JPH07101368B2 - Travel control device - Google Patents

Description

TECHNICAL FIELD The present invention relates to a travel control device for a moving body such as an unmanned vehicle.

[Prior Art] When transporting articles in factories and the like, unmanned vehicles are widely used. The running control method of this unmanned vehicle is as follows: (1) electromagnetic induction path (Fig. 4 (a)), (2) optical tape (Fig. 4 (b)), (3) wheel or drive A typical example is a self-sustaining system that utilizes the number of revolutions of the device (Fig. 4 (c)).

As shown in FIG. 4 (a), the electromagnetic induction path of (1) supplies a low-frequency current from the low-frequency oscillator 1 to the electromagnetic induction path 2, and the magnetic field generated by this is supplied to the unmanned vehicle 3. While being detected by the pickup (not shown), the vehicle travels on the electromagnetic guide path 2. In this case, a marker 4 for position detection is installed near the branch point and the stop point and is used for position detection of the unmanned vehicle 3 and branch / stop control. As the marker 4, an electromagnetic or optical proximity sensor is used.

With the optical tape of (2), as shown in FIG. 4 (b), a reflective tape 5 is attached to the floor surface, and traveling is performed while detecting this with an optical sensor (not shown) on the unmanned vehicle 3. To do. Some codes such as bar codes are recorded on the reflection tape 5 so that more detailed control can be performed.

As shown in FIG. 4 (c), the self-running type of (3) has pulse pickups 7a mounted directly on both sides of the vehicle body 6 and directly connected to the wheels 7, and the pulse output of the pulse pickup 7a is controlled by the control unit 8. While comparing and accumulating, the wheels 9 are driven by the driver 9 to travel while detecting the position and direction of the vehicle body 6.

[Problems to be Solved by the Invention] The above control methods (1) to (3) have the following drawbacks.

First, in the control methods (1) and (2), since the taxiway is set in advance, (a) it is difficult to carry out autonomous free running in an extreme environment or in an automated factory. (B) Traveling path There were problems such as high material costs, construction costs such as grooving, and tape sticking, and (c) difficulty in changing roads due to factory layout changes.

Further, in the control method of (3), (a) position errors caused by wheel slips and floor surface irregularities are accumulated, and traveling becomes uncertain.

(B) An ultrasonic sensor or the like is used as an auxiliary sensor in order to correct the accumulated position error, but sufficient reliability has not been obtained yet.

The present invention has been made under the background described above, and an object of the present invention is to provide a traveling control device that does not require a taxiway and is capable of highly reliable free traveling.

[Means for Solving Problems] A traveling control device according to the present invention includes: (a) a monocular image pickup unit having a focal length f and an optical axis having a depression angle α for picking up an image of a moving body moving on a plane; b) The position Pai of the feature point on the moving body is calculated by the following formula from the image of the feature point on the moving body and the vanishing line which is an infinite line generated by the central projection of the plane, and xai = (ξai / f) ・ {(f ・ tanα-ηa ₀ ) / (f ・ tanα-ηai)} ・ za ₀ yai = (ηai / f) ・ {(f ・ tanα-ηa ₀ ) / (f ・ tanα-ηai)}・ Za ₀ zai ＝ {(f ・ tanα−ηa ₀ ) / (f ・ tanα−ηai)} ・ za ₀ Position of the feature point on the moving body; Pai (xai, yai, zai) Criterion of the feature point on the moving body Position; Pa ₀ (ax ₀ , ya ₀ , za ₀ ) Position of the feature point on the image plane; Qai (ξai, ηai) Reference position of the feature point on the image plane; Qa ₀ (ξa ₀ , ηa ₀ ) Image plane Η ∞ = f · tan α The position of the other feature point on the moving body is determined by Pbi using the same equation. Calculated, xbi = (ξbi / f) · {(f · tanα-ηb 0) / (f · tanα-ηbi)} · zb 0 ybi = (ηbi / f) · {(f · tanα-ηb 0) / (f ・ tanα-ηbi)} ・ zb ₀ zbi ＝ {(f ・ tanα−ηb ₀ ) / (f ・ tanα−ηbi)} ・ zb ₀ x-axis of the line segment Pai, Pbi of these feature points on the plane An angle with and φi, the direction of the line segment is calculated by tan φi = {(zbi-zai) / (xbi-xai)} cosα, and a calculating means for calculating the position and direction on the plane of the moving body, (C) control means for controlling the traveling of the moving body based on the output of the computing means.

