Fast and high-precision positioning method suitable for optical polishing system of industrial robot

Abstract

The application discloses a quick high-precision positioning method suitable for an industrial robot optical polishing system, and installs an edge finder on a rotating main shaft of a polishing grinding head of the industrial robot optical polishing system, and a probe terminal of the edge finder is a standard ball head with a radius of r; a calibration tool coordinate system of the robot is determined, a tool center point TCP of the robot is fixed as a ball center position of the ball head of the edge finder probe, a size value of the tool coordinate system is measured, and the robot controller is input; the calibration ball head contacts a target position, corresponding TCP coordinates on a robot teach box are read, and a workpiece coordinate system of an optical mirror to be processed is solved according to the geometric principle that three points determine a plane and three points determine a circle. The method has the characteristics of sub-millimeter positioning precision, good safety performance and simple and quick operation.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of optical processing, and particularly relates to a fast and high-precision positioning method for an optical mirror polishing system of an industrial robot. BACKGROUND

[0002] Compared with general mechanical processing, optical processing has the characteristics of high safety factor and low scrap rate due to the high value of single optical component, high precision of finished product and high risk of breakage of optical component. The positioning accuracy of the optical component directly affects the processing precision and safety, and the positioning method needs to have high precision, good safety performance, simple and fast operation process and the like.

[0003] The polishing of the optical component based on the industrial robot is deterministic precision processing, and the first work is to accurately obtain the workpiece coordinate system of the optical mirror to be processed relative to the robot. The existing workpiece positioning method of the industrial robot generally adopts the workpiece coordinate definition method based on TCP (Tool Centre Position, tool center point) provided by the robot control system. Three marked points are needed on the workpiece, which represent the coordinate origin, the point on the x coordinate axis and the point on the y coordinate axis of the workpiece coordinate system. The TCP pose is kept unchanged, and the robot is manually translated to the three calibration points to complete the positioning. This positioning method needs to determine the marked points in advance, which is difficult to accurately mark on the actual mirror. On the other hand, in theory, the point needs to contact the target position, but the physical size of the sharp point tool in actual use will introduce a large error, and the optical mirror is fragile and easy to damage, which is a super-precision material, and the sharp metal is easy to cause damage

[0004] In addition, the general industrial robot processing application is that the robot is fixed in position, and the workpiece station is also fixed, so that only the workpiece needs to be positioned initially, or the pose of the workpiece on the processing table or processing line can be ensured to complete the positioning. The processing of the optical component, especially the processing of the large-aperture optical mirror, needs to cooperate with the detection light path, and once the detection light path configured for the mirror to be processed is adjusted, it is not easy to move, and the hoisting robot needs to be moved into the corresponding processing position. Therefore, the positioning work is relatively frequent, and the positioning accuracy needs to be high, and a lot of time is consumed. SUMMARY

[0005] In view of the above problems, the present application is based on the secondary development of the industrial robot, and a high-precision positioning method with high safety factor and simple and fast operation is designed and established for optical mirrors of various specifications and shapes, which has the characteristics of sub-millimeter positioning accuracy, good safety performance and simple and fast operation.

[0006] To achieve the above object, the present application provides the following technical solutions.

[0007] The quick high-precision positioning method suitable for the optical polishing system of industrial robot is characterized in that: an edge finder is installed on the rotating main shaft of the polishing grinding head of the optical polishing system of industrial robot, the probe terminal of the edge finder is a standard ball head with a radius of r; the tool center point TCP of the robot is fixed as the ball center position of the ball head of the edge finder by determining the calibration tool coordinate system of the robot; the size value of the tool coordinate system is measured and input into the robot controller; the calibration ball head contacts the target position, and the corresponding TCP coordinate on the robot teach box is read; a plane is determined by three points, and a circle is determined by three points according to the geometric principle, and the workpiece coordinate system of the optical mirror to be processed is solved.

