A mapping method and laser radar device based on mode switching

Abstract

The present invention discloses a mapping method and laser radar equipment based on mode switching, the method comprising: forming a rotational mapping mode by forming a longitudinal scan of the laser radar; forming a simultaneous positioning and mapping mode by forming a lateral scan of the laser radar; performing a panoramic coverage scan through the rotational mapping mode, switching to the simultaneous positioning and mapping mode after obtaining an initial point cloud map; in the simultaneous positioning and mapping mode, obtaining real-time point cloud data by covering multi-angle scene information through motion, performing a feature evaluation of whether the pose estimation of the real-time point cloud data is degraded, and switching back to the rotational mapping mode if the evaluation result shows degradation; splicing the point cloud data obtained in the two modes to complete the environmental mapping. The present invention has the advantages of the two modes, can improve the accuracy of environmental mapping, and enhance the scene coverage capability of environmental mapping.

Description

Technical Field

[0001] The present invention relates to the field of laser radar mapping, and in particular to a mapping method based on mode switching and a laser radar device. Background Art

[0002] The traditional rotating laser radar mapping method can only fix the working location and reconstruct the point cloud map of the surrounding environment, so it is impossible to construct a large-area indoor point cloud map, which greatly restricts the scope of application of this method. Directly performing point cloud registration on the reconstruction results of the multi-frame rotating laser radar mapping method will be affected by the slow acquisition speed, odometer drift, field of view occlusion and other problems of this type of method, resulting in low splicing accuracy. The traditional simultaneous positioning and mapping algorithm based on laser radar can quickly and low odometer drift construct indoor scene point cloud maps, but because the laser radar is placed horizontally, for areas far away from the laser radar in the environment, such as ceilings, floors, etc., only sparse point clouds can be obtained, and it is difficult to complete the point cloud map modeling of the environment with high resolution. Therefore, in order to overcome the shortcomings of the limited motion of the traditional rotating laser radar mapping method and the limited resolution of the traditional simultaneous positioning and mapping algorithm based on laser radar, the present invention proposes a laser radar device that relies on a mechanical structure to complete function switching, and a point cloud mapping method based on the switching of the rotating mapping mode and the simultaneous positioning and mapping mode. Summary of the invention

[0003] The purpose of the present invention is to provide a mapping method and a laser radar device based on mode switching to address the deficiencies of the prior art.

[0004] The objective of the present invention is achieved through the following technical solutions:

[0005] The present invention provides a mapping method based on mode switching, the method comprising:

[0006] The longitudinal scanning of the laser radar forms a rotating mapping mode;

[0007] The lateral scanning of the LiDAR is used to form a simultaneous positioning and mapping mode;

[0008] Perform panoramic coverage scanning through the rotating surveying mode, and switch to the simultaneous positioning and mapping mode after obtaining the initial point cloud map;

[0009] In the simultaneous positioning and mapping mode, the multi-angle scene information is covered by motion to obtain real-time point cloud data, and the feature evaluation of whether the pose estimation is degraded is performed on the real-time point cloud data. If the evaluation result shows degradation, it switches back to the rotation mapping mode;

[0010] The point cloud data obtained in the two modes are stitched together to complete the environment mapping.

[0011] Furthermore, the rotational mapping mode is achieved by a motor combined with a mechanical structure to drive the laser radar to rotate longitudinally, and at least one round of rotational scanning is performed at a fixed location.

[0012] Furthermore, in the rotation mapping mode, the point cloud data collected during the scanning process is stitched using the rotation angle value information fed back by the motor encoder to form a dense point cloud map of the current scene, specifically:

[0013] For the N frames of point cloud obtained by a round of rotation mapping, the motor encoder is used to obtain the corresponding rotation angle value θ i ,i=0,...,N; for the point cloud sequence numbered 1 to N, the difference in rotation angle between it and the point cloud numbered 0 is used The corresponding rotation matrix Project the point cloud to the laser radar coordinate system at the time of scanning the 0th frame to complete the point cloud stitching;

[0014] The difference in the rotation angle and its corresponding rotation matrix The specific form is:

[0015]

[0016]