[Operation] According to the above means, the plane in the three-dimensional space is based on the respective image forming positions of the image of the reference point and the images of the two or more feature points of the moving body formed on the image pickup screen by the image pickup means. The position and direction of the moving body that travels freely in the area are required. Therefore, autonomous and free running control of the moving body becomes possible.

It should be noted that when a moving body that moves freely on a plane is recorded as a continuous image by a fixed TV camera and the movement of the moving body in the original three-dimensional space is obtained from these image sequences, conventionally, Although an extremely complicated equation including a trigonometric function had to be solved, the above means allows the position and movement of the moving body to be obtained by simple addition, subtraction, multiplication and division.

[Embodiment] An embodiment of the present invention will be described below with reference to the drawings.

FIG. 1 is a block diagram showing the configuration of a traveling control device according to an embodiment of the present invention. In this figure, reference numeral 11 denotes an unmanned vehicle (moving body), which travels on a plane 12 having no taxiway under control. Reference numeral 13 denotes a monocular TV camera fixed at a predetermined position, which captures the unmanned vehicle 11 from the outside. In this case, the optical axis (z axis) of the TV camera 13
Are inclined by an angle α from the horizontal plane. It should be noted that there is no twist around the optical axis.

The image of the unmanned vehicle 11 taken by the television camera 13 is supplied to the arithmetic unit 14 having an A / D converter and an arithmetic circuit. This image contains the entire image of the unmanned vehicle 11. The arithmetic unit 14 extracts the images of two specific points (feature points) Pa and Pb of the unmanned vehicle 11 from these images, and performs arithmetic operations to be described later on these to continuously determine the position and direction of the unmanned vehicle 11. Calculated.
The calculation result is supplied to the control device 15, and the control device 15 controls the traveling of the unmanned vehicle 11 based on the calculation result. In addition,
The signal transmission from the control device 15 to the unmanned vehicle 11 may be wired or wireless and is appropriately selected.

Next, FIG. 2 is a diagram showing the relationship between Pa and Pb on the moving body and the image plane. In this figure, the optical axis of the television camera is the z axis, and the axis orthogonal to the z axis in the vertical plane including the z axis is y.
The axis orthogonal to the axis, the y axis, and the z axis is the x axis, and the lens focal length of the television camera is f. Also, the feature point Pa is
Pa ₀ → Pa ₁ → Pa ₂ ...... Moves in the three-dimensional space (xyz coordinate system) Pai (i = 0,1,2, ...)
The coordinates of (xai, yai, zai) and the image plane 16 (ξ−η
The coordinate of the image in the coordinate system is Qa as shown in Fig. 3.
i (ξai, ηai). The same applies to the feature point Pb.

With this setting, the reference point Pa ₀ (x
The point Pa ₁ (xa ₁ , ya ₁ , za ₁ ) after moving from a ₀ , ya ₀ , za ₀ ) is the image Qa ₀ (ξa ₀ , ηa ₀ ) of the reference point Pa ₀ on the image plane and the point Pa 1. ₁
Image _{Qa 1 (ξa 1, ηa 1} ) of can be calculated based on. Hereinafter, this calculation method will be described in detail.

<Basic Matters> First, the calculation method used in the present embodiment is a computer collection “Computer Vision (1981)” published on May 14, 1981 by the Computer Vision Research Group of the Information Processing Society of Japan.
It is based on some formulas published in the paper "Analysis of three-dimensional movement using virtual infinite point due to object movement" (Nagura, Saito, Kitahashi) in (Category 12-4). Therefore, before explaining the calculation method according to the present embodiment, the basic matters described in the above paper will be described in order to facilitate the understanding thereof.

FIG. 6 shows the origin O of the three-dimensional space (xyz orthogonal coordinate system).
Position the TV camera so that the center of the lens is located at
The case where a point P (x, y, z) in a three-dimensional space is imaged is shown. In order to match the coordinate system shown in Fig. 2 in Fig. 6, the coordinate axes are set differently from those published in the above paper, and the x, y, z parts in the paper are as follows. In the explanation, it is z, x, y.

