Method for registering two point sets

Abstract

The invention relates to a method for registering two point sets, in particular for use in navigation of a mobile device (100), comprising: providing (204) a current point set (202) based at least partially on data captured from the surroundings by means of a sensor (106); providing (210) a reference point set (212) based at least partially on data captured from the surroundings by means of a sensor; determining (220) a transformation to be used which transforms the reference point set and the current point set onto one another, wherein, in particular as part of an optimization process, ratios between tangents of points from the current point set and surface normals of points from the reference point set are factored in; and providing (230) information (232) relating to the transformation to be used for the registration, in particular for navigation of the mobile device

Description

[0001] R.414025 - 1 - Description Title Procedure for von zwei The present invention relates to a method for registering two sets of points, in particular for use in the navigation of a mobile device, a data processing system and a computer program for its execution, as well as a mobile device. Background of the invention: Mobile devices, such as vehicles or robots that move at least semi-automatically, typically move in an environment, in particular an environment to be processed or a work area, such as an apartment, a garden, a factory hall, or on the street, in the air, or in water. One of the fundamental problems of such or other mobile devices is to orient themselves, i.e., to know what the environment looks like and where the mobile device is located within it. For this purpose, the mobile device can be equipped with various sensors, such as cameras, lidar sensors, or radar sensors, with the help of which the environment of the mobile device can be determined.two- or three-dimensionally captured. This enables the mobile device to recognize its surroundings and navigate accordingly. Disclosure of the Invention: According to the invention, a method for registering two sets of points, a data processing system, a computer program for its execution, and a mobile device with the features of the independent patent claims are proposed. Advantageous embodiments are the subject of the dependent claims and the following description. R.414025 -. 2 -The invention generally deals with the registration of point sets, i.e., sets of points, for example, also in connection with mobile devices that move or can move within an environment or, for example, within a work area. Examples of such mobile devices (or mobile work equipment) are, for example, robots and / or drones and / or vehicles that move semi-automatically or (fully) automatically (on land, water, or in the air). Examples of robots include household robots such as cleaning robots (e.g., in the form of vacuuming and / or mopping robots), floor or street cleaning devices, construction robots, or lawnmower robots, as well as other so-called service robots, vehicles that move at least partially automatically, such as passenger transport vehicles or goods transport vehicles (also so-called industrial trucks, e.g., in warehouses), but also aircraft such as drones or watercraft.Another preferred application of point set registration is, for example, mobile mapping, in which a human user employs a device with a sensor and processing unit to capture point sets from the environment and then process them accordingly. Such a mobile device typically includes a control unit and a drive unit for moving the device, enabling it to move within the environment, for example, along a path. Navigation information can be determined for this purpose, such as specific instructions on the direction the mobile device should travel to follow the path. These instructions can then be implemented via the control unit and the drive unit. This process is generally referred to as the navigation of the mobile device. Furthermore, a mobile device can have one or more sensors that measure the environment.Information can be collected from the surroundings. As mentioned, this can include, for example, cameras, lidar sensors, radar sensors, or inertial measurement units (or inertial sensors), as well as radio odometry, which are used to capture the environment and, if applicable, the movement of the mobile device, e.g., in two or three dimensions. Depending on the type of R.414025-. 3 -Mobile devices can also be equipped with other or additional sensors. Sensors such as cameras, lidar sensors, or radar sensors can capture and provide information, particularly sensor data, about the environment. This data includes information about the mobile device's surroundings, such as the distances of the mobile device (or the respective sensor) to objects in the environment. Such data is primarily stored as a set of points (point set). In the case of a lidar sensor, each point represents the distance of the mobile device or lidar sensor to an object or a specific point on the object. In this context, the point set is also referred to as a point cloud. Such point sets can also be captured with other sensors, especially depth sensors. Typically, a scan by such a sensor generates this point set.A point cloud is captured; this is essentially a dataset containing distance information for each of several points. One way to determine the position and orientation, and thus also the navigation, of such a mobile device is to use localization based on SLAM. SLAM ("Simultaneous Localization and Mapping") is a robotics technique in which a mobile device, such as a robot, can simultaneously create a map of its environment and estimate its spatial position within that map. It thus serves to detect obstacles and supports autonomous navigation. Various approaches exist for representing maps and positions in SLAM. Conventional SLAM methods typically rely on geometric information such as nodes and edges. Nodes and edges are typically components of the SLAM graph.The nodes and edges in the SLAM graph can be designed differently; traditionally, the nodes correspond, for example, to the pose (position and orientation) of the mobile device or to certain environmental features at specific times, while the edges represent relative measurements. R.414025 -. 