Method for aligning two map data sets

Abstract

A method for aligning two map data sets, comprising: providing two map data sets each containing environmental information in which environmental information has been detected using a sensor of the mobile device, at least one of the two map data sets being a sparse map data set; providing the two map data sets as input feature data or determining input feature data based on the two map data sets; the method is performed based on sparse convolution by using a machine learning algorithm: aligning two map data sets, generating output data from input feature data via intermediate feature data in an intermediate hierarchy, including information on a transformation relationship between the two map data sets, performing the alignment including an adaptation process, the method comprises the following steps: determining a global map data set based on feature data by using global pooling, and adapting intermediate feature data of one or another of a plurality of intermediate hierarchies based on the global map data set; and providing the output data for determining navigation information.

Description

Technical Field

[0001] The invention relates to a method for aligning two map data sets in order to determine navigation information for a mobile device moving or to be moved in an environment, a mobile device, and a system and a computer program for carrying out the method. Background Art

[0002] Mobile devices, such as at least partially autonomous vehicles or robots, usually move in an environment such as a house, a garden, a factory hall or a road, in the air or in water. One of the basic problems of such or other mobile devices is navigation, in particular also self-orientation, i.e. knowing what the environment is like, in particular where obstacles or other objects are and where it is (absolutely) located. For this purpose, the mobile device can be equipped with various sensors, such as cameras, lidar sensors, radar sensors or inertial sensors or GNSS sensors (generalization of GPS sensors for rough positioning), with the help of which the movement and the environment of the mobile device can be detected, for example in two or three dimensions. . Summary of the invention

[0003] According to the invention, a method for aligning two map data sets, a mobile device and a system as well as a computer program for carrying out the method are proposed having the features of the independent patent claims. Advantageous embodiments are the subject matter of the dependent claims and the following description.

[0004] The invention generally relates to a mobile device that moves or at least can move in an environment such as a road or a work area. Examples of such mobile devices (or also mobile working devices) are, for example: robots and / or drones and / or vehicles that also move partially or (completely) automatically (on land, in water or in the air). Robots include, for example: domestic robots, such as cleaning robots (for example in the form of suction robots and / or mopping robots), floor or road cleaning devices, construction robots or lawn mowing robots, and also other so-called service robots, and vehicles that move at least partially automatically include, for example: passenger vehicles or freight vehicles (also called so-called ground vehicles, for example in warehouses, but generally also cars and trucks), but also aerial vehicles, such as so-called drones, or water vehicles.

[0005] Such a mobile device has in particular a control or regulation unit and a drive unit for moving the mobile device so that the mobile device can be moved in an environment, for example along a movement path. For this purpose, navigation information can be determined, that is, for example, specific instructions about the direction in which the mobile device should travel in order to follow the movement path. These instructions can then be implemented by the control or regulation unit and the drive unit. In general, this can be referred to as navigation of the mobile device.

[0006] In addition, the mobile device can have one or more sensors, by means of which the environment or information in the environment can be detected, and if necessary also from the mobile device itself. As mentioned above, these sensors can be, for example, cameras, lidar sensors, radar sensors, ultrasonic sensors or inertial measurement units (or inertial sensors) and radiometers, by means of which the environment and the movement of the mobile device can be detected, for example, in two or three dimensions. However, depending on the type of mobile device, other or additional sensors can also be provided.

[0007] One aspect of navigation is so-called mapping, which is used, for example, to create a map of the environment. Such maps can also be used as sensors to a certain extent. In this context, scan matching or map alignment is also discussed. One goal here is to determine an alignment transformation between input data, which can originate from any sensor, such as lane markings or radar echoes recognized by a vehicle camera. This transformation is usually the first step in the creation of a consolidated map from multiple partially overlapping sensor data (or representations derived therefrom). Generally speaking, this involves aligning two map data sets.

[0008] An example is also the scan matching of so-called point clouds of lidar sensors. In particular, in this case, an entire point cloud is measured or detected using a laser scanner; a point cloud is a collection of points in the environment determined using a laser scanner or lidar sensor. Each point can be assigned a distance to the mobile device or laser scanner and an orientation relative to a reference orientation of the mobile device or laser scanner. This point cloud usually corresponds to one or more "point lines" along the contour of the object in the field of view; however, if necessary, the points can also lie only approximately on such a line.

