JP2008152380A - Conveyance method of overhead crane using laser pointer and overhead crane system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an overhead crane, and a method for conveying an object to a target position in a three-dimensional space indicated by a laser pointer. <P>SOLUTION: In this method for automatically conveying the object along a conveyance path in the three-dimensional space from a conveyance start position to just above the target position by use of the overhead crane automatically operated through a controller, a plurality of cameras for imaging a spotlight are installed, a laser beam is irradiated on a target position floor surface by the laser pointer to generate the spotlight, the generated spotlight is imaged by at least one camera, three-dimensional space coordinates of a spotlight gravity center position are determined by use of imaged data thereof, the conveyance path is determined by the controller by use of the three-dimensional space coordinates as target position data, and the object is automatically conveyed from the conveyance start position to just above the target position along the conveyance path. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

The present invention relates to transportation of a suspended load (conveyed object) of an overhead crane, and more particularly, to a method and system for automatically conveying a suspended load from a conveyance start position to a target conveyance position indicated by a laser point.

  The overhead crane is used in a wide range of industrial fields such as various factories and warehouses compared to other transport devices such as transport vehicles because the object to be transported can move freely in a three-dimensional space and the size and weight of transported objects are less restricted. ing. However, since the overhead crane has a structure in which a load is suspended by a rope, the swinging of the load is likely to occur depending on the operation method of the crane and the trajectory of conveyance. In the case where a load swing occurs, there is a risk of collision with a load on the ground or collapse of the load. For this reason, conventionally, a skilled operator has performed an operation so as not to cause a load shake by an advanced operation technique. However, in the recent work environment, it is required to reduce labor costs and improve work efficiency, and it is difficult to train skilled operators. Therefore, various studies aiming at automation of cranes are being conducted.

  Research areas include route planning for avoiding obstacles and steadying control for restraining the movement of goods.

  In addition, as a study of steady-state control, as in Non-Patent Document 1 by Nishimura et al., The steady-state control by gain scheduling, and the non-patent document 2 by Hashimoto et al. There have been researches on steady rest.

  In research on route planning, as in Non-Patent Document 3 by Terashima et al., One of the present inventors, a conveyance route having the minimum energy and the shortest distance is derived by the branch and bound method. In this method, obstacles in a transport area are approximated by polygons, and a path that can be realized and minimizes an evaluation function is efficiently searched out of transport patterns having a vertex as a subgoal.

  However, in fully automatic control, the operator must go to the command device of the computer that manages the crane and control the crane by instructing the target transport position at that location, so the operator needs to go to the location where the command device is located. is there. For this reason, it is difficult to perform positioning in real time.

  Therefore, in the present invention, it is considered that the operator gives an instruction to the crane with a laser pointer. By pointing the spot light to the target transport position with a laser pointer, the camera measures the position of the spot light and uses that position as the target transport position to construct a system that automatically transports the crane while avoiding obstacles and controlling steadying. To do. In such a system, it is considered that the crane automatically conveys the load only by instructing the target conveyance position with the laser pointer, so that it can greatly contribute to the reduction of the work amount of the operator, the conveyance time, and the improvement of safety.

  The following non-patent literature showing prior art is incorporated herein by reference.

Non-Patent Document Non-Patent Document 1: Hidekazu Nishimura, Hideo Tanemura, Kenzo Nonami, Gain Schedule Positioning Control for Rope Length Variation of Traveling Crane, Transactions of the Japan Society of Mechanical Engineers (C), Vol. 62, no. 599, pp. 2692-2697, (1996)
Non-Patent Document 2: Yukio Hashimoto, Takeshi Tsuchiya, Toshihiko Matsuda, Ichiro Sugioka, Vibration Suppression Control of Crane Suspension Loads that do not require Load Swing Information, Vol. 30, No. 2, pp. 172-180, (1994)
Non-Patent Document 3: Akihiro Kaneshige, Kazuhiko Terashima, Ikuo Suzuki, Akira Lightning, Autonomous Overhead Crane Considering Obstacle Recognition and Path Planning, “The Japan Society of Mechanical Engineers Proceedings (C)”, Vol. 64, No. 618, (1998), pp. 487-494
Non-patent document 4: Seiji Iguchi, 3D image measurement, Shosodo, (1990)
Non-Patent Document 5: GK Schmidt, K. Azarm, Mobile robot path planning and execution based on a diffusion equation
strategy ”, Advanced Robotics 7-5 (1993), pp.479-490
Non-Patent Document 6: Takeo Saito, “Numerical Heat Transfer”, Yokendo, (1986)
Non-Patent Document 7: Sugihara Atsuyoshi, “Mathematics of Graphics”, Kyoritsu Shuppan, (1995)
Non-Patent Document 8: David F. Rogers, J. Alan Adams, Fujio Yamaguchi, “Computer Graphics”, Nikkan Kogyo Shimbun (1979)
Non-Patent Document 9: Teruo Sunaga, “Optimization Method in Mechanical Engineering”, Research on Machines, 41-8, (1989), pp. 867-872
Non-Patent Document 10: Noritaka Yanai, Motoshi Yamamoto, Akira Mohri, “Crane feedback control based on inverse dynamics calculation”, Transactions of the Society of Instrument and Control Engineers, 37-11, (2001), pp. 1048-1055
Non-Patent Document 11: Yanai N, Yamamoto M, Mohri A, “Anti-Sway Control for Wire-Suspended Mechanism Based on Dynamics Compensation”, Proc IEEE Int Conf Rob Autom, 4, (2002), pp.4287-4292
Non-Patent Document 12: Nobutoshi Takahashi, Yosuke Nakazawa, Kazunobu Umeda, Construction of a home robot operation system using a laser pointer, Proc. (2), (2002)
Non-Patent Document 13: PAROMTCHIK.IE, ASAMA.H, “Mobile robot guidance by means of a laser pointer”, Proc ASTED IntConf Model Identif Control, Vol.2, pp.718-721, (2001)

  The approach of the present invention is as follows. A system for recognizing spot light to determine the target moving position of the overhead crane is constructed. The spot light is generated by the operator by bringing the laser pointer to the target transport position of the transported object and irradiating the floor surface of the target transport position for several seconds with the laser light emitted from the laser pointer. The spot light is imaged by two cameras (for example, CCD cameras), and the position of the spot light is determined by a controller connected to the cameras. In addition, a laser pointer can be attached to a crane (for example, a crane carriage) so as to irradiate the target floor surface.