4 -SLAM graphs represent the interaction between a mobile device and environmental features. SLAM graphs are described in more detail, for example, in "Giorgio Grisetti, Rainer Kümmerle, Cyrill Stachniss, Wolfram Burgard, A Tutorial on Graph-Based SLAM, IEEE Intelligent Transportation Systems Magazine, Vol. 2(4), pp. 31-42, 2010". Based on such a SLAM graph, a map of the environment (environmental map) in which the mobile device moves can be determined or created. With each new data set containing information about the environment or, if applicable, about the mobile device, which is obtained from or based on one or more sensors of the mobile device, the map (or the SLAM graph) can be extended or updated. When localization using SLAM, it may be particularly necessary to reconcile two different sets of points (or point clouds). The aim is to bring both sets of points into agreement, at least within certain tolerances.This process can also be referred to as a match or scan match (the latter specifically refers to the case of a lidar sensor that captures data during a scan). A frequently used term in this context is "point cloud registration"; in this respect, it also refers to the registration of two point sets. A transformation is sought or determined that transforms a reference point set and a current point set into each other (as precisely as possible). This transformation, used for registration (typically comprising a rotation and a translation), then indicates how the mobile device moved from capturing the reference point set to capturing the current point set. Such a transformation thus allows navigation information to be determined for the mobile device and, in particular, enables the mobile device to be moved accordingly.Especially in the navigation of mobile devices, the current point set is the set of points last captured by the sensor, while the reference point set is an accumulation of several previously captured point sets. If a transformation is found... R.414025 -. 5 -Once a transformation has been found that (as accurately as possible) transforms the reference point set and the current point set, the current point set, taking the transformation into account, can be added to the reference point set to obtain an updated reference point set. This updated reference point set can then be used as the reference point set for finding a transformation when dealing with a new current point set. In many applications, including the navigation of mobile devices, sensors can be used that do not capture the point set or point cloud as (at least more or less) homogeneously distributed in space, but rather in rings or layers lying on infinite circular cones with finitely many opening angles. This can, to a first approximation, have a similar effect to if these points lay on parallel planes.Within the scope of the present invention, a method for registering two sets of points is proposed, which yields particularly good results when the current set of points is not homogeneously distributed in space. For example, the current set of points may only contain points that are arranged at least substantially in several different, spaced-apart, and parallel planes. In principle, however, such a method can also be used for homogeneously distributed sets of points or other sets of points. Here, a current set of points, e.g., a so-called point cloud, is provided, which is based at least partially on data acquired from the environment by means of a sensor, e.g., a lidar sensor. The set of points may have been acquired directly by the sensor or, if necessary, obtained by further processing, e.g., with a Kalman filter.It is also conceivable that the point set was derived or determined from a camera image or other representation of the environment using a machine learning model, e.g., a deep neural network. Furthermore, a reference point set is provided that is at least partially based on data captured from the environment by a sensor. R.414025 -. 6 -A transformation is then determined to be used, which transforms the reference point set and the current point set relative to each other, taking into account, particularly within the context of optimization, the ratios between tangents of points from the current point set and surface normals of points from the reference point set. Information about the transformation to be used for registration is then provided, especially for navigating the mobile device. Using the surface normals of points from two point sets, it can be checked whether the points can correspond at least approximately. If the normals of two points in the two point sets do not have approximately the same direction, it can be assumed, for example, that the points do not correspond. The surface normal of a point in a point set can be, for example,The surface normal can be determined by defining a (middle) plane based on neighboring points, and then calculating the normal to this plane at the location of the point in question. However, as has been