[0009] However, this point cloud alone is not enough to determine the position and / or orientation of the mobile device in the environment. To this end, the point cloud or point set is compared with a reference point cloud or a reference set of points. A transformation can then be determined that best makes the point cloud (or point set) cover the reference point cloud (or reference point set) or be consistent with it, that is, align the two with each other. Then, when the point cloud is detected relative to the reference point cloud or the coordinate system of the reference point cloud, the transformation then corresponds to the position and / or orientation of the mobile device. If the reference point cloud is a map of the environment or at least a part thereof, the current position and / or orientation of the mobile device in the environment can be determined. For example, the reference point cloud (or the map of the environment) can be expanded by constantly or repeatedly adding new point clouds or parts thereof.

[0010] SLAM is also mentioned in this context. SLAM (“Simultaneous Localization and Mapping”) refers to a method in robotics in which a mobile device, such as a robot, can or must simultaneously create a map of its environment and estimate its spatial position within this map. It is therefore used, for example, to detect obstacles and thus support autonomous navigation.

[0011] Based on such a SLAM graph, a map of the environment in which the mobile device moves (environmental map) can be determined or determined. With each new map data set containing information about the environment and / or the mobile device, the map (or SLAM graph) can be extended or updated, wherein the information is obtained from or based on one or more sensors of the mobile device.

[0012] In this case, an attempt is made to make the two map data sets, ie the existing map data set and the new map data set, consistent at least within a certain tolerance in order to thereby determine the movement or trajectory of the mobile device.

[0013] In principle, the mapping process on the one hand and the localization process on the other hand can also be decoupled from each other (i.e. a map is generated, loaded onto a mobile device, and then localization is performed in this map). Scan matching or alignment of two map data sets can be used in both cases, i.e. a combined or decoupled mapping and localization process.

[0014] Within the scope of the invention, a method is now proposed for aligning two map data sets to determine navigation information, such as a map or trajectory, for a mobile device that moves or is to move in an environment. For this purpose, two map data sets are provided, each of which contains environmental information. In this case, in both map data sets, the environmental information has been detected from the mobile device and / or the environment using sensors of the mobile device. However, it is not necessary to use the same sensors for both map data sets. In this case, the two map data sets are provided as input feature data or the input feature data are determined based on the two map data sets.

[0015] Then the two map data sets are aligned, i.e. matched. In general, there are different methods, for example in "C. Choy, W. Dong and V. Koltun, "Deep global registration", from: Proceedings of the IEEE / CVF conference on computer vision and pattern recognition, pp. 2514-2523,

[0016] In "Fully convolutional geometric features", Proceedings of the IEEE / CVF International Conference on Computer Vision, pp. 8958-8966, 2019", not only classical methods but also methods based on machine learning (ML) are described. Many of these methods use two steps: In the first step, so-called feature descriptors are generated, as described in "C. Choy, J. Park, and V. Koltun, "Fully convolutional geometric features", Proceedings of the IEEE / CVF International Conference on Computer Vision, pp. 8958-8966, 2019". Based on these feature descriptors, the transformation for alignment is then determined, usually as a combination of classical and ML methods.

[0017] Therefore, the alignment or matching of the two map data sets is performed in particular by using a machine learning algorithm. In this case, in particular, so-called convolutional neural networks (CNN) are considered as machine learning algorithms. In this case, output data are generated from input feature data via intermediate feature data (feature maps) in one or more intermediate layers (so-called hidden layers). The output data include information about the transformation relationship (or transformation for short) between the two map data sets. The output data can then be provided for determining navigation information.

[0018] For example, machine learning algorithms or CNNs that come into consideration are those described in “C. Choy, W. Dong and V. Koltun, “Deep global registration”, in: Proceedings of the IEEE / CVF conference on computer vision and pattern recognition, pp. 2514-2523, 2020” or in “C. Choy, J. Park and V. Koltun, “Fully convolutional geometric features”, in Proceedings of the IEEE / CVF International Conference on Computer Vision, pp. 8958-8966, 2019”.