  In addition, since there are obstacles on the straight line connecting the camera and the spot light, it may be possible to measure the spot light only with one camera, and the 3D position is measured with one camera. We propose an algorithm to The potential method based on the three-dimensional diffusion equation is applied to the obstacle avoidance path calculation. Compared with route planning based on graph theory or GA, the potential method is easy to apply to complex obstacle environments and has a short calculation time, so it is effective in complicated obstacle environments for cranes. Conceivable. Next, the obtained route is improved by the broken line approximation method, so that a route with few unnecessary broken points is derived. Next, the obtained path is represented by a quintic B-spline curve. The control input of the carriage is derived by solving the optimization problem that satisfies the device constraint and the obstacle avoidance constraint and minimizes the transportation time by the complex method, with the parameter representing the curve as the operation amount. By inputting the control input to the feedforward control system based on the inverse dynamics calculation, the trajectory tracking of the load and vibration suppression are performed.

  Further, it is assumed that all the obstacle position information is already known by the light cutting method described in Non-Patent Document 3.

BEST MODE FOR CARRYING OUT THE INVENTION

  FIG. 1 shows a schematic diagram of an overhead crane system 1 according to an embodiment of the present invention. The overhead crane of the system includes a carriage 2 and a frame 3 that supports the carriage 2 so that it can run in a plane. In the traveling direction (X axis) direction, the girder 4 moves, and in the transverse direction (Y axis), the carriage 2 with the conveyed object 10 suspended on the girder moves, so that independent conveyance in the X and Y directions is possible. is there. For the movement of the carriage, the drive of an AC servo motor (not shown) provided on the carriage is given a voltage command from the controller 6 to the motor via the timing belt 5A to control the carriage speed. Moreover, the conveyed product 10 is suspended by the wire rope 7 and moved in the vertical direction (Z-axis) by rotating a winding drum (not shown) below the carriage by driving an AC servo motor. The relationship between the carriage, the girder, the yayer rope, the conveyed product, and the servo motor is well known and will not be described in detail.

  In this embodiment, the maximum movement distance in the X, Y, and Z directions is 2.0 m, 1.0 m, and 1.2 m, and the conveyed product 10 is a steel ingot having a mass of 30 kg. Measurement of the swing angle of the rope 7 is performed by attaching a laser sensor (KEYENCE, VG-035) near the base of the rope.

  Two black-and-white CCD cameras (SONY, XC-HR58) 11A and 11B are fixed to the crane frame and used for imaging the spot light of the laser pointer. A colored glass filter (HOYA, R-60) is attached in front of the lens of the camera to block disturbance other than laser light. An image processing board (Linx, Galaxy ++ M2) is used for the image processing apparatus. The camera can image all floor surfaces in the X and Y axis directions within the cart movable range, and can image from a height of at least 0.3 m and a maximum of 1.0 m in the Z axis direction. A laser pointer (VEROS, LEPO650) that can be adjusted to a diameter of about 7 mm to 40 mm at a spot diameter of 3 m ahead is used.

  The controller 6 includes a computer that executes various calculations, and is configured to be connected to the camera and analyze an image captured by the camera to determine the position of the spot light. Each process described below is performed by the controller 6.

1. Method of Measuring Spot Light Position 1.1 Method for Obtaining Spot Light Position As shown in FIG. 1, in the present invention, two cameras 11A and 11B are fixed to a frame 3 of a crane for spot light recognition. Since the blind spot of the camera exists depending on the installation position of the obstacle, the situation assumed using FIG. 2 will be described.

  Like the area A in FIG. 2, the upper surface A1 of the larger obstacle and the floor surface A2 on the side thereof can be imaged by both cameras. The area B and area C in FIG. 2 can be imaged only by the camera 11A. When the surface spot light can be imaged with only one camera, the coordinate of the floor surface can be set to Z = 0 and the two-dimensional (X, Y) coordinates can be determined by the controller 6, but the spot light in the region C in FIG. It is impossible to determine the three-dimensional crane coordinates (X, Y, Z). However, in the present invention, three-dimensional crane coordinates (X, Y, Z) from (U, V) coordinates determined by imaging by one camera by using obstacle position information that is all grasped by the light cutting method. Can be determined.

1.2 In the case of two cameras When the two cameras can recognize the spot light, the crane coordinates of the spot light are obtained by the method described in this section. The camera parameters of the camera 11A in FIG. 2 are C _{A1 to} C _A11 , the camera coordinates are (U _A , V _A ), the camera parameters of the camera 111B are C _{B1 to} C _B11 , and the camera coordinates are (U _B , V _B ). Assuming that the coordinates of the spot light are (X, Y, Z), as described in Non-Patent Document 4, the following relationship is established. After expressing the following equation as a matrix, (X, Y, Z) is obtained by obtaining a least squares solution using a general inverse matrix.