shown, this approach does not work, or at least not always works well, especially for sets of points that are not distributed homogeneously or at least not sufficiently so. Conversely, it can even happen that points are incorrectly identified as not corresponding to each other, even though this is the case in reality; this is primarily because a surface normal often cannot be determined correctly. For an illustrative explanation, please refer to the figure description. As has now been shown, this can be circumvented by using a tangent instead of a surface normal for the actual set of points, which is usually the one that is not sufficiently homogeneous.As has been shown, a comparison between a tangent of a point from the current point set and the surface normal of a point from the reference point set is also possible and yields comparably good results. A tangent can also be calculated for less homogeneously distributed point sets, R.414025-. 7 -Especially for points existing in planes, the tangent can be reliably determined. In one embodiment, the tangent of the point is determined based on a direction originating from the point to a neighboring point, particularly the nearest one. This represents a particularly simple way to determine the tangent of a point. Likewise, the tangent of the point can be determined based on directions originating from the point to several neighboring points; for example, a certain averaging is possible. In another embodiment, the tangent of the point is determined based on eigenvalues ​​of a covariance matrix of several points neighboring the point, wherein the tangent is determined based on an eigenvector that corresponds to the largest eigenvalue of the covariance matrix. This represents a particularly accurate way to determine the tangent of a point.One way to register two sets of points is the so-called "Iterative Closest Point" method. This involves determining the transformation to be used, which transforms the reference point set and the current point set onto each other, and iteratively performing a determination process until a termination criterion is reached. In each determination process, an association is performed between the current point set and the reference point set, based on a current transformation, to obtain a selected set of pairs of corresponding points from the current point set and the reference point set. For the initial execution, the current transformation can be, for example, the identity mapping or a suitable estimate.The selected set of point pairs includes only point pairs where, in particular, the distance between the two points is minimal and the angle between the tangent of the point of the point pair from the current point R.414025 -. 8 -The set of points and the surface normal of the point in the point pair from the reference point set correspond to a predefined angle criterion; this angle criterion can, for example, be chosen such that the tangent and the surface normal enclose an angle of approximately 90°. A new transformation is then determined within the optimization process, based on the selected set of point pairs and the current transformation. Thus, the distance between the points and the angle between tangents and normals are taken into account during optimization using the selected set of point pairs. The new transformation is then used as the current transformation for the subsequent determination process, if necessary, i.e., if the termination criterion has not already been reached. The termination criterion can, for example, be that the new transformation deviates from the current transformation by less than a previously defined threshold value.Information about the new transformation present when the termination criterion is reached is then provided as information about the transformation to be used. Thus, the "Iterative Closest Point" method, taking surface normals into account, can also be used for current point sets that are less homogeneously distributed, particularly those comprising points distributed across only a few planes. The surface normals are used only for the reference point set, while tangents are used for the current point set. A data processing system or computing unit according to the invention, e.g., a control unit or a control unit of a mobile device, or a server or other computer, is configured, particularly programmatically, to carry out a method according to the invention, e.g., in one of the described embodiments.The invention also relates to a mobile device that has such a data processing system or that is configured to receive navigation information as described above. The mobile device preferably also includes a drive system and a control or regulating unit R.414025. 9 -for moving the mobile device according to the navigation information. The mobile device is preferably also configured to perform processing; in particular, the mobile device can be one as described above, e.g., a cleaning robot or a robotic lawnmower. The invention also relates to a device that has such a data processing system or that is configured to obtain display information that has been determined as described above. Implementing a method according to the invention in the form of a computer program or computer program product with program code for carrying out all method steps is also advantageous, since this incurs particularly low costs, especially if an executing control unit is also used for other tasks and is therefore already available.Finally, a machine-readable storage medium is provided with a computer program stored on it as described above. Suitable storage media or data carriers for providing the computer program are, in particular, magnetic, optical, and electrical storage devices, such as hard drives, flash memory, EEPROMs, DVDs, etc. Downloading a program via computer networks (Internet, intranet, etc.) is also possible. Such a download can be wired or wireless (e.g., via a WLAN network, a 3G, 4G, 5G, or 6G connection, etc.). Further advantages and embodiments of the invention will become apparent from the description and the accompanying drawing. The invention is schematically illustrated in the drawing using an exemplary embodiment and is described below with reference to the drawing. Brief description of the drawings R.414025 -. 