[0008] Further, the optical mirror to be processed is a rotationally symmetrical circular workpiece, and the positioning method steps specifically include:

[0009] 1) Calibrating the z-axis of the workpiece coordinate system; the z-axis vector is calculated by determining the plane with the z-axis as the normal vector; a target plane perpendicular to the z-axis is selected, the robot is controlled to make the calibration ball head contact the plane at an arbitrary pose, and the TCP coordinate on the robot teach box, i.e. the position of the ball center of the calibration ball head in the robot base coordinate system, is read; under the arbitrary contact pose, the connecting line between the ball center and the corresponding contact point is perpendicular to the target plane, then the plane composed of the three ball centers is parallel to the target contact plane, and the distance between the two planes is the ball head radius r;

[0010] 2) The coordinates of any three non-collinear points P1(x1, y1, z1), P2(x2, y2, z2), P3(x3, y3, z3) are obtained by controlling the robot, then:

[0011] P1P2=[(x2-x1),(y2-y1),(z2-z1)]

[0012] P1P3=[(x2-x1),(y2-y1),(z2-z1)]

[0013] The equation of the plane composed of the three ball centers is Ax+By+Cz-A*x1-B*y1-C*z1=0;

[0014] 3) Based on the geometric principle of determining a circle by three points, the robot is controlled to make the calibration ball head contact the cylindrical surface at an arbitrary pose, and the TCP coordinate on the robot teach box is read.

[0015] 4) Control robot to obtain the coordinate values of any three points on the cylindrical surface P4(x4, y4, z4), P5(x5, y5, z5), P6(x6, y6, z6), based on the principle of plane projection, the spherical center coordinates are projected onto the auxiliary calculation plane L; in the auxiliary calculation plane L, the center coordinates of the circle composed of the three projection points can be calculated by the following formula, let the center coordinates be (x0, y0, z0)

[0016]

[0017] 5) According to the actual geometric position of the dot contact plane, the distance h of the auxiliary calculation plane L to the origin of the workpiece coordinate system is calculated;

[0018] 6) Calculate the origin coordinates (x_work, y_work, z_work), the calculation formula is as follows:

[0019]

[0020] According to the position relationship between the auxiliary calculation plane L and the origin, the correct solution is selected;

[0021] 7) Calculate the direction of x axis and y axis; determine the direction of one of x, y, and then solve the other axis through vector cross product operation; make the probe ball head contact point tangent to the marking line of the previous process;

[0022] 8) Let the workpiece coordinate system of the optical mirror surface be T_work, through the calculation of the origin coordinates and the coordinate axis vectors, the following can be obtained:

[0023]

[0024] Where n x = Ax / ((Ax)^2+(Bx)^2+(Cx)^2)^0.5

[0025] n y = Bx / ((Ax)^2+(Bx)^2+(Cx)^2)^0.5

[0026] n z = Cx / ((Ax)^2+(Bx)^2+(Cx)^2)^0.5

[0027] o x = Ay / ((Ay)^2+(By)^2+(Cy)^2)^0.5

[0028] o y = By / ((Ay)^2+(By)^2+(Cy)^2)^0.5

[0029] o z= Cy / ((Ay)2+ (By)2+ (Cy)2)0 5

[0030] a x = A / ((A)2+ (B)2+ (C)2)0 5

[0031] a y = B / ((A)2+ (B)2+ (C)2)0 5

[0032] a z = C / ((A)2+ (B)2+ (C)2)0 5.

[0033] Further, the calibration method used in step 7) is as follows:

[0034] Directly mark two points on the target axis, P7(x7, y7, z7), P8(x8, y8, z8); use the projection method to project the target point onto the auxiliary calculation plane L to obtain the projection point coordinates (x7_p, y7_p, z7_p), (x8_p, y8_p, z8_p), then

[0035] When the target axis is the x-axis,

[0036] X = [(x7_p - x8_p), (y7_p - y8_p), (z7_p - z8_p)]

[0037] X = (Ax, Bx, Cx)

[0038] According to the right-hand rule, it can be solved by cross product operation

[0039] Y = cross (N, X)

[0040] Further, the calibration method used in step 7) is as follows:

[0041] Mark a point on the target axis. When there is only one marker point in the actual situation or the other direction calibration probe cannot be moved to, mark a point P7 on the target x-axis, project it onto the auxiliary calculation plane L, and calculate the x-axis direction from the obtained projection point and the center coordinates obtained by marking the plane;

[0042] When the target point on the x-axis is positive, then

[0043] X = [(x7_p - x0), (y7_p - y0), (z7_p - z0)]

[0044] When the target point on the x-axis is negative, then

[0045] X = [(x0 - x7_p), (y0 - y7_p), (z0 - z7_p)]

[0046] According to the right-hand rule, the y-axis direction is solved by the cross product operation.