In FIG. 6, the z-axis coincides with the optical axis of the television camera, and the x-axis and the y-axis are orthogonal to the z-axis at the origin O (lens center). Further, in FIG. 6, reference numeral 100 is an image pickup plane on which an image picked up by a television camera is formed. The imaging plane 100 is a plane parallel to the xy plane, and is located at a position O ′ separated from the origin O by the focal length f of the lens in the z-axis direction. Then, on the imaging plane 100, a ξ-η coordinate system is set which is composed of ξ axis and η axis which are parallel to the x axis and the y axis, and whose origin is at the position O ′. Although the imaging plane 100 is actually on the opposite side (that is, the −z side) from the point P that is the imaging target when viewed from the lens center (origin), it is separated by f on the z side in FIG. 6 for convenience of illustration. It is shown in only one position. It should be noted that whether the imaging planes are provided in the + z direction or the -z direction of the origin is provided, the matters described below still hold.

In FIG. 6, a point Q (ξ, η) is an imaging plane 100 (ξ-η) when the point P (x, y, z) in the three-dimensional space is centrally projected through the lens of the television camera. The image of the point P imaged in the coordinate system is shown.

As shown in FIG. 6, the image Q of the point P is located on the imaging plane 100 at the point where the straight line connecting the point P and the origin O intersects. Then, each coordinate value of the point Q in the ξ-η coordinate system can be expressed as follows by using the focal length f on the z axis and each coordinate value of the xyz coordinate system.

ξ = (f / z) x (1) η = (f / z) y (2) Next, we show how this straight line PO is mapped onto the image plane.

Now, as is well known, the direction cosine has l, m, n, and the point (x ₀ , y ₀ , z
The equation of a straight line passing through ( ₀ ) is (x−x ₀ / l) = (y−y ₀ / m) = (z−z ₀ / n) (3) where l ² + m ² + n ² = It is represented by 1.

By modifying this equation (3), x and y can be expressed as a function of z as follows.

x = (l / n) (z−z ₀ ) + x ₀ (4) y = (m / n) (z−z ₀ ) + y ₀ (5) Then, these expressions (4) and (4) 5) to the above formula (1)
By substituting in (2) and (2), the following equations are obtained.

ξ = {(z−z ₀ ) / z} · (l / n) · f + (f / z) · x ₀ …
(6) η = {(z−z ₀ ) / z} · (m / n) · f + (f / z) · y ₀ ...
(7) It is understood that the above equations (6) and (7) are equations that easily represent a straight line by eliminating z. Thus, when a straight line having a direction cosine l, m, n in the three-dimensional space and passing through the point (x ₀ , y ₀ , z ₀ ) is centrally projected, ξ −
The image formed on the η plane is a straight line and can be represented by equations (6) and (7).

Then, when ξ and η when z → mark ∞ in the above equations (6) and (7) are ξ∞ and η∞, only the first term remains, and ξ∞ = (l / n) · f …… (8) η∞ ＝ （m / n） ・ f …… （9）. The above equations (8) and (9) show that, when a group of straight lines having the same direction cosine is formed on the imaging plane 100, each image of each straight line converges to one point (ξ∞, η∞). Shows. This point is called the "vanishing point".

When the above equations (6) and (7) are expressed by using ξ∞ and η∞, ξ = ξ∞ {1- (z ₀ / z)} + (f / z) x ₀ (10) η = η∞ {1- (z ₀ / z)} + (f / z) y ₀ (11).

Now, the imaging plane 100 of the point P ₀ (x ₀ , y ₀ , z ₀ ) in the three-dimensional space
If the image formation position in (ξ-η coordinate system) is P ₀ ′ (ξ ₀ , η ₀ ), then ξ ₀ = (f / z ₀ ) x ₀ (12) η ₀ = (f / z ₀ ) Y ₀ ... (13)

Next, based on the obtained arithmetic expression, that is, using the imaging plane, a mathematical expression for calculating the unknown point P ¹ in the three-dimensional space from the known point P ⁰ is calculated.