[0017] Furthermore, in the rotation mapping mode, the point cloud data collected during the scanning process is spliced ​​using a point cloud registration algorithm to form a dense point cloud map of the current scene, specifically:

[0018] For the N frames of point clouds obtained by a round of rotational mapping, the common point cloud registration algorithms such as ICP (iterative closest point algorithm) or NDT (normal distribution transform) are used to complete the inter-frame transformation matrix estimation, and the loop detection algorithm and pose graph optimization algorithm are used to alleviate the drift problem of the point cloud registration algorithm. The optimized inter-frame transformation matrix results are used to complete the inter-frame point cloud fusion to ensure the accuracy of the point cloud fusion results.

[0019] Furthermore, in the simultaneous positioning and mapping mode, at least one laser radar continuously moves and scans in the environment to obtain point cloud data. The scanning process covers the multi-angle scene information that is missing in the rotational mapping mode, while estimating its own posture and constructing a point cloud map of the environment.

[0020] Furthermore, in the simultaneous positioning and mapping mode, during the process of estimating its own posture, the inter-frame posture estimation of the laser radar is realized by performing point cloud registration on the point cloud data of each frame; the point cloud registration algorithm includes but is not limited to point cloud registration algorithms such as ICP (iterative closest point algorithm) or NDT (normal distribution transformation), and pre-processing operations such as extracting corner points and surface points can also be performed on the point cloud data of each frame first;

[0021] In the process of building the point cloud map of the environment, the point cloud of each frame is subjected to rotation and translation transformation using the result of its own pose estimation to complete the point cloud stitching.

[0022] Furthermore, the feature evaluation of whether the pose estimation for real-time point cloud data is degraded is specifically as follows: the real-time point cloud data is registered with the existing point cloud map, and the registration optimization process uses the Gauss-Newton algorithm, wherein the variable to be optimized is multiplied by the Jacobian matrix to obtain the residual matrix; by judging the size of each item of the Jacobian matrix, the influence of the residual item on each dimension of the pose to be optimized is judged; if there is an item in the Jacobian matrix that is less than a set threshold (for example, the threshold is set to 0.01), the pose dimension corresponding to the item is degraded; Δe is the residual item, which is a scalar; ΔT is the pose to be optimized, which is a 61 vector; J is the Jacobian matrix, which is a 16 vector;

[0023] Δe=JΔT

[0024] J=[J1 J2 J3 J4 J5 J6]

[0025]

[0026] Among them, [Δr x ,Δr y ,Δr z ] represents the rotation angle of the laser radar in the x, y, and z directions, [Δt x ,Δt y ,Δt z ] represents the translation of the laser radar in the x, y, and z directions.

[0027] Furthermore, the point cloud data obtained in the rotational surveying mode is optimized, specifically: all point clouds are traversed, plane points are segmented, and a nonlinear optimization problem is constructed, in which the optimization function target is the thickness of the plane point cloud, and the optimization variable is the posture of the point cloud during collection; through Gauss-Newton optimization, the point cloud posture is continuously iterated to improve the accuracy of the rotated superimposed point cloud.

[0028] Furthermore, the point cloud data obtained in the two modes are spliced, specifically: the point cloud maps obtained by multiple rotational mapping modes are aligned; if the alignment fails due to insufficient common area or other reasons, the point cloud data collected by the simultaneous positioning and mapping modes at adjacent times are partially fused first to increase the common area of ​​the point cloud map, complete the alignment of multiple maps, and splice them to form a new point cloud map; finally, the point cloud data collected in the simultaneous positioning and mapping modes are re-run on the new map for the pose solution process, and the point cloud is projected onto the new map according to the optimized pose to complete the splicing of all point cloud data.