[0047] Further, the to-be-processed optical mirror is a rectangular workpiece, and the positioning method specifically comprises the following steps:

[0048] 1) The z-axis and the circular optical workpiece are calibrated by the same method, and an auxiliary calibration plane M is solved; the z-axis vector is N=(A, B, C);

[0049] 2) Select any two adjacent straight edges, mark two points on each edge, project them onto the plane M, and obtain two projected edges; the projected edge parallel to the x-axis is dy+r away from the x-axis, and the projected edge parallel to the y-axis is dx+r away from the x-axis; the straight line equations of the projected edges can be respectively represented as

[0050] a1x+b1y+c1=0

[0051] a2x+b2y+c2=0

[0052] According to the actual coordinate axis direction, the x-axis and y-axis directions are calculated

[0053] X=(Ax,Bx,Cx)

[0054] Y=(Ay,By,Cy)

[0055] 3) Shift the projected edge to the origin to coincide with the target axis, and the projection coordinates (x0, y0, z0) of the origin on the auxiliary calculation plane M can be obtained by the following formula

[0056]

[0057] There are four solutions in the equation set, and according to the positive and negative relationship between the projected edge and the actual x-axis and y-axis, the correct origin projection coordinates are selected;

[0058] 4) According to the actual distance between the auxiliary calculation plane M and the origin, the origin coordinates are solved by the above method, and the workpiece coordinate pose transformation matrix is solved.

[0059] Further, multi-robot cooperation is used for positioning, and the positioning method specifically comprises the following steps:

[0060] 1) A single robot is used to calibrate the workpiece coordinate system, and the remaining workpiece coordinate systems are solved through the relative positions between the robots;

[0061] 2) During the first positioning, the optical mirror is calibrated, and then the workpiece coordinate system in each robot is calibrated;

[0062] 3) In the subsequent processing cycle, only the workpiece coordinates of the optical mirror in any robot need to be calibrated, and then the pose of the mirror in other robots is solved through matrix transformation.

[0063] Compared with the prior art, the present application has the following advantages:

[0064] (1) The present application solves the positioning problem of optical mirrors based on industrial robots, which is simple to operate, has high safety factor, and has higher TCP positioning accuracy and lower requirements than traditional robots. It is very suitable for the application requirements of industrial robots in the field of optical special processing.

[0065] (2) Wide application range, can calibrate general rotationally symmetric circular workpieces and rectangular workpieces. It can also be used for any irregularly shaped optical mirror, and has good scalability and universality, and special complex mirrors can also be positioned.

[0066] (3) Effectively improves the positioning efficiency in the multi-robot cooperation mode, and the positioning accuracy can meet the requirements of the processing system. BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1 It is a 3D diagram of the positioning device of the present application and a position diagram of the workpiece and tool coordinate system.

[0068] Figure 2 It is a plane calibration diagram of the present application.

[0069] Figure 3 It is a diagram of three calibration points of the step surface as the calibration plane of the present application.

[0070] Figure 4 It is a diagram of three calibration points of the bottom surface as the calibration plane of the present application.

[0071] Figure 5 It is a diagram of three calibration points of the auxiliary plane as the calibration plane of the present application.

[0072] Figure 6 It is a diagram of the definition of the calibration distance of the present application.

[0073] Figure 7 It is a diagram of the positions of three calibration points when calibrating a cylindrical surface of the present application.

[0074] Figure 8 It is a diagram of two points on the x-axis of the present application.

[0075] Figure 9 It is a diagram of a point in the positive direction of the x-axis of the present application.

[0076] Figure 10 It is a diagram of a point in the negative direction of the x-axis of the present application.

[0077] Figure 11 The calibration principle diagram of the x-axis and y-axis of the rectangular mirror surface of the application.

[0078] Figure 12 The schematic diagram of the three-robot cooperative processing of the application.

[0079] Figure 13 The setting interface of the tool coordinate system in the embodiment of the application.

[0080] Figure 14 The coordinate value reading interface of the TCP point on the teach pendant in the embodiment of the application.

[0081] Marked in the figure: 1, robot, 2, polishing grinding head, 3, edge finder, 4, probe ball head, 5, tool coordinate system, 6, workpiece coordinate system, 7, optical mirror surface to be processed. DETAILED DESCRIPTION

[0082] The application will be further described in detail below with reference to the accompanying drawings.

[0083] The application is a fast and high-precision positioning method suitable for an optical polishing system of an industrial robot, which can quickly position a mirror surface at any position in the working space of the industrial robot, and the positioning precision can reach a sub-millimeter level. The method is suitable for optical mirror surfaces of various specifications and shapes, and can ensure the safety of the precision optical mirror surface.

