At present, industrial enterprises manufacture products with a constantly changing nomenclature by introducing robotic systems with elements of artificial intelligence into the production process. The latter allow to increase productivity in conditions when it is difficult or impossible for a person to perform certain production operations. The most important stages of production where industrial robots need to be used are the processing of workpieces and their assembly. At these stages, the workpieces must enter the working area in strict sequence, at the right time and place, and in a certain position. However, in the process of delivery of details, changes are possible, which leads to the need to use identification systems. Mechanical systems have proven themselves very well, however they are very cumbersome and difficult to maintain. The use of systems of technical vision, which allows for the recognition and spatial orientation of an object, seems promising. The study is carried out on the basis of the system of three equations obtained by the authors, showing the dependence of the change in the moments of inertia of a plane figure during its triple rotation in space. Triple rotation means the rotation of an object around three mutually perpendicular coordinate axes OX, OY and OZ at certain angles α, β and γ, respectively.
The application of artificial intelligence technology in robot systems enables to increase the efficiency by adapting to constant changes in the working condition and to achieve greater manufacturing flexibility [1, 2]. Intelligent multi-robot systems are in demand first of all for the work in restricted access conditions and when there is a need for effective decision making with minimal human operator participation [3, 4].
Contemporary robot systems are widely used in industrial production [5, 6]. They have great functional flexibility thanks to progressive actuating mechanism, microprocessor control systems with developed software, vision and other sensors, adaptive capabilities, and can replace people in the implementation of various types of operations [7, 8]. In addition, computer-aided systems are actively used in the food industry for sorting food products [9]. 2
One of the general purpose systems of intelligent robots are technical vision systems [10, 11]. They solve such problems as finding the research object, identifying it, determining its coordinates on the location in the manipulator working area, geometric parameters of the object to ensure its capture, and also industrial assembly and quality control [4, 9].
In the process of manufacturing the product, the main purpose of industrial robots is the installation of pre-oriented storage in the working area of the machine and the removal of completed parts from the machine with subsequent installation on a conveyor line. The parts are delivered only sequentially to the assembly area, i.e., at the right time and place [12, 13].
However, during transportation from one working area to another one, as a result of the influence of external factors, changes in the spatial orientation of products are possible. In this regard, it is promising to make identification of blanks at each stage of processing.
Currently, a number of methods have been developed for the recognition spatial images of objects, however, each of them has its faults. So, in [11], parallel transformation and rotation of the image being a special case of spatial displacements are studied. In [14, 15] the analysis is carried out on reference points, numbering of which remains constant for spatial distortions, which is not always achievable. In [16,17], image analysis is carried out along the contour, which is the most sensitive to distorting factors. In [18], moments of inertia are considered as the main features, however, an analysis of the properties of moments of inertia showed that the features, in this case, are integral for a wide range of objects, which makes it difficult to recognize objects of one cluster.
The process of recognizing a spatial object on images is significantly complicated by the change in all geometric features. This is due to the image undergoing such distortions as rotation and shear. Thus, it can be said that, the task of identifying features being invariant to spatial distortions of object images has not been solved completely. 3
In this article, statistical moments are proposed to be used as reference points for the image, and on the basis of this principle, an effective methodology for determining the orientation of objects in space has been developed.
One of the methods for recognizing the object located arbitrarily in space is the recognition of two-dimensional images of its sides by comparing them with reference images.
As a matter of fact, the side image of the object is a flat closed single-contour or multi-contour figure. Thus, the process of recognizing the object located arbitrarily in space can be reduced to the recognition of several plane figures located arbitrarily in space. If the flat figure is a solid body, then the analysis of its position in space can be made by analyzing the position of the fixed marker point located on a flat figure. In this case, arbitrary location of the plane figure, and consequently, a marker point in space, is considered as the rotations of the plane figure around three coordinate axes. The analysis of the plane figure position will be carried out by analyzing the position of the marker point projection on the frontal plane. In this case, the origin point is located in the center of the plane figure.
In the course of the research [19], the authors obtained the dependence of the
change in the coordinates of the marker point projection during the rotation of the
frontal plane around the horizontal axis OX, followed by rotation around the vertical
axis OY:
x 2 = x 0 cos ,
y2 = y0 cos x0 sin sin ,
(
After integrating expressions (
JX2 = cos3 cos JX0 2 cos2 sin sin cos JX0Y0 + + cos sin 2 cos sin 2 JY0 , JY2 = cos cos3 JY0 ,
JX2Y2 = cos2 cos2 JX0Y0 cos sin cos2 sin JY0 , inertia moment of the plane figure after its double rotation in space, along the axis OX, OY and the centrifugal inertia moment.
As it is known [20], the inertia moment of the section during the rotation of the
axes passing in the plane of the section around the axis passing perpendicular to the
plane of the section are related by equations (
where JX, JY, JXY are axial and centrifugal inertia moments of the section with respect to the initial axes; JU, JV, JUV are axial and centrifugal inertia moments of the section with respect to the rotated axes; γ is rotation angle.
Substituting expressions (
As a result, a system of three equations with three variables is obtained: α, β and γ.