Has a direction cosine l, m, n in a three-dimensional space and has a known point P ₀
The image forming position Q ₁ (ξ ₁ , η ₁ ) of the point P ₁ (x ₁ , y ₁ , z ₁ ) on the straight line passing through (x ₀ , y ₀ , z ₀ ) on the imaging plane 100 is expressed by the above equation ( 1
Substituting z = z ₁ into 0) and (11), we get:

ξ ₁ = ξ ∞ {1- (z ₀ / z ₁ )} + (f / z ₁ ) x ₀ (14) η ₁ = η ∞ {1- (z ₀ / z ₁ )} + (f / z ₁ ) y ₀ (15) Then, multiplying both sides of the above equation (14) by z ₁ , z ₁ · ξ ₁ = (z _{1 −} z ₀ ) · ξ ∞ + x ₀ · f When transformed, z ₁ · (ξ ₁ −ξ ∞) = −z ₀ · ξ ∞ + x ₀ · f (16)

On the other hand, when the above formula (12) is modified, x ₀ · f = z ₀ · ξ ₀ , and when this is substituted into the above formula (16), the following formula is obtained.

z ₁ · (ξ ₁ −ξ∞) = z ₀ · (ξ ₀ −ξ∞) (17) Perform the same calculation for η ₁ .

That is, by multiplying both sides of the equation (15) by z ₁ to obtain z ₁ · η ₁ = η∞ (z ₁ −z ₀ ) + f · y ₀ , and transforming this, z ₁ · (η ₁ −η∞ ) = − Z ₀ · η∞ + y ₀ · f (18)

On the other hand, when the above equation (13) is modified, y ₀ · f = z ₀ · η ₀ , which is substituted into the above equation (18) to obtain the equation (19) corresponding to the equation (17).

z ₁ · (η ₁ −η ∞) = z ₀ · (η ₀ −η ∞) (19) Then, when the above equations (17) and (19) are summarized, (z ₁ / z ₀ ) = { (Ξ ₀ −ξ∞) / (ξ ₁ −ξ∞)} = {(η ₀ −η∞) / (η ₁ −η∞)} ...
(20) is obtained.

On the other hand, ξ ₁ , η ₁ can be expressed as ξ ₁ = (f / z ₁ ) x ₁ …… (21) η ₁ = (f / z ₁ ) y ₁ …… (22). Equations (12) and (1
By (3) and, (x ₁ / x ₀ ) ＝ (ξ ₁・ z ₁ / ξ ₀・ z ₀ ) …… (23) (y ₁ / y ₀ ) ＝ (η ₁・ z ₁ / η ₀・ z ₀ ) …… (24) is obtained. Then, if each of these equations is transformed based on the above equation (20), (x ₁ / x ₀ ) = (ξ ₁ / ξ ₀ ) · {(ξ ₀ −ξ∞) / (ξ ₁ −ξ∞) }
…… (25) (y ₁ / y ₀ ) = (η ₁ / η ₀ ) ・ {(η ₀ −η∞) / (η ₁ −η∞)}
(26) is obtained.

The above equations (20), (25) and (26) show that the point P ₀ (x ₀ , y ₀ , z ₀ ) whose position is known in the three-dimensional space and the point P ₁ (x ₁ , If y ₁ , z ₁ ) are on the same line, the point P ₀
The position of (x ₀ , y ₀ , z ₀ ) in the three-dimensional space, the imaging position (ξ ∞, η ∞) on the imaging plane 100 (ξ-η coordinate system) of the point of infinity of the above straight line, point P _The position of the point P ₁ in the three-dimensional space is obtained based on the image forming position (ξ ₀ , η ₀ ) of the image plane ₀ of _{0 and} the image forming position (ξ ₁ , η ₁ ) of the point P ₁ of the image plane 100. It shows that you can.

The above is the basic matter of this embodiment among the matters described in the above paper.

<Calculation method in the present embodiment> Now, returning to FIG. 2, the feature point Pa in the three-dimensional space is Pa ₀ → P.
a ₁ → Pa ₂ ...... moves toward the point at infinity, and along with this,
As shown in FIG. 3, it is assumed that the image forming position Qa of the characteristic point Pa on the imaging plane is directed to the image forming position Qa∞ (ξa∞, ηa∞) corresponding to the point at infinity.

In this case, the following equation holds as is clear from the above equation (20).

(Za1 / za0) = (ξa∞−ξa0 / ξa∞−ξa1) = (ηa∞−ηa0 / ηa∞−ηa1) …… (2
7) Also, the object Pai (xai, yai, zai) and its image Qai (ξai, ηa
Between i) and ξai = (xai / zai) f ...... (28) ηai = (yai / zai) f ...... (29) holds (see above equations (1) and (2)). Therefore, if zai is obtained, the value of xai, yai becomes xai ＝ (ξai / f) zai …… (30) yai ＝ (ηai / f) zai …… (31), and from Qai (ξai, ηai) Pai (xai, yai, zai) is easily requested.