[0084] The method of the application adopts a calibration device, and a 3D edge finder 3 can approach the part from any direction (X-axis, Y-axis or Z-axis). The edge finder 3 is connected with a rotating main shaft of a polishing grinding head 2 installed on a flange of a robot 1, as shown in the figure. The probe terminal of the edge finder is a standard probe ball head 4 with a radius of r. The edge finder does not need to be tested and calculated, and there is no positive and negative sign problem. This greatly reduces the additional cost, improves the production efficiency, and reduces the labor intensity. The method specifically includes the following specific steps. Figure 1

[0085] The tool coordinate system 5 of the robot is determined. The TCP of the robot is fixed as the ball center position of the probe ball head of the edge finder. The size value of the tool coordinate system is measured and input into the robot controller. The calibration ball head is used to contact the target position, and the corresponding TCP coordinate on the robot teach pendant is read. According to the geometric principle that three points determine a plane and three points determine a circle, the workpiece coordinate system 6 of the optical mirror surface 7 to be processed is solved. The method includes the following specific steps.

[0086] (1) Positioning of rotationally symmetric circular workpieces

[0087] ​For the most common rotationally symmetric class of circular optical workpiece, first calibrate the z-axis of the workpiece coordinate system. By determining the plane with the z-axis as the normal vector, the z-axis vector is calculated. Select a target plane perpendicular to the z-axis, control the robot so that the calibration ball head contacts the plane at any pose, read the TCP coordinates on the robot teach pendant, i.e. the position of the ball center of the calibration ball head in the robot base coordinate system. As shown in Figure 3 , the line connecting the ball center and the corresponding contact point is perpendicular to the target plane at any contact pose. Then the plane L formed by the three ball center positions is parallel to the target contact plane, and the distance between the two planes is the radius r of the ball head.

[0088] Control the robot to obtain the coordinate values of any three non-collinear points P1(x1, y1, z1), P2(x2, y2, z2), P3(x3, y3, z3), then

[0089] P1P2 = [(x2-x1), (y2-y1), (z2-z1)]

[0090] P1P3 = [(x2-x1), (y2-y1), (z2-z1)]

[0091] Let the plane normal vector N = (A, B, C), which can be obtained by cross(P1P2, P1P3) or cross(P1P3, P1P2). Since in the actual processing process, the z-axis of the mirror coordinate system is always vertical upward, and the orientation of the robot base coordinate system is roughly the same, the C value of the normal vector is positive, and the normal vector coordinates are calculated accordingly. As shown in Figure 2 , the plane formed by the three ball centers is named as auxiliary calculation L, and its equation is Ax+By+Cz-A*x1-B*y1-C*z1=0.

[0092] For general optical workpieces, the mirror body bottom plane and the mirror step plane are both perpendicular to the z-axis of the mirror coordinate system, and can be used as contact planes, as shown in Figure 4 and Figure 5 When these two planes do not meet the conditions or the edge finder calibration probe is not easy to reach the target position, an auxiliary plane can be found as a reference, as shown in Figure 6 In order to improve the plane fitting accuracy, the three points should cover as large an area of the plane as possible.

[0093] Then determine the origin coordinates of the workpiece coordinate system. Based on the geometric principle of determining a circle from three points, control the robot so that the calibration ball head contacts the cylindrical surface at any pose, and read the TCP coordinates on the robot teach pendant, as shown in Figure 6 Similarly, in order to improve the circular fitting accuracy, the three points should cover as large an area of the cylindrical surface as possible.

[0094] The robot is controlled to obtain coordinate values P4(x4, y4, z4), P5(x5, y5, z5), P6(x6, y6, z6) of any three points on the cylindrical surface, and based on the principle of plane projection, the spherical center coordinate is projected onto the plane L. Taking point 4 as an example, the projection point coordinate (x4_p, y4_p, z4_p) can be calculated by the following equation:

[0095]

[0096] The same calculation process can obtain the coordinates (x5_p, y5_p, z5_p), (x6_p, y6_p, z6_p) of points 5 and 6 projected onto the plane L. Then on the plane L, the center coordinate of the circle formed by the three projection points can be calculated by the following formula, assuming the center coordinate is (x0, y0, z0)

[0097]

[0098] According to the actual geometric position of the dot contact plane, the distance h of the auxiliary calculation plane L to the origin of the workpiece coordinate system is calculated. As shown in the calibration position, the distance h = h1 - h2 + R can be calculated. Figure 7

[0099] Then the origin coordinate (x_work, y_work, z_work) is calculated, and the calculation formula is as follows:

[0100]

[0101] According to the position relationship between the plane L and the origin, the correct solution is selected.