10 -Figure 1 schematically shows a mobile device in an environment to illustrate the invention. Figure 2 schematically shows a process in one embodiment. Figure 3 shows sets of points to illustrate the invention. Embodiment(s) of the Invention Figure 1 schematically and by way of example shows a mobile device 100 in an environment 120, in particular a work area, to illustrate the invention. The mobile device 100 is, by way of example, a vacuum cleaner robot with a control unit 102 and a drive unit 104 (with wheels) for moving the vacuum cleaner robot 100, e.g., along a movement path 130. Furthermore, the vacuum cleaner robot 100 has, by way of example, a sensor 106 designed as a lidar sensor with a detection range. For better illustration, the detection range is chosen to be relatively small here; in practice, however, the detection range can also be up to 360° (e.g.,but at least 180° or at least 270°). The environment 120 can be detected by means of sensor 106, i.e., specific sets of points can be generated using environmental sensor data. In a scan using the lidar sensor, for example, a set of points, a so-called point cloud, can be generated, where each point indicates the distance of an object from the sensor, from which the laser beam is reflected. Furthermore, the robotic vacuum cleaner 100 has a computing unit or a data processing system 108, e.g., a control unit, by means of which data can be exchanged with a higher-level system 110, e.g., via a radio connection. In the system 110, for example, movement paths (or navigation information in general) can be determined, which are then transmitted to the system 108 in the robotic vacuum cleaner 100, which it is then supposed to follow.However, it may also be provided that a movement path (or navigation information in general) is determined in system 108 itself or R.414025 -. 11 -is obtained elsewhere. Instead of a movement path or navigation information, the system 108 can, for example, also receive control information that has been determined based on a movement path or navigation information, and according to which the control unit 102 can move the robot vacuum cleaner 100 via the drive unit 104 to follow a movement path. The movement path 130 is only indicated here by way of example. The robot vacuum cleaner 100 is intended, for example, to move independently in the environment 120 or to navigate there and thereby, for example, clean a floor. Furthermore, several different objects or obstacles are shown in the environment by way of example, namely a wall 140 and a cabinet 142. Although the invention is explained here and in the following in particular using the example of the robot vacuum cleaner, this also applies to other mobile devices such as robotic lawnmowers or other self-driving vehicles.This method is also suitable for other types of applications, such as the 3D reconstruction of objects using a 3D environment sensing device. Instead of the lidar sensor, a camera, radar sensor, or other depth sensor can also be used. Figure 2 schematically illustrates the process in one embodiment. The method is generally used for registering two sets of points (point clouds), and in particular for navigating a mobile device, such as the robotic vacuum cleaner shown in Figure 1. However, as already mentioned, such registration of two sets of points can also be used for other applications. In step 200, a current set of points 202 is acquired, for example, using a lidar sensor. This can also be referred to as a scan. Such a current set of points 202 is then provided, for example, in the form of a data set containing the corresponding information, in step 204.414025 -. 12 -In step 210, a reference point set 212 is provided, which, for example, has also been acquired using a lidar sensor. The reference point set 212 is also provided, for example, in the form of a data set containing the corresponding information. As already mentioned, the reference point set can be a cumulative compilation of previous current point sets. Figure 3 shows a current point set 300 and a reference point set 310 in a given environment. The current point set 300 comprises, for example, two subsets (rings) 302 and 304 of points, each lying in a plane parallel to the xy-plane; these two planes are spaced apart in the z-direction. This is a typical type of point set that can be obtained during a scan using a lidar sensor.In the vicinity, an obstacle 340 designed as a staircase is present; the staircase 340 has several steps, with the front face of the lowest step designated 342 and the top of this step designated 344. Additionally, the front face of the uppermost of the three steps is designated 338. The tops of the steps are parallel to the xy-plane, while the front faces are perpendicular to the xy-plane and parallel to the z-direction. In a step 220, a transformation to be used is then determined, which transforms the reference point set and the current point set onto each other. This can, in particular, involve iteratively performing a determination