In the present embodiment, the optical axis (z axis) of the camera has a depression angle α, and when the center of the image plane 16 is the origin O'as can be seen from FIG. 2, the erased line 20 shown in FIG. Is in the η direction at η = f · tanα (32). This can be intuitively understood with reference to FIGS. 5 (a) and 5 (b). In FIG. 5 (a), the plane 12 on which the moving body moves and the image plane 16 are x.
FIG. 5B is a view seen in a direction parallel to the axis, and FIG.
FIG. 3 is a view of the image plane 16 viewed from a direction in which the image plane 16 is viewed vertically.
A plane infinitely distant from the origin O in FIG.
When looking at each infinity point on 12, the line of sight to see that point is a plane
Parallel to twelve. The image of each point at infinity is parallel to the plane 12 in FIG.
A straight line passing through is imaged at the point where it intersects the image plane 16.

Not only straight lines in the horizontal plane but also images of straight lines parallel to the horizontal plane have vanishing points on the vanishing line (horizontal line) expressed by the equation (32). That is, the value of the η coordinate of the vanishing point of these straight lines is always f · tanα, and in FIG. 3, ηa∞ = ηb∞ = ηa∞b = f · tanα (33) holds. Then, from the above equations (27) and (33), zai = {(f · tan α−ηa ₀ ) / (f · tan α−ηai)} za _0.
(34) is obtained.

Then, substituting the equation (34) into the equations (30) and (31), xai = (ξai / f) · {(f · tan α-ηa ₀ ) / (f · tan α-ηai)} · za ₀ …
… (35) yai = (ηai / f) ・ {(f ・ tanα-ηa ₀ ) / (f ・ tanα-ηai)} ・ za ₀ …
(36) is obtained.

Thus, the reference point Pa whose position in the three-dimensional space is known is
_From the coordinates of the image Qa ₀ of _{0 and} the coordinates of the image Qai of the feature point Pai
You can easily find the coordinates of Pai. Therefore, the position of the feature point Pa moving along the horizontal plane in the three-dimensional space can be sequentially determined. Further, the position of the feature point Pb can be obtained by the same calculation.
The calculation formula for calculating the coordinates (xbi, ybi, zbi) of the feature point Pbi is shown below.

xbi = (ξbi / f) ・ {(f ・ tanα-ηb ₀ ) / (f ・ tanα-ηbi)} ・ zb ₀ ybi = (ηbi / f) ・ {(f ・ tanα-ηb ₀ ) / (f ・tanα-ηbi)} · zb ₀ zbi = {(f · tanα−ηb ₀ ) / (f · tan α−ηbi)} · zb ₀ To determine the direction of the moving body, on the plane 12, the straight line Pai,
Find the direction of Pbi. However, of the x-coordinate values and z-coordinates obtained as described above, the z-coordinate is inclined by the angle α with respect to the plane 12, so the result of correction by multiplying the z-coordinate value by the correction coefficient cosα It is used as the z coordinate value for calculating the moving direction. The straight line pai, Pbi is (xai, za
i), (xbi, zbi), so Pai, Pbi on plane 12
Let φi be the angle formed by x with the x-axis. Tanφi = {(zbi-zai) / (xbi-xai)} ・ cosα ……
(37) Here, since the operations of equations (35), (36) and (37) are extremely simple calculations, they are executed instantaneously and
The positions of Pa and Pb are obtained, and the position and direction of the unmanned vehicle 11 in the horizontal plane are obtained based on these positions.

In this embodiment, the control device 15 grasps the position and direction of the unmanned vehicle 11 by performing the above calculation, and the unmanned vehicle 11
Control the running of. That is, the control device 15 controls the unmanned vehicle 11 to
Notify only the data of the position and direction (rotation angle),
Or, by giving speed commands to the left and right wheels, unmanned vehicle 11
Control the running of.

Although the plane 12 is a horizontal plane in the above embodiment, the plane 12 is not limited to this and may be a plane that is uniformly inclined as a whole. Further, the control target is not limited to the unmanned vehicle, and can be applied to any object moving on a plane. Further, the television camera 13 is not limited to this, as long as it outputs a two-dimensional image signal at an appropriate speed. Also,
The depression angle α of the camera may be 0 or may be upward depending on the case.

