse scale parameter of the inverse Gamma distribution, respectively, and d represents the dimension of measurement;

[0107] 6.4 Performing Measurement Updates

[0108] The measurement update is performed in an iterative manner: first initialize the parameters: Then the iterative calculation is performed as follows:

[0109] for n=0:N-1

[0110]

[0111]

[0112]

[0113]

[0114] end

[0115] In the formula, N represents the number of iterations. After the iteration is completed, the output in, is the resolved time-varying measurement noise variance.

[0116] In addition, when there is auxiliary information such as satellite navigation, execute steps 2 to 4 to update the machine learning model online; when there is no auxiliary information such as satellite navigation, execute steps 2, 3, 5 and 6.3 and 6.4 in step 6 until the experiment is completed and navigation is completed.

[0117] According to another embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above method when executing the computer program.

[0118] It can be seen that the embodiment of the present invention relates to a vehicle adaptive autonomous navigation method assisted by a neural network. When satellite navigation is effective, an improved LSTM model for multi-parameter parallel prediction is trained to achieve high-precision prediction of motion parameters of different magnitudes; when satellite navigation is invalid, the trained improved LSTM model is used to predict vehicle speed and posture, assist inertial navigation for combined navigation, and in view of the problem of complex and time-varying noise in the prediction results of the LSTM model, a variational Bayesian filter is used for adaptive combined navigation. This enables high-precision, fully autonomous navigation and positioning of the vehicle that does not rely on reference information such as GNSS, and has important practical application value.

[0119] Features described and / or illustrated above for one embodiment may be used in the same or similar manner in one or more other embodiments, and / or combined with or used in place of features in other embodiments.

[0120] It should be emphasized that the term “include / comprises” when used herein refers to the presence of features, integers, steps or components, but does not exclude the presence or addition of one or more other features, integers, steps, components or combinations thereof.

[0121] The above method of the present invention can be implemented by hardware, or by hardware combined with software. The present invention relates to such a computer-readable program, which, when executed by a logic component, enables the logic component to implement the above-mentioned device or component, or enables the logic component to implement the above-mentioned various methods or steps. The present invention also relates to a storage medium for storing the above program, such as a hard disk, a magnetic disk, an optical disk, a DVD, a flash memory, etc.

[0122] The many features and advantages of these embodiments are apparent from this detailed description, and thus the appended claims are intended to cover all such features and advantages of these embodiments that fall within their true spirit and scope. Furthermore, since numerous modifications and changes will readily occur to those skilled in the art, it is not intended that the embodiments of the invention be limited to the exact construction and operation illustrated and described, but rather all suitable modifications and equivalents falling within the scope thereof are intended to be covered.

[0123] Parts of the present invention that are not described in detail are well known to those skilled in the art.

Claims

1. A neural network-assisted vehicle adaptive autonomous navigation method, characterized in that: The autonomous navigation method comprises: Step 1: Design an improved LSTM model for multi-parameter parallel prediction, including: The improved LSTM model designed includes four sub-models: 1) Sub-model 1: Horizontal velocity prediction model The horizontal velocity prediction model predicts the eastward and northward velocities. The neural network framework based on it is LSTM. The model input and output are designed as follows: Model input: gyroscope output minus harmful components such as the earth's rotation angular velocity Attitude quaternion Atti calculated by pure inertial navigation insQ , the navigation system acceleration f after deducting the gravity acceleration component n ; Among them, the navigation system acceleration f n Attitude calculation through raw accelerometer output combined with pure inertial navigation solution; Model output: eastward and northward velocities; 2) Sub-model 2: Celestial velocity prediction model The model framework and model input of the celestial velocity prediction model are the same as those of sub-model 1, and the model output is the celestial velocity; 3) Sub-model 3: Horizontal posture prediction model The horizontal attitude prediction model predicts the pitch angle and the roll angle, the neural network framework and the model input are the same as those of sub-model 1, and the model output is the pitch angle and the roll angle; 4) Sub-model 4: Heading prediction model The heading prediction model predicts the heading angle in quaternion form, the neural network framework and model input are the same as sub-model 1, and the model output is the attitude in quaternion form; Step 2: Collect inertial measurement unit data and perform inertial navigation solution; Step 3: When GNSS is valid, obtain satellite navigation data and perform integrated navigation solution, including: Conduct multiple GNSS-valid sports car tests, perform inertial / satellite combined navigation based on the inertial measurement unit data and GNSS data collected in step 2, and calculate the reference attitude quaternion Atti referQ and a baseline navigation system speed for training the improved LSTM model; Step 4: Based on the inertial navigation solution result of step 2 and the combined navigation result of step 3, the improved LSTM model designed in step 1 is trained; Step 5: Based on the improved LSTM model trained in step 4, inertial navigation data is used to predict vehicle attitude and speed information when GNSS is invalid; Step 6: Based on the prediction results of step 5, use variational Bayesian filtering to perform adaptive integrated navigation.