[0019] However, it has now been shown that the map datasets to be aligned are often so-called sparse map datasets, i.e. map datasets which have data only in a point-like manner, for example in space or in a detection area. Another term for a sparse map dataset is a sparsely occupied or weakly occupied map dataset. A specific example is a map dataset which includes images and / or positions of specific objects, such as lane markings, road posts or traffic signs. For example, in the case of images (here we are talking about digital images), only specific objects such as traffic signs can be of interest, while other areas are ignored.

[0020] Here, so-called sparse convolutions can be used to align the map datasets. This brings many advantages, such as a strong reduction in computational effort and storage requirements. However, sparse convolutions are usually only calculated at positions where the input tensor of the input data (input feature data) is not equal to zero, in order to ensure sparsity. Therefore, if the range of action of the sparse convolution is not sufficient to bridge the gaps in the data, the receptive field (Receptive Field), i.e. the detected area, of the neural network used or the machine learning algorithm in general may "break (aufreiβen)", if the range of action of the sparse convolution is not sufficient to bridge the gaps in the data. This is because the convolution kernel is usually not large enough to fill such gaps in the data. This can be compensated by either significantly increasing the size of the convolution kernel or using a large radius pooling operation; but all of this comes at the expense of a sharp increase in computational complexity or a loss of fine-grained information.

[0021] This problem is particularly relevant and unsolved in the context of the mentioned machine learning algorithms from "C. Choy, W. Dong, and V. Koltun, "Deep global registration," in Proceedings of the IEEE / CVF conference on computer vision and pattern recognition, pp. 2514-2523, 2020." and "Choy, J. Park, and V. Koltun, "Fully convolutional geometric features," in Proceedings of the IEEE / CVF International Conference on Computer Vision, pp. 8958-8966, 2019," since global correlations are often more relevant than local correlations for alignment.

[0022] Within the scope of the present invention, two map data sets are now aligned, at least one of which, but preferably both, are so-called sparse map data sets.

[0023] Here, performing alignment includes one or more adaptation processes, wherein one or each of the adaptation processes includes the following. Based on the feature data, a global map data set is determined by using a global pooling operation, such as global average pooling. Here, the feature data includes input feature data or intermediate feature data of the one or more intermediate levels. Then, based on the global map data set, the intermediate feature data of one or another of the intermediate levels is adapted.

[0024] In one embodiment, the adaptation of the intermediate feature data comprises at least one of the following processes: addition of the global map data set and the intermediate feature data, multiplication of the global map data set and the intermediate feature data, or concatenation of the global map data set and the intermediate feature data. If the multiple channels of the global map data set and the intermediate feature data are different from each other, in particular during the addition or multiplication, a convolution (or convolution) of the intermediate connection can be provided.

[0025] In one embodiment, performing the alignment includes multiple adaptation processes. Here, different intermediate feature data can be adapted in different adaptation processes of the multiple adaptation processes. Similarly, different global map data sets can be determined based on different feature data in different adaptation processes of the multiple adaptation processes.

[0026] In this way, the problem of receptive field collapse can be solved without significantly increasing the computational cost. The global context (i.e., the global map dataset) can be combined with the local information (the sparse map dataset or the existing sparse data there). In this way, better performance is obtained with almost the same computational complexity, or comparable performance is obtained with reduced computational complexity.

[0027] It is therefore recommended to combine global pooling methods (in an advantageous embodiment also including extended forms such as squeeze and excitation) with the following network architecture in order to prevent the receptive field of the network from being unnaturally reduced due to unfavorable input data, wherein the network architecture is used to calculate, for example, FCGF feature descriptors or corresponding estimates calculated using DGR for the purpose of alignment of two map data sets (for example in the form of point clouds).

[0028] In summary, one can start from a network architecture as described in "C. Choy, W. Dong and V. Koltun, "Deep global registration", from: Proceedings of the IEEE / CVF conference on computer vision and pattern recognition, pages 2514-2523, 2020" or in "C. Choy, J. Park and V. Koltun, "Fully convolutional geometric features", from: "Proceedings of the IEEE / CVF International Conference on Computer Vision", pages 8958-8966, 2019". The network architecture is used for the purpose of aligning the following point cloud or map data set, which contains at least one layer with sparse convolutions. The network architecture (i.e., a usual machine learning algorithm) can be trained here using given data and a given loss function, as described, for example, here.