[0029] The present invention also provides a laser radar device for implementing the above-mentioned mapping method based on mode switching, including a hardware device, a rotation surveying and mapping module, a simultaneous positioning and mapping module, a mode switching module and a point cloud map splicing module;

[0030] The hardware device includes a first rotating mechanism, a second rotating mechanism and a laser radar connected in sequence;

[0031] The rotating surveying and mapping module keeps the second rotating mechanism vertical, and the first rotating mechanism and the mechanical structure drive the laser radar to rotate longitudinally, so as to realize multi-angle longitudinal scanning of the laser radar. This state is the rotating surveying and mapping mode;

[0032] The simultaneous positioning and mapping module rotates the second rotating mechanism to horizontal, the first rotating mechanism has no output, and the laser radar continuously moves and scans in the environment to obtain point cloud data. The scanning process covers the multi-angle scene information missing in the rotation surveying mode, and estimates its own posture and constructs a point cloud map of the environment at the same time. This state is the simultaneous positioning and mapping mode;

[0033] The mode switching module switches to the simultaneous positioning and mapping mode after determining that the rotation surveying and mapping mode completes the panoramic coverage scan and obtains the initial point cloud map; in the simultaneous positioning and mapping mode, real-time point cloud data is obtained by motion coverage of multi-angle scene information, and a feature evaluation is performed on the real-time point cloud data to determine whether the pose estimation is degraded. If the evaluation result indicates degradation, the mode is switched back to the rotation surveying and mapping mode;

[0034] The point cloud map stitching module is used to stitch the point cloud data obtained in the two modes to complete the environment mapping.

[0035] The beneficial effects of the present invention are as follows: the present invention obtains dense and accurate mapping effects through the rotation mapping mode, completes motion estimation through simultaneous positioning and mapping mode, and then covers multi-angle scene information through motion. It evaluates whether the real-time point cloud pose estimation is degraded, and decides whether to switch to the rotation mapping mode based on the evaluation results. The present invention has the advantages of both modes, can improve the accuracy of environmental mapping, and enhance the scene coverage capability of environmental mapping. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the technical solution of the present invention, the following is a brief introduction to the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and should not be regarded as limiting the scope of protection of the present invention. In each of the drawings, similar components are numbered similarly.

[0037] Figure 1 A schematic diagram of a flow chart of a mapping method based on mode switching provided in one embodiment;

[0038] Figure 2 A schematic diagram of mode switching determination provided in an embodiment;

[0039] Figure 3 A hardware schematic diagram of a rotational mapping mode and a simultaneous positioning and mapping mode is provided in one embodiment, including a laser radar, a steering gear, and a motor. DETAILED DESCRIPTION

[0040] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0041] The components of the embodiments of the present invention generally described and shown in the drawings herein may be arranged and designed in a variety of different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present invention.

[0042] In the following, various embodiments of the present disclosure will be described more fully. The present disclosure may have various embodiments, and adjustments and changes may be made therein. However, it should be understood that there is no intention to limit the various embodiments of the present disclosure to the specific embodiments disclosed herein, but rather the present disclosure should be understood to cover all adjustments, equivalents and / or alternatives that fall within the spirit and scope of the various embodiments of the present disclosure.

[0043] Hereinafter, the terms "including", "having" and their cognates, which may be used in various embodiments of the present invention, are intended only to indicate specific features, numbers, steps, operations, elements, components or combinations of the foregoing items, and should not be understood as first excluding the existence of one or more other features, numbers, steps, operations, elements, components or combinations of the foregoing items or adding the possibility of one or more features, numbers, steps, operations, elements, components or combinations of the foregoing items.

[0044] Furthermore, the terms “first”, “second”, “third”, etc. are merely used for distinguishing descriptions and are not to be understood as indicating or implying relative importance.

[0045] Unless otherwise defined, all terms (including technical terms and scientific terms) used herein have the same meanings as those generally understood by those skilled in the art to which the various embodiments of the present invention belong. The terms (such as those defined in generally used dictionaries) will be interpreted as having the same meanings as the contextual meanings in the relevant technical field and will not be interpreted as having idealized meanings or overly formal meanings unless clearly defined in the various embodiments of the present invention.

[0046] Figure 1 A mapping method based on mode switching is provided in an embodiment, and the method includes:

[0047] Step S110, laser point cloud input.

[0048] Step S120, mode switching.

[0049] Step S130: If it is the initial state or the pose estimation is degraded, the rotation surveying mode is adopted.

[0050] Step S131: If the rotation mapping is completed or the pose estimation has not degraded, the simultaneous positioning and mapping mode is adopted.

