JPS63213005A - Moving object guidance method - Google Patents

Abstract

(57) [Summary] This bulletin contains application data before electronic filing, so abstract data is not recorded.

Description

[Detailed Description of the Invention] [Industrial Application Field] The present invention relates to the guidance and control of autonomous mobile objects (e.g. mobile robots), and in particular, to the guidance and control of autonomous mobile objects (e.g. mobile robots), and in particular to autonomous mobile objects that move autonomously using information from external sensors. Concerning the generation of information necessary for guidance.

[Conventional technology]

It is already known that part of the information necessary for autonomous movement of a mobile body is obtained from external sensors (for example, a range finder, a TV camera, etc.).

One of the ways in which information from external sensors is used is related to maps. Journal of the Robotics Society of Japan, Volume 2, No. 3 (June 1984)
Pages 15 to 23 describe a method of updating a map using an algorithm called associative memory interpolation using ranging data obtained from a laser beam projection type range finder. However, 1. This method is
It is assumed that the amount of movement of the moving object and the direction of the viewpoint are always accurately measured. In addition, IJCAI Proceedings 1983 (IJCAI Proceedings 1983)
ngs.

1983), pages 1125 to 1127, describe a method for obtaining accurate location information from image information from a TV camera and a map. This method takes into account that the position sensor has errors, and generates an approximate image model from the position information obtained from the position sensor and a map, and then converts this into a vertical edge image extracted from the image information from the TV camera. compared to
Determine the exact camera position from the relative position of the corresponding vertical edge. Based on this precise camera position and the map, we then generate an accurate image model that would be obtained from the camera at this position, compare this with the vertical edge image extracted from the camera image, and use the result to determine the scene changes. Detect the presence or absence of.

It is also known to use image information from a TV camera to obtain information regarding the movement or position of a mobile object, without being directly related to a map. Information Processing Society of Japan Computer Vision Subcommittee Computer Vision 35-5 (1
``Environment recognition for mobile robots using moving images'' presented in March 12, 1985) extracts vertical edges from multiple successive image information obtained from TV cameras while moving, and The feature points extracted using this method are associated between these images. Then, optical flow (movement of pixel brightness pattern) is determined for these feature points, and motion parameters are calculated using this. Also, Artificial Intelligence
17 (1981), pages 185 to 203, also describes a method for determining motion by calculating optical flow from successive image information.

[Problem that the invention seeks to solve]

The method described in the Journal of the Robotics Society of Japan, Vol. 2, No. 3 is as follows:
There is a practical problem in that this method does not take into account errors that are necessarily included in position information obtained from position sensors such as encoders. Furthermore, the method described in IJCAI Proceedings 1983 has the risk of causing errors because edge information extracted from image information is susceptible to noise, and there is room for improvement in this respect.

In addition, the method shown in Combita Vision 35-5 has difficulty in obtaining high accuracy due to the small number of feature points that can be used for matching, and the method shown in Artificial Intelligence 17 The described algorithm has difficulty calculating accurate optical flow in real images with many edge parts.

[Means for solving problems]

The present invention attempts to solve the above-mentioned problems by a new method of using distance information. That is, the present invention predicts the distance information that is expected to be obtained from the distance measuring means from the position information obtained from the position detecting means and the current document information in the storage means, and combines this predicted distance information with the actual information. Correlate the distance information obtained from the distance measuring means to estimate the accurate current position. Then, the information obtained in this estimation process is used to update the material information in the storage means.

To give a more specific example, in the first embodiment, the material information is a map, and a group of distance values to be obtained from the ranging sensor is predicted from the position information from the position detection means and the map, and this predicted The accurate current position is estimated by associating the distance value group obtained with the distance value group actually obtained from the distance measurement sensor. The map is then updated using the information obtained in this estimation process (results of association and current position).

In the second embodiment, the distance measuring means obtains distance image information from image information from a plurality of imaging means (for example, by stereoscopic viewing).
generate. The distance image information obtained from the distance measuring means in the previous process and the corrected position information are stored in the storage means as material information.

The distance image information to be obtained from the distance measuring means this time is predicted from the position information from the position detecting means, the distance image information in the storage means, and the old position information, and this predicted distance image information is actually used by the distance measuring means. The accurate position is estimated by associating the distance image information obtained from the Then, the old information in the storage means is replaced with the distance image information obtained from the distance measurement means this time and the corrected position information.