Solving the system of equations (
JU = JX cos2 + JY sin 2 − JXY sin 2 , JV = JX sin 2 + JY cos2 + JXY sin 2 , J UV = J XY cos 2 + J X − J Y sin 2 ,
2 JX3 = f (,, , JX0 , JY0 , JX0Y0 ) , JY3 = f (,, , JX0 , JY0 , JX0Y0 ) ,
JX3Y3 = f (,, , JX0 , JY0 , JX0Y0 ) . 4
In order to check the obtained theoretical results, computer simulation was carried out.
For a more detailed analysis of the proposed methodology, it is desirable to study objects belonging to the same cluster, but significantly differing in form. As a feature characterizing the shape of the object was chosen "shape indicator" defined by the expression [21]:
Area
Studies have shown that for real parts produced by flexible automated manufacturing, the shape index does not exceed 80. Therefore, abstract images were used in computer modeling. To simplify, stylized animal figures were chosen as images of the object.
Figure 1 presents four flat figures, which are the original images.
(
At the first stage, using the AutoCAD system, the original images were rotated in
the image plane at angles γ in increments equal to 40º (40º; 80º; 120º; 160º; 200º;
240º; 280º; 320º). As a result, 8 new images were obtained. Further, the moments of
inertia (JX3_meas, JY3_meas, JXY3_meas) were measured for the obtained images. In addition,
using the formulas (
; DY =
; DXY =
JX3_meas JY3_meas JXY3_meas
Figure 2 presents the graphs of the dependence of relative divergences D on the rotation angle γ for the moments of inertia JX3, JY3, JXY3, respectively.
At the second stage, using the AutoCAD system, the original images were rotated
around the horizontal axis at angles α in increments equal to 10º (10º; 20º; 30º; 40º;
50º; 60º; 70º; 80º). As a result, 8 new images were obtained. Further, similarly to the
first stage, moments of inertia were measured for the obtained images (JX3_meas,
JY3_meas, JXY3_meas), according to formulas (
.(
Figure 3 presents graphs of the dependence of the relative divergences D at rotation angle α for the moments of inertia JX3, JY3, JXY3, respectively. Fig. 2. The dependence of the relative divergences between the corresponding moments of inertia at angles of rotation of the object in the image plane Fig. 3. The dependence of the relative divergence between the corresponding moments of inertia at angles of rotation of the object around the horizontal axis
At the third stage, using AutoCAD system, the original images were rotated
around the vertical axis at β angles in increments equal to 10º (10º; 20º; 30º; 40º; 50º;
60º; 70º; 80º). As a result, 8 new images were obtained. Further, similarly to the first
stage, moments of inertia were measured for the obtained images ((JX3_meas, JY3_meas,
JXY3_meas); according to formulas (
At the fourth stage, using the AutoCAD system, the original images were rotated
in the image plane at angles γ in increments equal to 40º, with subsequent rotations
around the horizontal axis at angles α in increments equal to 10º and around the
vertical axis at angles β in increments equal to 10º (10º, 10º, 40º; 20º, 20º, 80º; 30º, 30º,
120º; 40º, 40º, 160º; 50º, 50º, 200º; 60º, 60º, 240º; 70º, 70º, 280º; 80º, 80º, 320º). As a
result, 8 new images were obtained. Further, similarly to the first stage, moments of
inertia (JX3_meas, JY3_meas, JXY3_meas) were measured for the obtained images; according
to the formulas (
Figure 5 presents the graphs of the dependence of the relative divergence D at the rotation angles α, β, and γ for the moments of inertia JX3, JY3, JXY3, respectively. Fig. 5. The dependence of the relative divergence between the corresponding moments of inertia at rotation angles of the object in the image plane, around the horizontal and vertical axes
As it can be seen from Figure 2 that the graphs are oscillatory in nature. That is, it is possible to come to such a conclusion that the angle of the object rotation in the image plane does not significantly affect the value of the divergence D, and is located in certain acceptable intervals. The reason for the dispersion of the divergence D is the appearance of distortion of discrete images with low resolution.
Additional criteria for assessing the divergence D is the shape indicator. The higher the shape indicator, the greater the dispersion of divergence. The reason for this is the distortion of the pixels of the contour of the object during rotation.
It can be seen from Figure 3 and Figure 4 that the graphs are exponential in nature. That is, it is possible to come to such a conclusion that the angle of the object rotation around the horizontal or vertical axis has a significant effect on the value of the divergence D only at its extreme values. At the same time, at small and average values, it is located in certain acceptable intervals. Similarly, additional criteria for assessing the divergence D can serve as a shape indicator. The higher the shape indicator, the greater increasing rate of the exponent. The reason for this, in addition to low resolution, it serves as the change in the image area.
As it is seen from figure 5 that the graphs are complex oscillating-exponential in nature. In this graph, the exponents have a greater speed than the graphs in figures 3 and 4. So, it is possible to come to such a conclusion that for the objects randomly located in space, the value of the divergence D will be essentially already close to the extreme values of the rotation angle. At the same time, when increasing the indicator, the graphs acquire an N-shaped form.
As it can be seen from the above-mentioned statements, taking into account the
computational error, the system of equations (
This equilibrium system can be used in flexible automated production to clarify the spatial position in the working area of a processing or assembly machine. Thus, it can be applied to autonomous mobile robots to search for objects in this area.