[0029] However, the network architecture is now modified in such a way that global pooling is used to introduce global context, for example, at different points in the network. To this end, any layer with feature data (input feature maps, i.e., direct network input, i.e., input feature data, or hidden layers, i.e., intermediate feature data) and a certain number of channels (e.g., C channels) is processed using global pooling (e.g., global average pooling) on ​​a parallel path added to the architecture.

[0030] In an advantageous representation, this can be done, for example, using a squeeze and excitation block. The result of this block (the so-called 1_C characteristic map)

[0031] It is then combined with any other feature maps of the network (i.e., intermediate layers with intermediate feature data), for example, by positional addition, multiplication, or concatenation. If, oBdA, the latter feature map (intermediate feature data) has a different number of channels from C (e.g., D channels) in the case of addition or multiplication, this number can be aligned by an intermediately connected convolution (e.g., a so-called convolution).

[0032] The modifications of the network can be repeated arbitrarily frequently and for any combination of layers as mentioned. Similar to the representation in "J. Hu, L. Shen and G. Sun, "Squeeze-and excitation networks", from: Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7132-7141, 2018", any network architecture can be modified, for example, the Inception architecture or the ResNet type architecture can be modified. However, no further modifications to the training framework are required, such as modifications involving data or loss functions. The added layers or levels can be retained in the network at runtime. Since the volume of the globally pooled data (global map dataset) is very small, the number of additional operations generated is very small and only insignificantly prolongs the running time.

[0033] The system or computing unit according to the invention for data processing, for example a control unit of a control device or a mobile device, or a server or another computer, is particularly programmed to carry out the method according to the invention, for example in one of the described embodiments.

[0034] The invention also relates to a mobile device which has such a system for data processing or is configured to obtain navigation information determined as described above. The mobile device also has a sensor for detecting environmental information and is configured to perform navigation based on the navigation information.

[0035] It is also advantageous to implement the method according to the invention in the form of a computer program or computer program product with a program code for executing all method steps, because this leads to particularly low costs, especially if the control device for execution is also used for other tasks and therefore exists anyway. Finally, a machine-readable storage medium is provided, on which a computer program as described above is stored. Suitable storage media or data carriers for providing computer programs are particularly magnetic, optical and electrical memories, such as hard disks, flash memories, EEPROMs, DVDs, etc. The program can also be downloaded via a computer network (Internet, intranet, etc.). Such downloading can be carried out in a wired or cable-connected or wireless manner (for example, via a WLAN network, 3G, 4G, 5G or 6G connection, etc.).

[0036] Further advantages and embodiments of the invention are apparent from the description and the drawings.

[0037] The invention is schematically illustrated in the drawings using embodiments and is described below with reference to the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 A mobile device is schematically shown in an environment for explaining the invention.

[0039] Figure 2 A map data set used to explain the present invention is schematically shown.

[0040] Figure 3 In one embodiment, a flow chart for explaining the method of the present invention is schematically shown.

[0041] Figure 4 The alignment of two map datasets is schematically shown. DETAILED DESCRIPTION

[0042] exist Figure 1 , a mobile device 100 is shown schematically and by way of example in an environment 120 for explaining the invention. The environment 120 comprises, for example, a road 140 with road markings 142. The mobile device 100 is, for example, a vehicle having a control or regulating unit 102 and a drive unit 104 for moving the vehicle 100 (using wheels), for example, along a movement path 130, which here extends by way of example along the road 140 or a lane of the road.

[0043] Furthermore, the vehicle 100 has a sensor 106, designed as a camera, with a detection range, for example. For better illustration, the detection range is selected to be small here; however, in practice, the detection range can also be up to 180°, for example. Likewise, further cameras can also be provided. Using the sensor 106, the environment 120 can be detected, i.e., an image of the environment or generally environmental information can be generated or detected.

[0044] In addition, the vehicle 100 has a computing unit or system 108 for data processing, such as a control device, by which data can be exchanged with a higher-level system 110, for example via an indicated radio connection. For example, in the system 110, a movement path (or navigation information in general) can be determined, which is then transmitted to the system 108 in the vehicle 100, and the vehicle 100 should then follow the movement path. However, it can also be provided that the movement path (or navigation information in general) is determined in the system 108 itself or the movement path is obtained there in another way. But instead of the movement path or navigation information, the system 108 can also obtain control information that has been determined based on the movement path or navigation information, and the control or regulation unit 102 can move the vehicle via the drive unit 104 according to the control information to follow the movement path. The movement path 130 is shown here only by way of example.