[Effect]

According to the present invention, the distance information that should be obtained is approximately predicted based on the position information including the error from the position detection means, and the predicted distance information is correlated with the actually obtained distance information. , the current position can be estimated, and the influence of errors can be corrected or removed. The material information is updated to be more accurate using the information obtained in this estimation process, and as a result, the accuracy of the next estimation is increased. Since neither vertical edges nor optical flows are used, the above-mentioned problem does not occur.

For example, in the first embodiment, the actual position of a specific point on the map can be detected from the association between the predicted distance value group and the actually obtained distance value group, so the accurate current position can be estimated. By using this current position and the results of the correspondence, the map is corrected to be more accurate. The aforementioned difficulties due to the use of vertical edges are eliminated.

Regarding the second embodiment, from the correspondence between each point of the predicted distance image information and the actually obtained distance image information, it is possible to determine the difference between the position indicated by the position information from the position detection means and the actual position. The deviation is known and therefore the amount of correction to the output of the position detection means can be determined. The corrected position information and the current distance image information are used to predict the next distance image information. The above-mentioned difficulties associated with the use of vertical edges and optical flows do not occur.80 [Embodiment] Fig. 1 shows the relationship between functional blocks in the first embodiment of the present invention, and Fig. 2 shows the relationship between the functional blocks of the first embodiment of the present invention. The processing process according to this embodiment is shown in a flowchart. For mobile objects,
Although not shown, there is a position sensor, such as an encoder, that measures information regarding the position of a moving object (position, orientation, etc.), and a distance sensor (such as a laser beam projection type) that measures the distance from the moving object to an external object. A range finder) is provided, and plane map information (hereinafter simply referred to as a map) is provided in advance. This pre-given map (a priori map) shows the planar shape of the moving area surrounded by walls and the positions and planar shapes of some objects existing there, but it also shows the location, size, and number of objects. is not necessarily accurate. It is assumed that the shapes of objects that may exist within the moving area are known, and that the actual flow side is limited to objects having a rectangular planar shape (for example, a rectangular parallelepiped).

First, an overview will be explained with reference to FIGS. 1 and 2. The distance data generation unit 11 predicts the distances of various points on external objects, that is, the distance data that should be obtained from the distance measurement sensor at the present time, from the data on the position and orientation of the moving body obtained from the position sensor and the a priori map. Calculate the value (
Figure 2 21).

This predicted value includes errors in the map itself and errors in the position sensor. The distance data predicted in this way and the distance data actually obtained from the distance measuring sensor are grouped into segments corresponding to individual surfaces in segmentation units 12a and 12b, respectively (FIG. 2 22). . Independently of this segmentation processing, the predicted distance data and the actual distance data are subjected to a default correspondence by the low-level matching unit 13 (FIG. 2 23).
. Although the flowchart of FIG. 2 shows segmentation followed by low-level matching, these may be performed in the reverse order or in parallel.

The high-level matching unit 14 receives the processing results of the segmentation units 12 a and 12 b and the processing results of the low-level matching unit 13 , and combines these with basic environmental structure knowledge (positions of corners where walls meet, etc.) 15 The mapping of the segments by low-level matching is corrected as necessary (Fig. 2, 24), and the accurate position and orientation of the moving object is determined using the results of the mapping (Fig. 2).
Figure 25).

Finally, the map updating unit 16 updates the high level matching unit 1
Based on the processing result of step 4, the a priori map is corrected (addition/subtraction of objects, correction of two positions, etc.) (FIG. 2, 26). The accurate position and orientation information determined as described above is also used for controlling the moving object as necessary.