process 222 until a termination criterion is reached. This can, in particular, be based on the so-called "Iterative Closest Point" (ICP) algorithm; this will be described in more detail below to illustrate an embodiment of the invention.The classical ICP algorithm is a method for registering two point sets or point clouds, which involves two point sets ^. ^ (Reference point set) and ^ ^ (current point set) takes as input and determines or estimates its relative transformation ^ by iteratively performing an association step R.414025 - 13 - followed by an optimization step. The association step generates a set of corresponding point pairs ^ = {(^, ^)^:^} of reference points ^^ ∈ ^^ and current points ^ ^^ ^ ∈ ^^, e.g., by selecting points ^ ^ ^, which is closest to ^ ⊕ ^ ^ ^ lie. During optimization, the current estimate for ^ (i.e., a current transformation) is continuously refined, for example by minimizing a cost function over the currently selected correspondences. This cost function is defined, for example, as follows: ^ ^ − ^ ⊕ ^ ^ ^ ^^ Ω ^ ^ ^ ^^ ^ − ^ ⊕ ^ ^ ^^ Here, Ω ^^ an information matrix that takes into account potential uncertainties contained in the points themselves or in the data mapping. The so-called "Normal Iterative Closest Point" method (NICP algorithm) improves the ICP algorithm in both the association and optimization steps by (among other things) adjusting the surface normals. ^ ^ and ^ ^ ^all points in ^^ and ^^ are taken into account. During the association, the nearest point correspondences are not only discarded if their distance is greater than a threshold, but also if the angle ^ between the surface normals of the points in question is greater than a predefined value: Here, ^^ is the rotation matrix of the transformation ^. During optimization, the NICP algorithm minimizes, instead of the first equation above, a cost value that includes not only the Euclidean distance between corresponding points, but also the difference between their (transformed) surface normals. R.414025 - 14 - with the error vector Considering not only the position but also the normal direction of each point in the NICP algorithm significantly aids scan matching, i.e., the registration of two point sets, by improving accuracy, convergence speed, and convergence radius. As has been shown and already explained, it is not always possible to calculate reliable surface normals for point sets, especially when working with point sets acquired during a single scan of, for example, a rotating 3D lidar sensor, as commonly used in robotics and automated driving. Such point clouds typically consist of a limited number (e.g., 16) of rings (i.e.,Point sets on infinite circular cones with different opening angles (or approximately in planes), which limits the resolution of the captured point set in one direction (vertically), in contrast to a significantly higher resolution in the horizontal direction. This can be seen in Figure 3. Points from two successive rings, e.g., rings 302 and 304 according to Figure 3, belong to the currently captured point set 300, while the reference point set 310 can be assumed to be densely sampled on the surfaces of the walls and stairs. It should be noted here that only two points 312 and 314 from the reference point set 310 are shown as examples. Due to the large distance between the two rings 302 and 304, their points can lie on different surfaces with very different normals; this is shown as an example in Figure 3.The points of ring 302 lie on the front of a stair step, while the points of ring 304 lie on the top of a stair step. R.414025 -. 15 - Would the normal vector for the point ^ ^^ (Point 306 in Figure 3) calculated using neighboring points in a local neighborhood could either fail due to a degenerate (non-planar) point set or result in a surface normal pointing in the wrong direction. The former would occur if only points on the same ring were used, while the latter could occur if the neighborhood area were enlarged and points from the next ring, belonging to a different surface, were included. In contrast, the present invention makes it possible to apply concepts similar to "Normal Iterative Closes Point" (NICP), even when scans consist of only limited sets of rings, where it is not possible to calculate accurate surface normals. For this purpose, less demanding features in the form of tangents or... are used for the current point set.Tangent vectors are used that do not require a specific 2D coverage of the locally planar region to be calculated. As it turns out, it is often not possible to calculate reliable surface normals with scans from ring-based 3D lidar sensors (or generally with comparable point sets). However, it is generally possible to calculate tangent vectors between successive points of the same ring if they lie on a locally planar surface field. Even though this tangent direction does not contain as much information as the normal, it still allows for a significant improvement in the registration of two point sets. The approach proposed here will also be called the "Normal-Tangent Iterative Closest Point" (NTICP) method, since it can be assumed that the normals are based on the typically much denser reference point set ^, as described for NICP. ^can be calculated, but not, or at least often not, on the current point cloud. Against this background, each determination process 222 (i.e., each iteration) now includes, step 224, performing an association between R.414025 - 16 -The current point set and the reference point set are transformed, based on a current transformation, to obtain a selected set of point pairs 226 of corresponding points from the