[0051] Step S140, stitching the point cloud data obtained in the two modes to complete the environment mapping.

[0052] Specifically, the longitudinal scanning of the LiDAR constitutes a rotational mapping mode, which performs a panoramic coverage scan and switches to a simultaneous positioning and mapping mode after obtaining an initial point cloud map.

[0053] The rotational mapping mode can be achieved by a motor combined with a mechanical structure to drive the laser radar to rotate longitudinally, performing at least one round of rotational scanning at a fixed location.

[0054] In the rotation mapping mode, the point cloud data collected during the scanning process can be stitched using the rotation angle value information fed back by the motor encoder to form a dense point cloud map of the current scene. Specifically:

[0055] For the N frames of point cloud obtained by a round of rotation mapping, the motor encoder is used to obtain the corresponding rotation angle value θ i ,i=0,...,N; for the point cloud sequence numbered 1 to N, the difference in rotation angle between it and the point cloud numbered 0 is used The corresponding rotation matrix Project the point cloud to the laser radar coordinate system when scanning the 0th frame to complete the point cloud stitching; the difference in rotation angle and its corresponding rotation matrix The specific form is:

[0056]

[0057]

[0058] In the rotation mapping mode, the point cloud data collected during the scanning process can be stitched using the point cloud registration algorithm to form a dense point cloud map of the current scene. Specifically:

[0059] For the N frames of point clouds obtained by a round of rotational mapping, the common point cloud registration algorithms such as ICP (iterative closest point algorithm) or NDT (normal distribution transform) are used to complete the inter-frame transformation matrix estimation, and the loop detection algorithm and pose graph optimization algorithm are used to alleviate the drift problem of the point cloud registration algorithm. The optimized inter-frame transformation matrix results are used to complete the inter-frame point cloud fusion to ensure the accuracy of the point cloud fusion results.

[0060] Specifically, the lateral scanning of the lidar constitutes a simultaneous positioning and mapping mode; in the simultaneous positioning and mapping mode, multi-angle scene information is covered by motion to obtain real-time point cloud data.

[0061] In the simultaneous positioning and mapping mode, at least one laser radar continuously moves and scans in the environment to obtain point cloud data. The scanning process covers the multi-angle scene information missing in the rotation mapping mode, and estimates its own posture and constructs a point cloud map of the environment. The following methods can be used:

[0062] In the process of estimating its own posture, the inter-frame posture estimation of the LiDAR is realized by performing point cloud registration on the point cloud data of each frame; the point cloud registration algorithm includes but is not limited to point cloud registration algorithms such as ICP (iterative closest point algorithm) or NDT (normal distribution transformation), and the point cloud data of each frame can also be pre-processed such as extracting corner points and surface points;

[0063] In the process of building the point cloud map of the environment, the point cloud of each frame is subjected to rotation and translation transformation using the result of its own pose estimation to complete the point cloud stitching.

[0064] Figure 2 A flowchart of a feature evaluation method for determining whether pose estimation of real-time point cloud data is degraded is provided in an embodiment, including:

[0065] Step S210, constructing an optimization function of the residual and the pose.

[0066] Step S220, solving the Jacobian matrix.

[0067] Step S230, determine whether it is less than a threshold.

[0068] Step S240: If the value is less than the threshold, the mode is switched back to the rotation surveying mode.

[0069] Step S241: If it is greater than the threshold, continue the simultaneous positioning and mapping mode.

[0070] The specific process is as follows: the device uses the rotation mapping mode when it is initialized, and switches to the simultaneous positioning and mapping mode after completion. The point cloud pose estimation degradation evaluation method is used to determine whether to execute the mode switch, and this operation process is continuously repeated until the mapping task is completed.

[0071] Specifically, the point cloud data obtained in the two modes can be spliced ​​in the following way: align the point cloud maps obtained in multiple rotational mapping modes; if the alignment fails due to insufficient common area or other reasons, first partially fuse the point cloud data collected in the simultaneous positioning and mapping modes at adjacent times to increase the common area of ​​the point cloud map, complete the alignment of multiple maps, and splice them to form a new point cloud map; finally, re-run the pose solution process on the new map for the point cloud data collected in the simultaneous positioning and mapping modes, project the point cloud onto the new map according to the optimized pose, and complete the splicing of all point cloud data.