Next, details of each process will be explained. Data from a position sensor such as an encoder is as shown in Figure 3 (A).
It shows that the moving body is at the coordinates (X-axis, y□) and facing the direction (angle from the X-axis) ol, but as shown in Figure 3 (B), the true coordinates are (X21 yz)
, and the true direction is assumed to be θ2. However, X21
y21 θ2 is unknown. In Figure 3 (A), ψ
represents the known viewing angle of the ranging sensor. The distance data generation unit 11 generates data X1+Vx+ obtained from the position sensor.
01 and the a priori map, calculate the distances of various objects within the viewing angle ψ in FIG. 3(A). An example of a graph of distance data calculated in this way is shown in Figure 4 (A).
Shown below. In this example, assume that the moving area is a rectangular area surrounded by walls, and that the a priori map indicates that two rectangular parallelepiped objects are present in this area. The vertical axis of the graph is the distance, and the horizontal axis is the angle 0 measured from one end of the field of view (see FIG. 3(A)). Figure 4 (B) is
An example of a graph of distance data actually obtained from a distance measurement sensor is shown. In this example, objects corresponding to the two rectangular parallelepipeds shown on the a priori map are placed in the actual movement space with somewhat different sizes and positions from those on the map, and objects that are not shown on the a priori map are placed in the actual movement space. Suppose that there exists a third rectangular parallelepiped object.

The segmentation units 12a and 12b examine the rate of change in distance with respect to θ, consider points with a large rate of change as boundaries, and form a plurality of segments.

As a result, for the distance data calculated from the a priori map, the segments ao, a shown in FIG.
t, a2. a3 is obtained, and segment b shown in FIG. 4(B) is obtained for the distance data from the distance measuring sensor. ,
b□l b2t b31 b4. bstb6 is obtained.

The low-level matching unit 13 performs correspondence between distance measurement points of distance data calculated from an a priori map and distance measurement points of distance data from a distance measurement sensor. This association is a process of determining the distance measurement point of the other corresponding to each distance measurement point of one, and is, for example,
The method described in the publication can be implemented by using distance instead of brightness. By combining this correspondence and the segmentation results, the segments shown in FIGS. 4(A) and 4(B) can be tentatively correlated as follows.

a[1(-)bll al,)b□ 2ob2 a3ob3. b4. b5. bG The high-level matching unit 14 performs processing when there is no one-to-one correspondence as in a3 above, and determines the correct position.
Perform the following:

First, one segment i obtained from the a priori map
, processing will be described when a plurality of segments j1 to jV obtained from data from a ranging sensor are associated with each other. In this case, these multiple segments j1 to
jK into groups based on the mean and variance of the distance values, then modify the grouping so that the context is not unnatural, and then correspond to segment i based on the mean and variance of the distance values. Determine the group of segment j to be used. FIG. 5 shows segments j1-j, which are generally associated with segment i. First, based on the average and variance of the distances, (j + j31 Js), (j21
The groups J9), (j41 js+js), and (j7) are formed. However, this grouping results in unnatural relative positions. For example, group (j41 j6
+ je ) indicates a single object, there would be j5 between j4 and 56, which is further away than them, which is unreasonable. However, it is not unreasonable that j7 exists between j6 and jul, which is closer than them. Similarly, combining j2 and j9 into a single group would lead to unreasonable results. Therefore, subgroups separated by more distant segments are modified to form different groups. Through this process, (j + J31 j5), (j2), (j4), (
The groups JGrJ8), (j7), (jg) are obtained, and each group is considered as a single segment corresponding to a single object. Then, one of the segments obtained in this way is divided into segments i based on the mean and variance of the distances.
map to. Other segments are considered objects not on the a priori map and undergo additional processing in the map update described below.

In addition, the correspondence between segment i obtained from the a priori map and segment j obtained from ranging sensor data is
Even if it is obtained by low-level matching, if another segment i′ obtained from the a priori map that is associated with j with a higher probability is found by high-level matching, the association is modified, Segment j is subject to deletion in map update.

Next, determining the correct position and orientation will be explained. It is generally possible to predetermine fixed feature points on an a priori map, typically corners where walls meet. The pair of walls forming this corner is known on the map, and therefore it is also known which of the segments obtained from the a priori map correspond to these walls.

In the example of FIG. 3A, segments al and 82 correspond to these walls, and the points of contact of both segments correspond to the corners. Therefore, once the association of segment 1- is completed as described above, the segment obtained from the ranging sensor data corresponding to the wall can be specified. In the example of FIG. 3(B), bl and b2 correspond to al and 82, respectively. As a result, a geometrical relationship as shown in FIG. 6 is obtained. In FIG. 6, the coordinates of corner C are segment a
It is known as the intersection of the walls corresponding to 1 and 82, and
Distance ρ from sensor S to segment b1.

ρ′ and the angle between them can also be known from the ranging sensor data. Therefore, using these, the sensor S
In other words, the position and orientation of the moving object can be calculated.