Formula 1

１・３ １台のカメラの場合
障害物によってカメラの死角が生じる。このような場合はカメラ１台しかスポット光を認識できない場合もある。このときは（２）式によりスポット光の２次元クレーン座標を求める。（２）式はＺ＝０のときの（１）式を変形させた式である。（２）式はカメラ１１Ａのものであるが，カメラ１１Ｂのものも同様な式で求めることができる。

1.3 In the case of one camera, the blind spot of the camera is caused by an obstacle. In such a case, the spot light may be recognized only by one camera. At this time, the two-dimensional crane coordinates of the spot light are obtained by equation (2). The expression (2) is an expression obtained by modifying the expression (1) when Z = 0. Although the equation (2) is for the camera 11A, the equation for the camera 11B can also be obtained by a similar equation.

Formula 2

１つのカメラで３次元位置を求めるアルゴリズム
図２のＣ領域（小さな方の障害物の上面）に吊り荷を搬送したい場合の例を図３に示す。Ｃ領域は、先に述べたように、Ａ_１領域を有する大きい方の障害物にじゃまされてカメラ１１Ｂでは撮像できないが、カメラ１１Ａで撮像可能である。

Algorithm for obtaining a three-dimensional position with one camera FIG. 3 shows an example in which a suspended load is to be transported to the area C (the upper surface of the smaller obstacle) in FIG. C region, as previously described, can not be captured with the camera 11B is disturbed obstacle larger with A ₁ region can be captured by the camera 11A.

Consider a case where a laser beam is applied to the C region obliquely from above as indicated by a broken line in FIG. Since the spot light is formed in the region C, the pot light is imaged by the camera 11A. By a method described later (algorithm for obtaining the center of gravity of the spot light), the center of gravity B of the spot light is determined image-wise from the captured spot light image, and the optical axis of the camera 11A is aligned with the B point via the controller 6. The position C of the camera 11A is known and its coordinates are (X ₃ , Z ₃ ). Let the unknown coordinates of point B be (X ₂ , Z ₂ ). The unknown coordinates of the intersection A between the optical axis of the camera 11A and the floor surface (surface on which two obstacles are placed) are defined as (X ₁ , Z ₁ ). B (X ₂ , Z ₂ ), that is, the target transport position is obtained by the method described below with reference to FIG.

1) First, the coordinates A (X ₁ , Z ₁ ) are obtained by the equation (2).

2) Using the known coordinates C (X ₃ , Z ₃ ), Z for searching the Z coordinate of the obstacle is defined as Z = Z ₃ .

3) Z-10 [mm] is calculated, and a coefficient X for searching the X direction is obtained by the following equation (3).

Formula 3

４）３）を数回計算する。

4) Calculate 3) several times.

5) The obstacle position information is compared with X and Z, and X and Z immediately before X <X ₂ and Z <Z ₂ are established are obtained and the process ends.

In step 1) of the above algorithm, the coordinates (X ₁ , Z ₁ ) of the point A on the floor surface are the same as the coordinates B (X ₂ , Z ₂ ) and A (X ₁ , Z ₁ ) on the image plane of the camera. Since it is in the U and V coordinates, it can be obtained by using the assumption that Z = 0 and the equation (2). By calculating the above 3) several times, X = X ₃ and Z = Z ₃ at first were gradually increased to X and Z approaching X ₂ and Z ₂ , and finally X <X ₂ changes as Z _{<Z 2} is satisfied. By the above calculation, the coordinates B (X ₂ , Z ₂ ) of the target transport position on the obstacle can be obtained.

  For the sake of simplicity of explanation, only the XZ plane shown in FIG. 3 has been described, but the same applies to the YZ plane. By using this calculation method, 3 A dimension position can be obtained. The merit of using this calculation method is that it is not necessary to associate the coordinates of the image plane of the camera with the three-dimensional coordinates, so that it is troublesome to associate with the three-dimensional coordinates every time the position of the obstacle is changed. , It is possible to save the trouble of changing the program for the correspondence.

  The above equation (3) is obtained by deforming a linear equation connecting two points in space. This method is performed on the premise that all the obstacle position information is known by the light cutting method.

2. Spot light position measurement experiment 2.1 Confirmation of accuracy is performed by obtaining the coordinates of a stationary object with cameras calibrated by two cameras. The reason for obtaining the coordinates of the stationary object is that positioning with the laser pointer spot light in millimeters is difficult, and it is easier to obtain the coordinates of the stationary object to check the measurement error. is there. Table 1 shows an example in which three-dimensional coordinates are actually obtained, with the original three-dimensional coordinates on the left and the measurement results on the right. The unit is mm. The maximum error was 11 mm, and the minimum error was 0 mm.

2.2 Measurement with one camera Table 2 shows the measurement results when the coordinates of an object stationary with a calibrated camera in the obstacle environment shown in FIG. The original three-dimensional coordinates are shown on the left of the table, and the measurement results are shown on the right. The unit is mm. Although the camera used for imaging is the camera 11A, the same result is obtained when the image is captured by the camera 11B, and a description thereof will be omitted. From this result, the three-dimensional coordinates could be determined. The maximum error was 14 mm and the minimum measurement error was 0 mm.

2. Derivation of center of gravity of spot light Generally, spot light has a size. Depending on how the laser pointer is applied, it becomes a large ellipse, and there is a problem that the measured value changes depending on which position of the ellipse is measured. Therefore, the present invention solves this problem by obtaining the position of the center of gravity of the spot light. As a method for obtaining the center of gravity of the spot light, the algorithm described below is used.

Algorithm for finding the center of gravity of a spot light:
1) A luminance value is acquired from an image captured by a camera, and coordinates having a luminance value of 200 or more (the darkest region in the example of FIG. 5) are acquired.

2) Acquire the four coordinates (A, B, C, D) that are the top, bottom, left, and right among the coordinates having the luminance value of 200 or more (the darkest area).

3) Calculate the coordinates of E by calculating (A + D) / 2 and (B + C) / 2. This method for obtaining the center of gravity is known and commonly used.