[0072] In one embodiment, a laser radar device for implementing the above-mentioned mapping method based on mode switching is provided, and the laser radar device includes a hardware device, a rotation surveying and mapping module, a simultaneous positioning and mapping module, a mode switching module and a point cloud map stitching module;

[0073] The hardware device includes a first rotating mechanism, a second rotating mechanism and a laser radar connected in sequence;

[0074] Rotating surveying and mapping module, keeping the second rotating mechanism vertical, the first rotating mechanism and the mechanical structure drive the laser radar to rotate longitudinally, so as to realize multi-angle longitudinal scanning of the laser radar. This state is the rotating surveying and mapping mode;

[0075] The simultaneous positioning and mapping module rotates the second rotating mechanism to the horizontal direction, the first rotating mechanism has no output, and the laser radar continuously moves and scans in the environment to obtain point cloud data. The scanning process covers the multi-angle scene information missing in the rotation mapping mode, and estimates its own posture and constructs a point cloud map of the environment at the same time. This state is the simultaneous positioning and mapping mode;

[0076] The mode switching module switches to the simultaneous positioning and mapping mode after determining that the rotation surveying and mapping mode completes the panoramic coverage scan and obtains the initial point cloud map; in the simultaneous positioning and mapping mode, real-time point cloud data is obtained by covering multi-angle scene information through motion, and a feature evaluation is performed on the real-time point cloud data to determine whether the pose estimation is degraded. If the evaluation result indicates degradation, the mode is switched back to the rotation surveying and mapping mode;

[0077] The point cloud map stitching module is used to stitch the point cloud data obtained in the two modes to complete the environment mapping.

[0078] Specifically, Figure 3 As shown, the first rotating mechanism can be implemented by a motor, and the second rotating mechanism can be implemented by a steering gear, but it is not limited thereto.

[0079] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A mapping method based on mode switching, characterized in that: The method includes: The longitudinal scanning of the laser radar forms a rotating mapping mode; The lateral scanning of the laser radar constitutes a simultaneous positioning and mapping mode. In this mode, the laser radar continuously moves and scans in the environment to obtain point cloud data. The scanning process covers the multi-angle scene information missing in the rotation mapping mode, and estimates its own posture and constructs a point cloud map of the environment at the same time; In the process of estimating its own posture, the point cloud data of each frame is registered to realize the inter-frame posture estimation of the LiDAR. In the process of building the point cloud map of the environment, the result of its own posture estimation is used to apply rotation and translation transformation to the point cloud of each frame to complete the point cloud splicing. Perform panoramic coverage scanning through the rotating surveying mode, and switch to the simultaneous positioning and mapping mode after obtaining the initial point cloud map; In the simultaneous positioning and mapping mode, the multi-angle scene information is covered by motion to obtain real-time point cloud data, and the feature evaluation of whether the pose estimation is degraded is performed on the real-time point cloud data. If the evaluation result shows degradation, it switches back to the rotation mapping mode; The point cloud data obtained in the two modes are stitched together to complete the environment mapping.

2. The mapping method based on mode switching according to claim 1, characterized in that: The rotational mapping mode is achieved by a motor combined with a mechanical structure driving the laser radar to rotate longitudinally, and at least one round of rotational scanning is performed at a fixed location.

3. The mapping method based on mode switching according to claim 1, characterized in that: In the rotation mapping mode, the point cloud data collected during the scanning process is stitched using the rotation angle value information fed back by the motor encoder to form a dense point cloud map of the current scene, specifically: For the N frames of point cloud obtained by a round of rotation mapping, the motor encoder is used to obtain the corresponding rotation angle value θ i ,i=0,...,N; for the point cloud sequence numbered 1 to N, the difference in rotation angle between it and the point cloud numbered 0 is used The corresponding rotation matrix Project the point cloud to the laser radar coordinate system when scanning the 0th frame to complete the point cloud stitching.