The map update unit 16 updates the a priori map using the results of the matching process described above.

First, the distance data obtained from the ranging sensor is converted into coordinate data in the same coordinate system as the a priori map, taking into account the sensor position determined as described above. 7th
FIG. 7(B) shows the distance data from the ranging sensor converted in this way, and FIG. 7(A) shows the portion of the a priori map corresponding to FIG. 7(B). Next, parallel movement is performed so that the vertices of corresponding segments coincide. The apex of a segment is generally the endpoint of the segment, however, where a segment closer to the sensor hides a portion of a segment further away, only the endpoint of the nearer segment is treated as the apex. For example, in FIG. 7(A), the end point v1, which is the point of contact between segments a1 and a2, is the vertex, but regarding al and ao in front of it, ao
Only the end point vo of is a vertex. Therefore, Fig. 7 (A
), VO, vt, va are the vertices, and Fig. 7 (
In B), V'0. V' t, v' a, V'
a, v' 5 is the vertex.

By the way, from the result of segment mapping mentioned above,
These vertices can also be mapped. In the case of FIGS. 7(A) and (B), vo is v'o.

V' to vl 1. V'8 corresponds to V8, and v'
4 and V'B have no corresponding vertices. The vertices defined in this way are used to modify the map. First, the a priori map is translated and rotated so that vertices v1 and v't corresponding to the corners overlap, and segments al and bl and a2 and b2 corresponding to the walls forming the corners overlap, respectively. Each vertex on the a priori map is then independently translated to overlap the corresponding vertex on the map obtained from the ranging sensor data, and each segment extending from these vertices is rotated to correspond. Overlay the segment, thereby modifying the position of each object.

Further, a segment having vertices at both ends is matched with a corresponding segment by a reduction/enlargement operation, thereby modifying the dimensions of the object.

If there are segments and vertices on the a priori map that do not have corresponding segments and vertices on the ranging sensor data, the corresponding objects are deleted from the a priori map. vice versa,
b 41t in Figure 7(B)) gg V' 41
If there is a segment and a vertex on the ranging sensor data that do not have a corresponding segment and vertex on the a priori map, as in V' 5, an object whose planar shape is a rectangle defined by this segment and vertex will be on the a priori map. will be added.

According to this embodiment, the accurate position at each point in time is determined using distance measurement data obtained from moment to moment and position data including errors, and the built-in map is gradually updated to be more accurate. Can be done. Since it uses known feature points on the map such as corners, it is easy to determine the exact location, and it also performs segmentation processing and grouping (clustering) processing based on the average and variance of distances. As a result of its introduction, the influence of noise in ranging data is reduced.

FIG. 8 shows the relationship between the functional blocks of the second embodiment of the present invention, and FIG. 9 shows a flowchart of the processing process according to this embodiment. In this embodiment, the mobile object is equipped with a position sensor (encoder, etc.) which is not necessarily accurate, and two TV cameras for obtaining distance information using the principle of stereoscopic vision.

First, an overview will be explained with reference to FIGS. 8 and 9. The distance image generation unit 31 generates distance image data of the outside world from the raw image data sent from the two TV cameras using the principle of stereoscopic vision (FIG. 9, 41). This distance image data and data on the position and orientation (line of sight) of the moving body obtained from the position sensor are stored in the distance image/position information storage section 32 (FIG. 9, 42). The predicted distance image generation unit 33 calculates the current distance image generation unit based on the newly input current position/orientation data and the position/orientation data and distance image data from the previous processing held in the storage unit 32. Predictively generate distance image data to be obtained from 31 (9th
Figure 43). The distance image matching unit 34 matches between each point within the field of view between the predicted distance image data generated by the predicted distance image generation unit 33 and the current actual distance image data generated by the distance image generation unit 31. (FIG. 9, 44), and the attitude detection unit 35 uses the result of the association to determine the amount of correction for the position/orientation data obtained from the encoder, and stores the position/orientation data in the storage unit 32. Correct the orientation data (FIG. 9, 45). This correction amount is also used to control the moving body as necessary.