current point set and the reference point set. The selected set of point pairs includes only those point pairs where the angle between the tangent of the point of the point pair from the current point set and the surface normal of the point of the point pair from the reference point set corresponds to a predefined angle criterion. In step 228, a new transformation is then determined within the framework of the optimization and based on the selected set of point pairs and the current transformation. The new transformation is then used as the current transformation for the subsequent determination process, if necessary. The calculation or determination of tangents for each point ^ ^ ^ ^ ∈ ^ beiIn ring-based point sets, for example, the consideration of the nearest neighboring point can be used. ^ ^ ^ ^ and the calculation of the tangent as ^ ^ ^ = (^ ^ ^^^ − ^ ^ ^ )^ be, whereby ( ⋅ )^ can be considered as an operator for normalizing the L2 norm. A more accurate method for calculating tangents, especially with (considerable) noise in the measured 3D positions, is to consider a neighborhood of points around the point under consideration ^ ^^ in the same ring (i.e., the same plane), and to calculate a covariance (or scattering) matrix Σ. ^ ^ to use and calculate the eigenvalue decomposition: where ^^ are the eigenvalues ​​in ascending order. The eigenvector corresponding to the largest eigenvalue can then be chosen as the tangent direction. This has the additional advantage that points for which no reliable tangent direction can be calculated can be determined based on the curvature σ. ^ = R.414025 - 17 -(λ^ + λ^) / (λ^ + λ^ + λ^) can be identified, which should be close to zero. It should be noted that this curvature is similar to the curvature measure σ^ = λ^ / (λ^ + λ^ + λ^) used by the NICP algorithm, but differs from it to some extent. In Figure 3, a tangent to point 306 from the current point set 300 is labeled 308. A surface normal to point 312 from the reference point set 310 is labelled 316, a surface normal to point 314 from the reference point set 310 is labelled 318. In step 224 of the association in the proposed procedure, potential point correspondences are not only disregarded (or discarded), i.e., they are not in the selected set of point pairs, if their distance is greater than a threshold, but also if the surface normal ^ ^ ^ of the point ^ ^ ^ and the surface tangent ^ ^ ^ of the point ^ ^^ do not (or not sufficiently) match. That is, if the angle β is larger than a threshold value ^^: The angle ^ in this case is the angle by which ^ ^ ^ must be rotated until it is orthogonal to ^ ^ ^ is. Figure 3 shows that this applies, for example, to the tangent 308 and the surface normal 318 of point 314. However, this does not apply to the tangent 308 and the surface normal 316 of point 312. Furthermore, in step 228 of the optimization, a cost function similar to that used in the NICP algorithm is minimized, which also follows the third equation above, but uses a different error vector instead of the fourth equation above, which instead minimizes the angle ^: R.414025 - 18 -In step 230, information 232 about the new transformation present when the termination criterion is reached is provided, i.e., information about the transformation to be used for registration. In step 240, navigation information 242 for the mobile device can then be determined based on the transformation. Furthermore, in step 250, the current point set can be added to the reference point set, taking into account the transformation to be used, in order to obtain an updated reference point set. The above description assumes that the normals of the points ^ ^ ^ in the reference point set ^^ can be calculated based on a local neighborhood, as is done in NICP. This is a valid assumption if ^ ^a local map or point set, which was obtained, for example, by accumulating several previously registered point sets or scans. After the registration of the reference and current point sets proposed here, a new reference point set can be obtained by linking the reference and the transformed current point set. During initialization, however, there may not yet be a dense accumulated reference point set. In this case, the classic ICP algorithm can be used (which manages entirely without tangents and normals); thus, no normal information would be used, nor would surface normals be calculated. In summary, the advantages can be presented as follows: Surface tangents are used instead of surface normals, particularly in cases where the current point set does not allow for a reliable calculation of surface normals, e.g.due to limited resolution in one direction. In particular, a combination of surface tangents and normals is used for association to avoid false associations between points with incompatible surface normals and - R.414025 -. 19 -to prevent tangents. In particular, a combination of surface tangents and normals is used within the cost function of the optimization problem, which is solved during point set registration. It should be noted that the system described here is only an exemplary, very simple incremental scan-matching system. The advantages mentioned can also be applied to much more complex systems, including, but not limited to, the fusion of other sensor sources (e.g., inertial data), the introduction of additional terms into the optimized cost function, further filtering of both the reference and the current point set, and dynamic switching on a point basis between the association and optimization cost function proposed here and that of NICP, which is based on a metric that may include surface statistics around the current point.