[0045] To determine the mentioned navigation information, images captured by camera 106 or, in general, map data sets can be used, in particular in the case of other types of sensors. For example, the images can here respectively include or depict roadway markings or their positions, while other information in the images is ignored. This is then a so-called sparse map data set.

[0046] exist Figure 2 In FIG. 1 , two such map data sets or images are schematically shown for explanation purposes. For example, these map data sets or images may be composed of Figure 1 Detected by a camera of a vehicle in the vehicle. Lane markings should be seen both in map data set 200 and in map data set 210, respectively, but at different positions within the image representing the map data set. However, apart from the lane markings, no further information is present in the image, i.e., these are sparse map data sets.

[0047] In the context of vehicle navigation, the two map data sets 200 and 210 should now be aligned with each other, i.e. matched, in order to find a transformation relationship (or transformation) that maps one of the map data sets to the other. This transformation relationship then represents the movement of the vehicle between the points in time at which the two map data sets or images were detected. This is especially true in the case where multiple observations come from one vehicle. In the case of decoupling of mapping and positioning, this may be observations of the same or similar position made by multiple vehicles at different points in time.

[0048] It should be mentioned here that the two images or map data sets are shown only as an example and for explanation purposes. Instead of two images, it is also possible to align an image with an already existing map, which itself is based on a plurality of images. After the alignment, the new image can then be used to expand the map. In this case, one of the map data sets would be the map, and the other of the map data sets would be the (new) image.

[0049] Figure 3 The flow chart for explaining the method of the present invention in one embodiment is schematically shown. In step 300, two map data sets 302, 304 are provided, each of which has environmental information. As mentioned above, in at least one of the two map data sets, the environmental information is detected from the mobile device and / or the environment by a sensor of the mobile device. In addition, at least one of the two map data sets is, for example, a reference to Figure 2 Explained sparse map dataset.

[0050] In step 310, the two map data sets are provided as input feature data 312, and more precisely as input data for a machine learning algorithm, such as a CNN. It is also conceivable that the input feature data is determined based on the two map data sets. As already mentioned above,

[0051] For example, feature descriptors may be extracted here. Input feature data here refers to input data for a machine learning algorithm.

[0052] In step 320, an alignment, i.e. matching, of the two map data sets is then performed. This is done by using a machine learning algorithm 330, such as a CNN, and based on sparse convolutions. The input feature data 312 are fed to the CNN as input data (network input). Output data 336 are obtained, which then include information about the transformation relationship between the two map data sets.

[0053] CNN 330 may include a plurality of intermediate layers (so-called hidden layers). Input feature data (input feature map) can be processed into output data 340 via different intermediate feature data (feature maps) in the intermediate layers, for example 332, 334. Depending on the type of CNN, more intermediate layers or intermediate feature data are possible.

[0054] For example, an adaptation process 340 is now performed, wherein a global map data set 344 is determined based on feature data by using global pooling at step 342. The feature data may include or be, for example, input feature data, or, as exemplarily shown here, include or be intermediate feature data of one of a plurality of intermediate levels.

[0055] In step 346 , based on the global map data set 344 , intermediate feature data of another intermediate level in the plurality of intermediate levels, exemplarily the intermediate feature data 334 , are adapted.

[0056] In this case, there may be a plurality of such adaptation processes 340 , in which further feature data are then respectively used to obtain a corresponding global map data set and further intermediate feature data are also adapted.

[0057] As mentioned, the adaptation may include, for example, addition, multiplication or concatenation, possibly including convolution with intermediate connections if necessary.

[0058] The output data 336 is then provided for determining navigation information at step 350. In particular, at step 360, navigation information 362 is determined based on the initial data, wherein the navigation information includes, for example, a map of the environment and / or a trajectory for the mobile device.

[0059] exist Figure 4 4 shows this alignment or matching in another view. Here, a sparse convolution 402 is performed based on an input feature map 400 (here exemplarily 3D), i.e., feature data (e.g., network input or feature data in a hidden layer). In this case, a kernel 404 is used, which is applied to the input feature map 400 to obtain an output feature map 406 (e.g., in a hidden layer).