Next, details of each process will be explained. The generation of distance image data by the distance image generation section 31 is based on the principle of binocular stereoscopic vision, and the details are described in Japanese Patent Laid-Open No. 117672/1983. In short, this method searches between images from two TV cameras corresponding to a person's eyes, and for each pixel in one image, a pixel that is an image of the same external point is found in the other image. The amount of parallax (disparity)
Determine S, and calculate the coordinates (x, y
t2). The generated distance image data is the amount of parallax for each pixel and the coordinates of the corresponding external boundary point.

The predicted distance image generation unit 33 calculates the coordinates of each point indicated by the previous distance image data based on the difference between the previous (corrected) position and orientation and the position and orientation indicated by the current position sensor output.
The predicted distance image data is obtained by converting the coordinates into coordinates on a coordinate system having the position and orientation indicated by the position sensor output, and removing portions that cannot be seen by the camera as a result of this coordinate conversion.

The distance image matching section 34 first performs the distance image generation section 3
From the distance image data sent from 1, using the previous and current position and orientation data, remove the part that was not captured by the camera at the previous position and orientation. Then, the correspondence described in the first step is performed.

The matching is performed within each group by grouping various coordinate points having the amount of parallax within a certain range, taking into account the error in the amount of parallax S. As shown in FIG. 10(A), the amount of parallax S is in the range O<S<d (hereinafter referred to as (0, d
) is a real number, but its value has an error range ΔS due to various factors related to distance image generation processing.

Then, the error in the amount of parallax S causes an error in the coordinates Cxt y+ z) of the corresponding external boundary point calculated using it.

FIG. 11 shows, as an example, the relationship between the depth y and the amount of parallax S. If the true amount of parallax is within the range of ΔS before and after the amount of parallax β obtained by generating the distance image, the true value of y is y (
s-ΔS) and y(s+ΔS). X and 2 also change depending on the error in the amount of parallax. FIG. 10(B) shows the range (S-ΔS, s+ΔS) in the predicted distance image.
The coordinate point group (Plo,
P2'.

......, PNO), and Fig. 10 (C) shows,
In the current distance image obtained from the raw image, coordinate points (Pr”
, P2',..., PMl). All coordinate points have a possibility of correspondence between these two groups.

Therefore, for a certain amount of parallax S, the range (S - ΔS, s
+ΔS] between the set of coordinate points of the predicted distance image (represented by Do(s)) and the set of similar coordinate points of the current distance image (represented by Dz(s)). So, D
The coordinate point Pki in Dz(s) corresponding to each coordinate point PLO in o(s) is determined by the following equation.

(However, PJoEDO (S) + Pl'EDI (S)
) That is, a pair of coordinate points whose sum of distances to all other coordinate points belonging to each set are as similar as possible are determined to be corresponding. Pk
``, conversely, the one that best corresponds to Pk'' is selected from among these PIOs.

The above correspondence divides the entire range of parallax amount (0°d) into a multivalued s1.
2. ... will be carried out for each of them.

Finally, the posture detection unit 35 first detects the pair of corresponding coordinate points (P l., P b ') obtained for each range of the amount of parallax S (S-ΔS, s+ΔS) as described above. The variance σ (s) is calculated using the following equation.

However, K is the number of pairs in the desk, and if K is 0, σ(s) is set to +ω.

Next, the set (p O□, Plkm) with the minimum variance is selected, the position correction amount M is calculated using the following equation, and it is added to the position/orientation data obtained from the position sensor.

M=ΣPOt+++, P'kwa This process, as shown in FIG.
Let o and Fo be the true position of the moving object this time and the position indicated by the position sensor as T1 and Fl, respectively, then find the vector quantity, add it to Fl, and find the position of point F* from this. corresponds to

According to this embodiment, by performing correspondence between successive images using distance information derived from the images, it is possible to obtain higher accuracy than with the conventional technology using optical flow for gray scale images, Furthermore, compared to the conventional technique that uses feature points on vertical edges, it is possible to use a much larger number of corresponding points, resulting in improved accuracy. Furthermore, within a certain range of parallax considering the error range,
Correlation further improves accuracy.

〔Effect of the invention〕

As is clear from the above, according to the present invention, by using distance information for accurate position estimation and updating of document information, it is possible to obtain information necessary for guiding and controlling a moving object with high accuracy. .