  The luminance value is divided into 0 to 255 levels. An image of concrete or the like has a luminance value of less than 200, but the spot light has a luminance value of 200 or more. Therefore, by acquiring an image having a luminance value of 200 or more from the captured image, only the spot light can be acquired. Since the luminance value around the spot light (in the example of FIG. 5, the light-colored region and the surrounding background) is less than 200, it can be excluded when acquiring the luminance value. Since only the spot light image (dark color region in the example of FIG. 5) remains in the image captured by this processing, it is easy to determine the position of the coordinates (A, B, C, D).

  An experiment was conducted to determine the position of the spot light by this method. The spotlight had sufficient brightness and could be easily recognized by the camera.

3. Derivation of Obstacle Avoidance Path 3.1 - potential Method As described in Non-Patent Document 5, the diffusion method uses a diffusion equation to diffuse a hypothetical diffusive material in the transport region and its concentration gradient (potential Field) to obtain a route. The three-dimensional diffusion equation is as follows.

Formula 4

差分法により数値計算を行うため，（４）式を差分化すると、非特許文献６に示されるように、次式となる。

Since numerical calculation is performed by the difference method, when the equation (4) is differentiated, as shown in Non-Patent Document 6, the following equation is obtained.

Formula 5

さらに、境界条件として、以下の（６）式

Furthermore, as a boundary condition, the following equation (6)

Equation 6

を恒久的に与え、それ以外のグリッドの初期条件として以下の（７）式

As the initial condition for other grids,

Equation 7

を与える。荷物の大きさを無視するために，荷物を円柱と仮定し，荷物半径だけ障害物を拡大するものとした。荷物下端の位置を荷物経路のＺ座標とするため、障害物はＸ−Ｙ軸方向への拡大処理のみ行う。

give. In order to ignore the size of the load, it was assumed that the load was a cylinder and the obstacle was enlarged by the load radius. Since the position of the lower end of the load is used as the Z coordinate of the load route, the obstacle is only enlarged in the XY axis direction.

  FIG. 6B shows an example in which the potential field is generated using the equations (5) to (7) in the three-dimensional obstacle environment shown in FIG. Here, the start point S is (0.1 [m], 0.1 [m], 0.3 [m]), and the goal point G is (1.9 [m], 0.9 [m], 0 .3 [m]) and the conveyed object radius was 0.15 [m] (corresponding to 3 grids when the grid width Δh = 0.05 [m]), the obstacle was enlarged. The obstacle area expanded around the obstacle in FIG. However, the enlarged obstacle area is shown only on the ground (Z = 0 [m]). From FIG. 6, density C = 1 at the goal point, which is a boundary condition, density C = 0 within the obstacle area, and outside the obstacle area, the density is closer to 1 and the density decreases as the distance from the goal point increases. In the experiment, the obstacle enlargement process is set to 0.2 [m] (the load radius 0.15 [m] + the safety margin 0.05 [m]). Therefore, by referring to the density of 26 grids (marked in the figure) around the starting point (basic grid (i, j, k) indicated by black circles in FIG. The route obtained by connecting the selected grids at this time becomes the obstacle avoidance route, and an example in which the avoidance route is derived is shown in FIG. Is an avoidance route.

  Here, the procedure of the potential method based on the diffusion equation is summarized below.

Potential method based on the diffusion equation:
1) A target three-dimensional transport area (X, Y, Z) is divided by a mesh having a grid width Δh, and obstacles are arranged on the corresponding grid.

2) Enlarge the obstacle by the conveyed object radius.

3) The initial density _{Co, i, j, k} of all grids is given by the equations (6) and (7).

4) Update the density C _{t, i, j, k} of all grids excluding the boundary condition using the equation (5).

5) Go to 6) if the end condition of equation (8) is satisfied. If you are not satisfied, go to 4).

6) The given start grid S is set as the selected grid P.

7) The maximum density grid is selected from the 26 grids around the selected grid P, and the selected grid P is stocked and updated.

8) If the density C of the selected grid P = 1 (goal point G), the process ends. Otherwise go to 7).

The selected grid P stocked in this procedure becomes an avoidance path. The following equation is used as the diffusion termination condition.

Equation 8

ここで、Ｃｔ、Ｓは時刻ｔにおけるスタート地点Ｓの濃度である。（８）式はスタート地点における各計算ステップごとの濃度の変化比率を示している。この終了条件は定常するまでの拡散回数が障害物環境によって異なるため導入した。εＣｓは拡散プロセスの定常状態を判定する閾値であり、ε_Ｃｓ＝０．０１とし、拡散パラメータｒは０．０１とした。

Here, Ct and S are the concentrations of the start point S at time t. Equation (8) shows the concentration change ratio for each calculation step at the start point. This termination condition was introduced because the number of diffusions until steady state varies depending on the obstacle environment. εCs is a threshold value for determining the steady state of the diffusion process, ε _Cs = 0.01, and the diffusion parameter r is 0.01.

3-2 Broken Line Approximation Method As shown in FIG. 8, the route obtained by the potential method is a route having many break points. The carriage track is easily affected by break points, and unnecessary break points cause an increase in transport time. Therefore, the point group of the maximum density grid is approximated by a straight line by the broken line approximation method. This method reduces unnecessary break points. In the approximation, the approximation is performed on the condition that the route does not enter the obstacle area. FIG. 9 shows an outline of a polygonal line approximation method using an obstacle environment. The starting point indicated by _ in the figure is the starting point of the line segment. The end point of the line segment is scanned from the goal point to the point group of the route data (in the figure, mark) to search for a straight line that does not collide with the obstacle. The broken line in the figure is not selected because it enters the obstacle area. If a straight line that does not collide with an obstacle is determined, the straight line is searched with the end point of the straight line as a new start point. When this operation is repeated, an approximate result as shown in FIG. 10 is obtained. The broken line in the figure represents a path obtained by the potential method, and the solid line represents an approximate path obtained by linear approximation. It can be seen that the number of folding points of the approximate route is reduced from 14 to 4 and the transport distance is shortened. The procedure of the broken line approximation method is shown below.