EFFECTS OF THE INVENTION As described above, according to the present invention, a moving object moving on a plane is photographed by a monocular fixed camera, and the position of the reference point on the plane and the reference point in the image are handled. Since the position and direction of the moving body on the plane are obtained based on the position of the image and each position of the image of at least two feature points of the moving body, the traveling of the moving body is controlled by the following. Produce an effect.

(1) Since the calculation for obtaining the position of the moving body from the image is simple, real-time control can be easily realized.

(2) No taxiway is required, and free running control is possible. Therefore, it can be applied not only to the production line but also to the field of extreme work and welfare.

(3) Control that is not affected by wheel slippage or the like is possible.

(4) Since a monocular camera is sufficient, the device can be simplified and the cost can be reduced.

(5) Since multiple moving objects can be simultaneously grasped from the outside world,
Compared with a conventional system in which each mobile body individually follows travel control, there is an advantage that travel control relating to a plurality of mobile bodies such as collision prevention can be performed easily and reliably.

[Brief description of drawings]

FIG. 1 is a block diagram showing a configuration of an embodiment of the present invention, FIG. 2 is a diagram showing a relationship between feature points Pa and Pb on a moving body and an image plane, and FIG. 3 is corresponding to feature points Pa and Pb. Qa, Qb on the image plane
And FIG. 4 is a diagram for explaining a stroke-out, FIG. 4 is a diagram for explaining a conventional traveling control method, and FIGS. 5 (a) and 5 (b).
Is a diagram for explaining the relationship between the plane 12 and the image plane 16 in one embodiment of the present invention. FIG. 6 shows a point P (x, y,
It is a figure explaining the relationship between z) and the image formation position Q (ξ, η) when this point P is imaged on the image plane by central projection. 11 …… Unmanned vehicle (moving body), 12 …… Plane, 13 …… TV camera (shooting means), 14 …… Computing device, 15 …… Control device,
16 ... Image plane, 20 ... Strike, Pa, Pb ... Feature points in three-dimensional space, Qa, Qb ... Image of feature points in image plane.

Continuation of front page (56) References JP-A-59-62916 (JP, A)

Claims (1)

[Claims] 1. (a) a monocular image pickup means having a focal length f having an optical axis of a depression angle α for picking up an image of a moving body moving on a plane; and (b) an image of a characteristic point on the moving body and the plane. The position Pai of the feature point on the moving body is calculated by the following equation from the vanishing line which is the infinite line generated by the central projection of, and xai = (ξai / f) ・ ((f ・ tanα-ηa ₀ ) / ( f ・ tanα-ηai)} ・ za ₀ yai = (ηai / f) ・ {(f ・ tanα-ηa ₀ ) / (f ・ tanα-ηai)} ・ za ₀ zai ＝ {(f ・ tanα-ηa ₀ ) / (f · tan α−ηai)} · za ₀ Position of feature point on moving body; Pai (xai, yai, zai) Reference position of feature point on moving body; Pa ₀ (xa ₀ , ya ₀ , za ₀ ). Position of the feature point on the image plane; Qai (ξai, ηai) Reference position of the feature point on the image plane; Qa ₀ (ξa ₀ , ηa ₀ ) A vanishing line representing the plane on the image plane; η∞ = f · tanα The position of the other feature point on the moving body is calculated by Pbi using the same equation, and xbi = (ξbi / f) ・ {(f ・ tanα-ηb ₀ ) / (f ・ tanα-ηbi)} ・ zb ₀ ybi = (ηbi / f) ・ {(f ・ tanα-ηb ₀ ) / (f ・ tanα-ηbi)} ・ zb ₀ zbi ＝ {(f ・ tanα-ηb ₀ ) / (f ・ tanα-ηbi)} ・zb _{0 The} line segment direction is calculated by tan φi = {(zbi−zai) / (xbi−xai)} · cosα, where φi is the angle of the line segments Pai and Pbi of these feature points with the x-axis on the plane. A traveling control, comprising: a computing means for computing the position and direction of the moving body on a plane; and (c) a control means for controlling the traveling of the moving body based on the output of the computing means. apparatus.