2. A neural network-assisted vehicle adaptive autonomous navigation method according to claim 1, characterized in that: When designing the sub-model 4, the loss function in the form of quaternion is designed as follows: Among them, Atti predQ =[q 0p q 1p q 2p q 3p ] T and Atti referQ =[q 0t q 1t q 2t q 3t ] T are the quaternion forms of the predicted attitude and the reference attitude respectively; ΔQ = [Δq0 Δq1 Δq2 Δq3] T Atti is the posture prediction result predQ With the reference posture Atti referQ The difference between them is calculated as: The reference attitude here is calculated by inertial / satellite combined navigation.

3. A neural network-assisted vehicle adaptive autonomous navigation method according to claim 1 or 2, characterized in that: The step three specifically includes: Collect inertial measurement unit data, perform inertial navigation solution, and obtain gyroscope output minus harmful components Attitude quaternion Atti calculated by pure inertial navigation insQ ; and based on Atti insQ The navigation system acceleration f is calculated by subtracting the gravity acceleration component from the accelerometer output n , used as input for the parallel LSTM model.

4. The method for vehicle adaptive autonomous navigation assisted by a neural network according to claim 3, characterized in that: The step six specifically includes: Based on the inertial measurement unit data collected in step 2, the prediction results in step 5 are used as reference information, and the variational Bayesian filter is used for integrated navigation. The execution process of the steps is as follows: 6.1 Establish the integrated navigation state space model, including state equations and measurement equations; 6.2 Initialize the integrated navigation algorithm parameters; 6.3 Execution time update; 6.4 Perform measurement update.

5. The method for vehicle adaptive autonomous navigation assisted by a neural network according to claim 4, characterized in that: In step 6.1: The state equation is X k =Φ k,k-1 X k-1 +w k-1 , the state quantity X includes the north sky eastward misalignment angle North sky east velocity error δv n =[δV n δV u δV e ] T , Latitude Error Altitude error δh, longitude error δλ, carrier system gyro drift ε b =[ε x ε y ε z ] T , load system accelerometer zero bias Load system arm error L out , time delay T d ; The measurement equation is Z k =H k X k +V k , measure Z k To improve the difference between the attitude and velocity information predicted by the LSTM model and the inertial navigation solution results.

6. The method for vehicle adaptive autonomous navigation assisted by a neural network according to claim 5, characterized in that: In step 6.2: Initialize the parameters of the integrated navigation algorithm based on variational Bayesian filtering, including the state estimation result m k , estimated mean square error P k 、System noise variance matrix Q k , the initial value of the shape parameter of the inverse Gamma distribution α0, and the initial value of the inverse scale parameter of the inverse Gamma distribution β0.

7. The method for vehicle adaptive autonomous navigation assisted by a neural network according to claim 6, characterized in that: In step 6.3, the time update is performed according to the following formula: Among them, Φ k / k-1 According to the inertial navigation error equation, ρ i ∈(0.9,1],i=1,…,d is the attenuation coefficient, and They are the shape parameter and inverse scale parameter of the inverse Gamma distribution, and d represents the dimension of measurement.

8. The method for vehicle adaptive autonomous navigation assisted by a neural network according to claim 7, characterized in that: In step 6.4, the measurement update is performed in an iterative manner: First initialize the parameters: i=1,…,d, and then the iterative calculation is performed as follows: for n=0:N-1 end In the formula, N represents the number of iterations, and the output is is the resolved time-varying measurement noise variance.

9. A neural network-assisted vehicle adaptive autonomous navigation method according to any one of claims 1 to 8, characterized in that: The autonomous navigation method further comprises: When there is auxiliary information such as satellite navigation, execute steps 2 to 4 to update the machine learning model online. When there is no auxiliary information such as satellite navigation, execute steps 2, 3, 5, and 6.3 and 6.4 in step 6 until the test is completed and navigation is completed.

10. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method according to any one of claims 1 to 9 when executing the computer program.

Images