Polyline approximation method:
1) The selected grid obtained by the potential method is P _i (i = 1,..., N), and s = 1 and g = n.

2) It is determined whether a straight line from the grid P _s to the grid P _g passes through the obstacle area. _{Alternatively} , it is determined whether the position of the point cloud of P _j (j = s,..., G) from the periphery of the obstacle region is within the allowable maximum value e _max .

3) If the straight line passes through the obstacle area or the point group exceeds the allowable maximum value, go to 2) as g = g-1. Otherwise, stock and 4) to as a break point the P _g.

4) If g = n, the process ends. If g is not n, s = g, g = n and go to 2).

4). Derivation of luggage trajectory in consideration of various constraint conditions In a control system using 4 · 1 5th order B-spline curve inverse dynamics calculation, the luggage trajectory is required to be capable of fourth-order differentiation. A luggage trajectory is expressed using a B-spline curve. Luggage trajectory expressed by a quintic B-spline curve in the interval [i, i + 1], (i = 0,..., N−1)

Equation 9

と時刻ｔ（ｓ）を次式で定義する。

And time t (s) is defined by the following equation.

Equation 10

本発明では折れ線近似法により得られた折れ点を用いることとする。ｓは０≦ｓ＜１とする曲線パラメータ，Ｎ_ｊ（ｓ）は５次Ｂスプライン基底関数であり，deBoor-Coxの公式（非特許文献７及び８）により次式のように導出される。

In the present invention, a break point obtained by a broken line approximation method is used. s is a curve parameter satisfying 0 ≦ s <1, N _j (s) is a quintic B-spline basis function, and is derived as follows by the deBoor-Cox formula (Non-Patent Documents 7 and 8).

Equation 11

従って，荷物軌道

Therefore, the package trajectory

Formula 12

は重みＮ_ｊ（ｓ）を与えた周囲６点の制御点の線形結合により求められる。なお，（１０）式のスプライン基底関数Ｎ_ｊ（ｓ）はｓの５次式で与えられることから，得られる荷物軌道

Is obtained by linear combination of six surrounding control points given weight N _j (s). Note that since the spline basis function N _j (s) in the equation (10) is given by the fifth-order equation of s, the obtained luggage trajectory

Equation 13

は４階微分可能となる。

Becomes 4th order differentiable.

4.2 Formulation of optimal control problem Control point vector describing control point and end time

Equation 14

と定義し，各種制約条件を考慮して評価関数を定式化し、最適解を導出する。制約条件に応じて与えるペナルティ項を付加した評価関数Ｊを次式で定義する。

And formulate the evaluation function in consideration of various constraints and derives the optimal solution. An evaluation function J to which a penalty term given according to the constraint condition is added is defined by the following equation.

Equation 15

ここで，ｌは制約条件の数，Ｗはペナルティ項の重み係数である。

Here, l is the number of constraints, and W is the weighting factor of the penalty term.

Expression (14) is an evaluation function for the purpose of deriving a high-speed trajectory under constraint conditions. The weight W of the penalty term is 10,000. W is to provide a sufficiently large value with respect to the transport time t _f, the trajectory satisfying the constraint condition can be derived. Moreover, h _i (t) is a penalty function and must always be a positive value, and therefore is given by the following equation according to the constraint condition g _i (t).

Equation 16

（１２）式では制約条件を満足しないときにのみペナルティ項が加算される。従って，制約条件を満足しない軌道は最適化過程で排除され，制約を満足し，かつ搬送時間の短い軌道が得られる。

In equation (12), a penalty term is added only when the constraint condition is not satisfied. Therefore, trajectories that do not satisfy the constraints are eliminated in the optimization process, and trajectories that satisfy the constraints and have a short transport time are obtained.

4.3 Speed and acceleration constraints of the motor Next, various constraints will be described. Since motors have finite speeds and accelerations, it is necessary to consider motor device constraints. Expressing the constraints in the optimal control problem in the form of g _i (t) ≧ 0,

Equation 17

及び台車加速度

And trolley acceleration

Equation 18

の制約は次式となる。

The constraint of is given by

Equation 19

Ｙ軸についても同様である。Ｚ軸についてもモータの装置制約を考える。Ｚ軸のロープ巻き上げ下げ速度

The same applies to the Y axis. Consider the device restrictions for the Z-axis as well. Z-axis rope hoisting and lowering speed

Equation 20

及びロープ巻き上げ下げ加速度

And rope hoisting / lowering acceleration

Equation 21

の制約は次式となる。

The constraint of is given by

Equation 22

制約条件として，台車速度

As a constraint, the carriage speed

Equation 23

及び台車加速度

And trolley acceleration

Formula 24

とした。また，残留振動抑制のためには搬送スタート地点及びゴール地点において荷物と台車は停止していなければならない。そのため，搬送スタート地点及びゴール地点では

It was. Also, in order to suppress residual vibration, the luggage and cart must stop at the transfer start point and goal point. Therefore, at the transfer start point and goal point

Formula 25

の条件が与えられる。

Conditions are given.

Entry restraint constraint using 4.4 Laplace equation A constraint condition for obstacle avoidance using the Laplace equation is used as a constraint to restrain entry of the load into the obstacle region. By using this constraint condition, it is possible to evaluate whether the obtained package trajectory has entered the obstacle area. Luggage trajectory for constraints in the following steps

Equation 26

により定まるポテンシャル場

Potential field determined by

Equation 27

を生成する。搬送領域内に２つのポテンシャル場Ｃｏ，Ｃｎを（１５）式のラプラス方程式により導出する。

Is generated. Two potential fields Co and Cn are derived from the Laplace equation (15) in the transfer region.