Claims

R.414025 - 20 -Claims 1. A method for registering two sets of points, in particular for use in the navigation of a mobile device (100), comprising: providing (204) a current set of points (202) which is at least partially based on data acquired from the environment by means of a sensor (106); providing (210) a reference set of points (212) which is at least partially based on data acquired from the environment by means of a sensor; determining (220) a transformation to be used which transforms the reference set of points and the current set of points towards each other, wherein, in particular within the framework of an optimization, ratios between tangents of points from the current set of points and surface normals of points from the reference set of points are taken into account; and providing (230) information (232) about the transformation to be used for the registration, in particular for the navigation of the mobile device. 2.The method of claim 1, further comprising, for at least a subset of the points of the current set of points, determining the tangent of the point.

3. The method of claim 2, wherein the tangent of the point is determined based on a direction originating from the point to a, in particular nearest, adjacent point, or wherein the tangent of the point is determined based on directions originating from the point to several adjacent points. R.414025 - 21 -4. A method according to claim 2, wherein the tangent of the point is determined based on eigenvalues ​​of a covariance matrix of several points adjacent to the point, wherein the tangent is determined in particular based on an eigenvector which eigenvector belongs to the largest of the eigenvalues ​​of the covariance matrix.

5. A method according to any one of the preceding claims, wherein the current set of points comprises only points that are arranged at least substantially in several different, spaced-apart rings or at least approximately parallel planes.

6. A method according to claim 5, and according to claim 3 or 4, wherein the one or more adjacent points lie at least substantially on the same of the several rings or in the same of the several planes.

7. A method according to any one of the preceding claims, wherein the determination (220) of the transformation to be used,which transforms the reference point set and the current point set into each other, comprises an iterative execution of a determination process (222) until a termination criterion is reached, wherein each determination process comprises: - performing (224) an association between the current point set and the reference point set, based on a current transformation, to obtain a selected set of point pairs (226) of corresponding points of the current point set and the reference point set, wherein the selected set of point pairs includes only point pairs where an angle between the tangent of the point of the point pair from the current point set and the surface normal of the point of the point pair from the reference point set corresponds to a predefined angle criterion,-Determining (228) a new transformation within the framework of optimization and based on the selected set of point pairs and the current transformation, and, R.414025 - 22 -- Using the new transformation as the current transformation for the subsequent determination process, if necessary; wherein information about the new transformation present when the termination criterion is reached is provided as the information about the transformation to be used.

8. Method according to any one of the preceding claims, further comprising: Adding (250) the current point set, taking into account the transformation to be used, to the reference point set to obtain an updated reference point set.

9. Method according to any one of the preceding claims, wherein the current point set and / or the reference point set have each been at least partially detected by means of a sensor of the mobile device.

10. Method according to claim 9, wherein the sensor comprises a depth sensor, in particular a lidar sensor. 11.Method according to any one of the preceding claims, further comprising: Determining (240) navigation information (242) for the mobile device, based on the transformation to be used.

12. Data processing system, comprising means for executing the method according to any one of the preceding claims.

13. Mobile device (100) comprising a system according to claim 12, and / or wherein the mobile device is configured to receive navigation information determined according to a method according to claim 11, and is configured to navigate based on the navigation information, preferably with a control unit and a drive unit for moving the mobile device according to the navigation information, wherein the mobile device is preferably a vehicle that moves at least partially automatically, in particular a passenger transport vehicle. R.414025 - 23 -14. A computer program comprising instructions which, when executed by a computer, cause the computer to perform the process steps of a method according to any one of claims 1 to 11 when executed on the computer.

15. A computer-readable storage medium on which the computer program according to claim 14 is stored.

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