[Brief explanation of the drawing]

Fig. 1 is a block diagram showing the relationship between functional blocks of the first embodiment of the present invention, Fig. 2 is a flowchart of the first embodiment, and Fig. 3 shows the position/direction of the moving body indicated by the position sensor and the actual position.・A diagram showing the orientation in contrast, Figure 4 is a graph showing the predicted distance data and actual distance measurement data in contrast,
Figure 5 is a diagram showing an example of one-to-many correspondence between segments;
The figure is a plan view showing the geometric relationships used to determine accurate position and orientation, FIG. 7 is a plan view showing an example of the relationship between segments and vertices, and FIG. A block diagram showing the relationship between functional blocks, Figure 9 is the second
Flowchart of the embodiment, FIG. 10 is a diagram showing the error in the amount of parallax and the distribution of coordinate points caused by it, FIG. 11 is a graph showing the relationship between the amount of parallax and depth, and FIG. 12 is for explaining the position correction process. is a vector diagram. 11... Predicted distance data generation unit, 12a, 12b...
- Segmentation unit, 13.14...Matching unit that performs correspondence and position estimation, 16...Map update unit, 21...Predicted distance data generation process, 22...Segmentation process, 23-25... - Correspondence is and position estimation processing, 26...Map update processing, 31...Distance image generation unit, 32...Storage unit for distance image and position/orientation data, 33...Predicted distance image Generation section, 34.
. . . A matching unit that matches the actual distance image and the predicted distance image; 35 . . . A position detection unit that determines the amount of position correction;
41...Distance image generation process, 42...Storage of distance image and position/orientation data, 43...Predicted distance image generation process, 44...Associating process, 45...Position correction process.

Claims (1)

[Scope of Claims] 1. Distance measuring means for obtaining information regarding distances from a moving object to various points on external objects, position detecting means for obtaining information regarding the current position of the moving object, and a guidance control system. In the mobile object guidance device, the moving object guidance device includes a storage means for storing document information for the purpose of the present invention, and a position estimating means connected to the distance measuring means and the position detecting means. a step of predicting from the output information of the position detection means and the material information in the storage means; and a more accurate current position of the moving body by associating the information obtained in the prediction step with the output information of the distance measuring means. A method for guiding a moving object, the method comprising: estimating the amount of information obtained by the estimating step; and updating material information in the storage means using the information obtained in the estimating step. 2. The moving object guidance method according to claim 1, wherein the distance measuring means is a distance measuring sensor that outputs a distance value, and the material information is map information. 3. In claim 2, the estimating step includes:
a step of dividing a group of distance values from the distance measuring sensor into a first segment group; a step of dividing a group of distance values obtained in the prediction step into a second group of segments; and a step of associating segments between a second group of segments. 4. In claim 3, the matching step groups a plurality of segments associated with a single segment into a plurality of segment groups based on their distance values, and divides the group into a plurality of segment groups based on their distance values. A method for guiding a mobile object, the method comprising the step of associating with segments. 5. In claim 3 or 4, the estimating step includes estimating the current position based on predetermined feature points on the map information and points on the first segment group corresponding thereto. A mobile object guidance method, including: 6. The moving body guiding method according to claim 5, wherein the predetermined characteristic point is a corner where two walls are in contact with each other. 7. The mobile object guidance method according to claim 3, 4, 5 or 6, wherein the updating step updates the map using the estimated current position and the result of the association. 8. In claim 1, the distance measuring means includes a plurality of imaging means and means for generating distance image information consisting of information regarding distances of various points on the external object from the outputs of the plurality of imaging means. The material information in the storage means is distance image information and moving object position information obtained in the previous process, and the estimation step determines the amount of correction of the position information obtained from the position detection means, In the moving object guidance method, the updating step replaces the information in the storage means with the distance image information obtained in the current process and the corrected position information. 9. In claim 8, the distance image information includes the amount of parallax between corresponding pixels based on a stereoscopic viewing method, and the estimating step includes the coordinate points indicated by the distance image information from the distance measuring means and the amount of parallax obtained from the prediction. A method for guiding a moving object, comprising the step of associating coordinate points indicated by distance image information obtained for each range divided based on the accuracy of the amount of parallax. 10. In claim 9, the estimating step includes a step of examining the degree of correspondence between the coordinate points in the various ranges of the amount of parallax, and a step of determining the distance between the corresponding coordinate points belonging to the range with the highest degree of correspondence. A moving object guidance method, comprising the step of determining the correction amount based on the amount of correction.