Equation 28

ここで，初期条件としてＣｏ，Ｃｎ＝ｅｘｐ１，それぞれの境界条件として（１６）式

Here, as initial conditions, Co, Cn = exp1, and as the respective boundary conditions, equation (16)

Equation 29

を用いる。

Is used.

From the boundary condition of the equation (16), Co is a potential field having a value only within the obstacle region, and Cn is a potential field having a value only inside and outside the obstacle region. The potential constraint C _r is obtained using the obtained two potential fields.

Equation 30

ここでｌｏｇをとるのはＣ_ｏ及びＣ_ｎの指数的な変化を考慮するためである。図１１（ａ）に障害物環境、図１１（ｂ）にラプラス方程式により生成されたポテンシャル制約Ｃ_ｒを示す。同図より生成されたポテンシャル場Ｃ_ｒは必ず障害物領域内で正、領域外で負、境界で零となることが確認できる。また、搬送領域全域で勾配を有し、障害物が密集する領域ほどポテンシャル値Ｃｒは大きくなっている。ここで、Ｃ_ｒが負であれば障害物領域に侵入しないことから、進入抑制のための制約条件は次式で与えられる。

Here take log is to consider the exponential change of C _o and C _n. Figure 11 (a) an obstacle environment showing the potential constraints _{C r} generated by the Laplace equation in FIG. 11 (b). It can be confirmed from the figure that the generated potential field _Cr is always positive within the obstacle region, negative outside the region, and zero at the boundary. In addition, the potential value Cr is larger in a region having a gradient in the entire conveyance region and where obstacles are densely packed. Here, if _Cr is negative, it does not enter the obstacle region, so the constraint condition for entry suppression is given by the following equation.

Formula 31

４・５ コンプレックス法
（９）、（１０）式で、４階微分可能な荷物軌道

4/5 complex method (9), (10), 4th-order differential luggage trajectory

Equation 32

は表現できる。しかし、（１０）（１１）式において制御点

Can be expressed. However, in (10) and (11), the control point

Equation 33

と搬送終端時刻ｔ_ｆを決定する必要がある。従って、これらの変数を操作量とし、障害物回避等の各種制約条件を満足する最適制御問題を考える。そこで、制御点及び終端時刻を記述する制御点ベクトルを

It is necessary to determine the transport end time t _f a. Therefore, using these variables as manipulated variables, an optimal control problem that satisfies various constraints such as obstacle avoidance is considered. Therefore, the control point vector describing the control point and the end time is

Equation 34

と定義し、これを非線形最適化手法の一種であるコンプレックス法（非特許文献９）により最適化する。制御点の数を折れ線近似法により得られた折れ点の数Ｎとすれば、始端と終端の位置は固定されるため、

This is optimized by a complex method (Non-patent Document 9) which is a kind of nonlinear optimization method. If the number of control points is the number N of broken points obtained by the broken line approximation method, the positions of the start and end points are fixed.

Formula 35

は３（Ｎ−２）＋１の最適化変数を有する。また、コンプレックス法における初期点の数Ｍは最適化変数の２倍程度にすることが好ましいとされているので、Ｍ＝６（Ｎ-２）＋１個の初期点を与えることとした（非特許文献９）。制御点ベクトル

Has 3 (N−2) +1 optimization variables. In addition, since the number of initial points M in the complex method is preferably about twice the optimization variable, M = 6 (N−2) +1 initial points are given (non-patent) Reference 9). Control point vector

Equation 36

をコンプレックス法により改善する手順を以下に示す。

The procedure for improving the above by the complex method is shown below.

Complex algorithm optimization algorithm :
1) The control point vector obtained by the broken point approximation method

Formula 37

とし、残りのＭ−１個の制御点ベクトル

And the remaining M-1 control point vectors

Equation 38

の要素を次式により決定する。

Is determined by the following equation.

Formula 39

ここで、ｉ＝１，・・・，Ｎ，２，・・・，Ｍ、Ｄ_ｘ，Ｄ_ｙ，Ｄ_ｚ，Ｄ_ｔｆは各制御点の探索域に対応して設定する値、ｒは区間[−０.５,０.５]の一様乱数である。

Here, i = 1,..., N, 2,..., M, D _x , D _y , D _z , and D _tf are values set corresponding to the search area of each control point, and r is a section It is a uniform random number of [−0.5, 0.5].

2) A control point vector that calculates an evaluation function for the trajectory determined by each control point vector and gives the maximum value _JH of the evaluation values

Formula 40

と最小値Ｊ_Ｌを与える制御点ベクトル

And control point vector giving minimum value J _L

Formula 41

を求める。

Ask for.

3) When ε is a convergence determination constant, the process ends when J _H −J _L ≦ ε, and the process proceeds to 4) when J _H −J _L > ε.

4) Maximum point

Equation 42

を除く制御点ベクトルの重心

Center of gravity of control point vector excluding

Equation 43

を求める。次式

Ask for. Next formula

Formula 44

により最大点

Max points by

Formula 45

と重心

And center of gravity

Equation 46

とを結ぶ直線上で改良点

Improvements on the straight line connecting

Equation 47

を求め、その評価値Ｊ_Ｃとおく。

And the evaluation value _JC is set.

5) If J _C <J _H

Formula 48

を

The

Formula 49

で置き換え、２）へ。Ｊ_Ｃ≧Ｊ_Ｈならばε_αを十分小さな値として、α≧ε_αならαをα・βで置き換え４）へ、α＜ε_αならαを初期値に戻し、

Replace with 2). If J _C ≧ J _H , set ε _α to a sufficiently small value; if α ≧ ε _α , replace α with α · β 4), and if α <ε _α , return α to the initial value,

Formula 50

を

The

Formula 51

に置き換え４）へ。

To 4).