4. The mapping method based on mode switching according to claim 1, characterized in that: In the rotation mapping mode, the point cloud data collected during the scanning process is stitched using a point cloud registration algorithm to form a dense point cloud map of the current scene, specifically: For the N frames of point clouds obtained by a round of rotational mapping, the point cloud registration algorithm is used to estimate the inter-frame transformation matrix, and the loop closure detection algorithm and pose graph optimization algorithm are used to alleviate the drift problem of the point cloud registration algorithm. The optimized inter-frame transformation matrix results are used to complete the inter-frame point cloud fusion to ensure the accuracy of the point cloud fusion results.

5. The mapping method based on mode switching according to claim 1, characterized in that: The feature evaluation of whether the pose estimation of real-time point cloud data is degraded is specifically as follows: the real-time point cloud data is registered with the existing point cloud map, and the registration optimization process uses the Gauss-Newton algorithm, wherein the variable to be optimized is multiplied by the Jacobian matrix to obtain the residual matrix; by judging the size of each item of the Jacobian matrix, the influence of the residual item on each dimension of the pose to be optimized is judged; if there is an item in the Jacobian matrix that is less than a set threshold, the pose dimension corresponding to the item is degraded; Δe is the residual item, which is a scalar; ΔT is the pose to be optimized, which is a 6×1 vector; J is the Jacobian matrix, which is a 1×6 vector; Δe=JΔT J=[J1J2J3J4J5J6] Among them, [Δr x ,Δr y ,Δr z ] represents the rotation angle of the laser radar in the x, y, and z directions, [Δt x ,Δt y ,Δt z ] represents the translation of the laser radar in the x, y, and z directions.

6. The mapping method based on mode switching according to claim 1, characterized in that: The point cloud data obtained in the rotational mapping mode is optimized, specifically: all point clouds are traversed, plane points are segmented, and a nonlinear optimization problem is constructed, where the optimization function target is the thickness of the plane point cloud, and the optimization variable is the posture of the point cloud during acquisition; through Gauss-Newton optimization, the point cloud posture is continuously iterated to improve the accuracy of the rotated superimposed point cloud.

7. The mapping method based on mode switching according to claim 1, characterized in that: The point cloud data obtained in the two modes are stitched together, specifically: the point cloud maps obtained by multiple rotation surveying modes are aligned; If the alignment fails, the point cloud data collected in the simultaneous positioning and mapping modes at adjacent times will be partially fused first to increase the common area of ​​the point cloud map, complete the alignment of multiple maps, and stitch them together to form a new point cloud map; finally, the point cloud data collected in the simultaneous positioning and mapping modes will be re-run on the new map for the pose solution process, and the point cloud will be projected onto the new map according to the optimized pose to complete the stitching of all point cloud data.

8. A laser radar device implementing the method as claimed in any one of claims 1 to 7, characterized in that: It includes hardware equipment, rotation surveying and mapping module, simultaneous positioning and mapping module, mode switching module and point cloud map stitching module; The hardware device includes a first rotating mechanism, a second rotating mechanism and a laser radar connected in sequence; The rotating surveying and mapping module keeps the second rotating mechanism vertical, and the first rotating mechanism and the mechanical structure drive the laser radar to rotate longitudinally, so as to realize multi-angle longitudinal scanning of the laser radar. This state is the rotating surveying and mapping mode; The simultaneous positioning and mapping module rotates the second rotating mechanism to horizontal, the first rotating mechanism has no output, and the laser radar continuously moves and scans in the environment to obtain point cloud data. The scanning process covers the multi-angle scene information missing in the rotation surveying mode, and estimates its own posture and constructs a point cloud map of the environment at the same time. This state is the simultaneous positioning and mapping mode; The mode switching module switches to the simultaneous positioning and mapping mode after determining that the rotation surveying and mapping mode completes the panoramic coverage scan and obtains the initial point cloud map; in the simultaneous positioning and mapping mode, real-time point cloud data is obtained by motion coverage of multi-angle scene information, and a feature evaluation is performed on the real-time point cloud data to determine whether the pose estimation is degraded. If the evaluation result indicates degradation, the mode is switched back to the rotation surveying and mapping mode; The point cloud map stitching module is used to stitch the point cloud data obtained in the two modes to complete the environment mapping.

Images