[0060] In the input feature map 400, the underlying sparse map data set can be identified, which is shown by the dark cuboids (information) relative to the light cuboids (no information). Since the kernel 404 only covers two cuboids here in the example, when applied to the input feature map 400, there are gaps between the dark cuboids that the kernel cannot bridge. This results in that there is no interaction or no interaction between the dark cuboids in the output feature map 406.

[0061] Now here is applied global pooling 410, where information representing the interactions between the cuboids of the input feature map 400 is extracted from the input feature map 400, i.e. the global map dataset 412412. This is then combined with the output feature map 406 in step 414, so that the interactions or correlations between the dark cuboids (which represent said information) are then generated there by the information existing in the global map dataset 412.

Claims

1. A method for aligning two map data sets (302, 304) to determine navigation information for a mobile device (100) moving or to be moved in an environment (120), the method comprising: Providing (300) two map data sets (302, 304), each of which contains environmental information, wherein in the two map data sets, the environmental information has been detected from the mobile device (100) and / or the environment (120) using a sensor (106) of the mobile device (100), and wherein at least one of the two map data sets is a sparse map data set; providing (310) the two map data sets as input feature data (312) or determining input feature data based on the two map data sets; By using a machine learning algorithm (330), in particular a convolutional neural network based on sparse convolution, performing (320): aligning the two map data sets (302, 304), wherein output data is generated from the input feature data (312) via intermediate feature data (332, 334) in one or more intermediate levels, wherein the output data (336) includes information about a transformation relationship between the two map data sets, The performing of the alignment comprises one or more adaptation processes (340), wherein one or each of the adaptation processes comprises: - determining (342) a global map dataset (344) based on feature data by using global pooling, wherein the feature data comprises the input feature data or intermediate feature data of the one or more intermediate levels, and - adapting (346) the intermediate feature data (344) of the one intermediate level or another intermediate level of the plurality of intermediate levels based on the global map data set (344); and The output data (336) is provided (350) for use in determining navigation information.

2. The method according to claim 1, wherein: Adapting the intermediate feature data includes at least one of the following processes: - adding the global map data set and the intermediate feature data, - multiplying the global map data set with the intermediate feature data, - Concatenating the global map data set and the intermediate feature data.

3. The method according to claim 1 or 2, wherein: When the numbers of channels of the intermediate feature data and the global map dataset are different from each other, adapting the intermediate feature data respectively includes convolutions of intermediate connections. The method according to claim 1 , wherein performing the alignment comprises a plurality of adaptation processes.

5. The method according to claim 4, wherein: Different intermediate feature data are adapted in different adaptation processes of the multiple adaptation processes.

6. The method according to claim 4 or 5, wherein: In different adaptation processes of the multiple adaptation processes, different global map data sets are determined based on different feature data.

7. The method according to any of the preceding claims, wherein the sensor of the mobile device comprises one of the following sensors: a camera, a radar sensor, a lidar sensor, an ultrasonic sensor. 8 . The method according to claim 1 , wherein the environmental information of at least one of the two map data sets comprises an image and / or a position of at least one of the following objects: lane markings, road posts, traffic signs.

9. The method according to any one of the preceding claims, further comprising: The navigation information (362) is determined (360) based on the output data, wherein the navigation information includes in particular a map of the environment and / or a trajectory of the mobile device.

10. A system (108, 110) for data processing, comprising: Apparatus for carrying out the method according to any of the preceding claims.

11. A mobile device (100) having a system (108) according to claim 10 and / or being configured to obtain navigation information which has been determined according to the method according to claim 9, The mobile device (100) has a sensor (106) for detecting environmental information and is configured to perform navigation based on the navigation information. The mobile device preferably has a control or regulating unit and a drive unit for moving the mobile device as a function of the navigation information.

12. The mobile device (100) according to claim 11 is designed as a transport vehicle that moves at least partially automatically, in particular as a passenger transport vehicle or as a freight transport vehicle, and / or as a robot, in particular as a household robot, such as a cleaning robot, a floor or road cleaning device or a lawn mowing robot, and / or as a drone.

13. Computer program comprising instructions which, when the computer program is executed on a computer, cause the computer to perform the method steps of the method according to any one of claims 1 to 9 when the program is executed by the computer.

14. A computer-readable storage medium having stored thereon a computer program according to claim 13.

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