Here, as shown in FIG. 10, the trajectory generation simulation of the above method is performed. As a condition, the number of initial control points and the initial value are given by the broken line obtained by the broken line approximation method using the obstacle environment. The initial value of α is 1.3, and the initial value of β is 0.5 (Non-Patent Document 9). Further, the search area D _x = D _y = D _z = 0.1 m, D _tf = 1s, ε = 0.01, and ε _α = 0.01. The positions of the initial control point and the improved control point at this time are shown in FIG. Although the improved control point is located outside the transport area, the B-spline trajectory obtained from this control point performs obstacle avoidance within the transport area under the constraint of the Laplace potential field.

  The result of the actual trajectory generation simulation result is shown by the thick solid line in FIG. It can be seen that the path (broken line in the figure) that was a broken line is represented by a curve, and further, an obstacle is avoided.

5. 5. Construction of control system for vibration suppression control and trajectory tracking 5.1 FF control by inverse dynamics calculation In the present invention, the trajectory tracking and vibration suppression of a load are feedforward by reverse dynamics calculation described in Non-Patent Document 10. Perform by control. This method is a package trajectory

Formula 52

を実現する台車軌道

Bogie track to realize

Formula 53

を力の釣り合いから得られる以下の（２１）式

The following equation (21) obtained from the balance of force

Formula 54

によって導出する手法である。ここで，ｇは重力加速度である。さらに，この台車軌道をモータの逆モデルに入力することで，実際の天井クレーンの台車軌道及び荷物軌道が

This is a method derived by Here, g is a gravitational acceleration. Furthermore, by inputting this bogie track into the inverse model of the motor, the bogie track and the load track of the actual overhead crane can be changed.

Formula 55

となるＦＦ制御入力

FF control input

Formula 56

を得る。ＦＦ制御入力導出の過程は図１３となる。ただし，（４３）式及びモータの逆モデルはそれぞれ入力の２階微分を含むことから，荷物軌道は４階微分可能なものしか実現することができない。そのため，本発明では５次Ｂスプライン曲線を導入することで４回微分可能な荷物軌道

Get. The process of deriving the FF control input is shown in FIG. However, since the equation (43) and the inverse model of the motor each include a second-order derivative of the input, only a load trajectory capable of fourth-order differentiation can be realized. Therefore, in the present invention, a package trajectory that can be differentiated four times by introducing a fifth-order B-spline curve.

Formula 57

を得ている。

Have gained.

  Next, assuming that the motor of the overhead crane is a first-order lag system, the given bogie track

Formula 58

を実現する制御入力

Control input to realize

Formula 59

は次式により求められる。

Is obtained by the following equation.

Formula 60

ここで，

here,

Formula 61

は各軸のモータゲインを成分とする対角行列，

Is a diagonal matrix whose component is the motor gain of each axis,

Formula 62

は各軸のモータ時定数を成分とする対角行列である。（２２）式より，台車軌道

Is a diagonal matrix with the motor time constant of each axis as a component. From equation (22), bogie track

Equation 63

が与えられれば，それを実現する制御入力

Control input to achieve that

Formula 64

を導出できる。

Can be derived.

5.2 Simulation and transport experiment In the obstacle environment shown in Fig. 6 (a), the simulation and transport experiment were conducted by integrating the methods described in each section. The results are shown in FIG. The track on the upper side of the three-dimensional diagram is the rope feed point of the bogie, the track on the lower side is the suspension load center, the thin line is the rope, the obstacle is in the center of the map, and the floor around it is The obstacle area expanded by the radius of the suspended load. In the two-dimensional graph, the position indicates the position of the suspended load core, and the speed and acceleration are the speed and acceleration of the bogie track. The swing angle is that of the rope. From the experimental results, the maximum residual vibration is 0.081 [rad], and the residual vibration can be satisfactorily suppressed. The positioning error is 10 [mm], and the simulation result and the experimental result almost coincide. It also satisfies the maximum speed and maximum acceleration constraints.

6). Transport experiment to the spot light position The target transport position is illuminated with the spot light of the laser pointer, and the suspended load is operated to the spot light position. The target transport position is the spot light position measured by the camera, but if the coordinates where the Z axis is recognized by the camera are used as they are as the target transport position, the lower part of the load will collide with the obstacle. The target transport position is set by adding 0.15 [m] to the value. FIG. 15 shows experimental data when the crane is actually operated to the position of the spot light. The suspended load can move to the upper part of the spot light, and it can be confirmed from the figure that obstacles can be avoided while suppressing residual vibration.

  In the above-described embodiment, two cameras are used. However, it is also possible to use two cameras that can provide two or more cameras and pick up an image of the spot light.

The effect of the invention It has been experimentally shown that a three-dimensional position can be measured within an error of 11 mm when measuring spot light with two cameras, and within an error of 14 mm when measuring spot light with one camera. Route planning using the potential method, simultaneous optimization of the control points and transport time of the fifth-order B-spline curve using the complex method, and suppression of residual vibrations and obstacles by applying a damping FF control system based on inverse dynamics calculation We were able to achieve object avoidance. In addition, these elemental technologies were integrated, and the crane was operated to the spot light position, and it was shown that positioning was possible while suppressing residual vibration and avoiding obstacles to the spot light position.

The perspective view of the crane system of this invention. The perspective view which shows the spot light measurement environment in the crane system of FIG. Schematic which shows the relationship between a camera position and a spot light position. The figure which shows an obstacle environment. Explanatory drawing for calculating | requiring the gravity center of spotlight. 6A is a diagram illustrating a three-dimensional obstacle environment, and FIG. 6B is a diagram illustrating a potential field by three-dimensional diffusion. The figure which shows the basic grid and surrounding 26 grid in a diffusion method. The figure which shows the obstruction avoidance path | route obtained by the potential method. The figure which shows the concept of a broken line approximation method. The figure which shows the example of a broken line approximation method. The figure which shows the penetration | invasion restrictions using a Laplace equation. The figure which shows the improved conveyance path by a B-spline curve. The figure which shows the concept of FF control. The figure which shows the result of conveyance control. The figure which shows the conveyance experiment result to a spot light position.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Crane system 2 Carriage 3 Frame 4 Girder 5A, 5B Timing belt 6 Controller 7 Wire rope 10 Carrying object 11A, 11B Camera

Claims (16)

A method of automatically transporting a transported object along a transport path in a three-dimensional space from a transport start position to a position directly above a target transport position using an overhead crane that is automatically operated via a controller:
Install multiple cameras to image the spotlight;
Irradiate the floor surface of the target transport position with a laser pointer to generate spot light;
Imaging the generated spot light with at least one camera, and determining the three-dimensional spatial coordinates of the center of gravity of the spot light using the imaging data;
The controller determines the conveyance path by using the three-dimensional space coordinates as the target conveyance position data, and automatically moves the conveyance object from the conveyance start position to just above the target conveyance position along the conveyance path. Transport to
An automatic conveyance method comprising: 2. The automatic transfer method according to claim 1, wherein at least two cameras are installed and no obstacle exists between any two of the at least two cameras and the spot light. Imaging the spot light with the two cameras and determining the three-dimensional spatial coordinates of the center of gravity of the spot light using the imaging data, wherein only one of the at least two cameras is When the spot light can be picked up and another camera cannot pick up the spot light due to an obstacle, the spot light is picked up by one camera that can pick up the spot light and the spot data is used An automatic transport method comprising determining three-dimensional spatial coordinates of a center of gravity position. 3. The automatic conveyance method according to claim 2, wherein when there is one camera capable of imaging the spot light, the imaging data obtained by the one camera capable of imaging the spot light and the position of the camera are known. And determining the three-dimensional coordinates of the position of the center of gravity of the spot light using the coordinates of the obstacle and the position information of the obstacle previously obtained by the light cutting method. The automatic transfer method according to claim 3, wherein when an obstacle exists on a straight line connecting the transfer start position and the spot light center of gravity position, the potential method based on a three-dimensional diffusion equation is applied. An automatic conveyance method for calculating a broken line-shaped obstacle avoidance path for avoiding a three-dimensional obstacle as an obstacle, and conveying the conveyed object on the obstacle avoidance path. 5. The automatic transfer method according to claim 4, wherein the automatic transfer method includes determining a transfer path in which the number of broken lines of the obstacle avoidance path is reduced by applying a broken line approximation method with respect to the obstacle avoidance path. Method. 6. The automatic conveyance method according to claim 5, wherein the conveyance path in which the number of broken lines is reduced is represented by a quintic B-spline curve, and the curve is defined as a conveyance path. 5. The automatic conveyance method according to claim 4, comprising using a constraint condition for obstacle avoidance using a Laplace equation. 6. The automatic conveyance method according to claim 5, comprising applying a complex method to the conveyance path having a reduced number of broken lines to nonlinearly optimize the conveyance path. 7. The automatic conveyance method according to claim 6, comprising performing FF control by inverse dynamics calculation on the conveyance path of the quintic B-spline curve. Using spot light generated by irradiating the floor surface of the target transport position of the transported object with a laser pointer and using a ceiling crane, the transported object is transported in a three-dimensional space from the start position to the position just above the target transport position. A crane system that automatically transports along a transport path:
A carriage capable of moving a conveyed product in the vertical direction and movable in a horizontal plane; and an overhead crane including a frame that supports the carriage so as to be horizontally movable;
At least one camera that images the spotlight;
A controller that is connected to the at least one camera and determines the three-dimensional space coordinates of the center of gravity of the spot light using the picked-up spot light, the three-dimensional space coordinates as the target transport position of the overhead crane A controller that commands the drive;
Comprising a crane system. The crane system according to claim 10, wherein the at least one camera is a CCD camera. The crane system according to claim 10, wherein the at least one camera is fixed to the frame of the overhead crane. 11. The crane system according to claim 10, wherein the controller has two cameras, and when there are no obstacles between the two cameras and the spot light, the controller captures images using the two cameras. The spot light imaging data is used to determine the three-dimensional spatial coordinates of the center of gravity of the spot light, and only one of the two cameras can capture the spot light, and the other cameras are obstacles. When the spot light cannot be picked up due to the above, a crane system that determines the three-dimensional spatial coordinates of the spot light barycentric position using image data of the spot light picked up by the one camera. 14. The crane system according to claim 13, wherein when the number of cameras that can image the spot light is one, the controller includes the imaging data obtained by the one camera that can image the spot light, and A crane system that determines a three-dimensional coordinate of a spot light barycentric position using known coordinates of a position and positional information of the obstacle previously obtained by a light cutting method. 15. The crane system according to claim 14, wherein the controller applies a potential method based on a three-dimensional diffusion equation when an obstacle exists on a straight line connecting the conveyance start position and the spot light gravity center position. Then, a broken line-shaped obstacle avoidance path for avoiding the three-dimensional obstacle of the obstacle is calculated, and the obstacle avoidance path is used as the transport path to instruct the driving device of the overhead crane. 15. The crane system according to claim 14, wherein the controller applies a broken line approximation method with respect to the obstacle avoidance path to determine a conveyance path in which the number of broken lines of the obstacle avoidance path is reduced, and the determination is performed. A crane system for instructing a conveying path to the overhead crane driving device.

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