[0102] Further, the directions of the x-axis and the y-axis are calculated. Since the z-axis direction has been determined, only the direction of one of the x-axis and the y-axis needs to be determined, and the other axis is solved by vector cross product operation. The axis direction is generally marked on the cylindrical surface in the previous machining process, so that the probe ball head contact point is tangent to the marking line.

[0103] According to the specific shape and actual installation form of the optical workpiece, two calibration methods are generally used.

[0104] 1) Directly mark two points P7(x7, y7, z7), P8(x8, y8, z8) on the target axis, as shown in Figure 8 Similarly, the projection method is used to project the target point onto the auxiliary calculation plane L to obtain the projection point coordinates (x7_p, y7_p, z7_p), (x8_p, y8_p, z8_p). Assuming that the value of point 7 on the coordinate axis is greater than that of point 8, then

[0105] When the target axis is the x-axis,

[0106] ​X = [(x7_p - x8_p), (y7_p - y8_p), (z7_p - z8_p)]

[0107] X = (Ax, Bx, Cx)

[0108] According to the right-hand rule, the x-axis direction can be solved by the cross product operation

[0109] Y = cross (N, X)

[0110] 2) Hit a point on the x-axis, when there is only one marker point in the actual situation or the other direction is not easy to move to the probe, hit a point P7 on the x-axis, project it onto the auxiliary calculation plane L, and calculate the x-axis direction from the obtained projection point and the center coordinates obtained by hitting the plane.

[0111] When the target point is positive on the x-axis, as shown in Figure 9 , then

[0112] X = [(x7_p - x0), (y7_p - y0), (z7_p - z0)]

[0113] When the target point is negative on the x-axis, as shown in Figure 10 , then

[0114] X = [(x0 - x7_p), (y0 - y7_p), (z0 - z7_p)]

[0115] Similarly, according to the right-hand rule, the y-axis direction can be solved by the cross product operation

[0116] Similarly, when the target axis is the y-axis, the y-axis direction can be calibrated as Y = (Ay, By, Cy) using the above method, and the x-axis can be solved by the cross product operation X = cross (Y, N).

[0117] Let the workpiece coordinate system of the optical mirror be T_work, and the origin coordinates and coordinate axis vectors can be calculated to obtain:

[0118]

[0119] where n x = Ax / ((Ax)^2+(Bx)^2+(Cx)^2)^0.5

[0120] n y = Bx / ((Ax)^2+(Bx)^2+(Cx)^2)^0.5

[0121] n z = Cx / ((Ax)^2+(Bx)^2+(Cx)^2)^0.5

[0122] ox = Ay / ((Ay)2+ (By)2+ (Cy)2)0 5

[0123] o y = By / ((Ay)2+ (By)2+ (Cy)2)0 5

[0124] o z = Cy / ((Ay)2+ (By)2+ (Cy)2)0 5

[0125] a x = A / ((A)2+ (B)2+ (C)2)0 5

[0126] a y = B / ((A)2+ (B)2+ (C)2)0 5

[0127] a z = C / ((A)2+ (B)2+ (C)2)0 5

[0128] (2) Rectangular workpiece positioning

[0129] Further, for rectangular optical workpieces, the z-axis and circular optical workpieces are calibrated in the same way, and the auxiliary calibration plane M is solved. The z-axis vector is N = (A, B, C).

[0130] Then select any two adjacent straight edges, as shown in Figure 11 Each edge is marked with two points, and the projection on the plane M is obtained, and two projection edges are obtained. The projection edge parallel to the x-axis is dy + r away from the x-axis, and the projection edge parallel to the y-axis is dx + r away from the x-axis. The straight line equations of the projection edges can be represented as

[0131] a1x + b1y + c1 = 0

[0132] a2x + b2y + c2 = 0

[0133] According to the actual coordinate axis direction

[0134] X = (Ax, Bx, Cx)

[0135] Y = (Ay, By, Cy)

[0136] Shift the projection edge to the origin to coincide with the target axis, and the projection point coordinates (x0, y0, z0) of the origin on the auxiliary calculation plane M can be obtained from the following formula

[0137]

[0138] There are 4 solutions of the equation set, according to the positive and negative relationship between the projection edge and the actual x-axis and y-axis, the correct origin projection coordinates are selected.

[0139] Finally, according to the actual distance between the auxiliary calculation plane M and the origin, the origin coordinates are solved by the above method, and the workpiece coordinate pose transformation matrix is solved.

[0140] (3) Multi-robot cooperative positioning method

[0141] For the processing of super large caliber mirror, multiple robots are needed to cooperate in processing, so the workpiece coordinate system of the optical mirror in each robot needs to be calibrated. Generally, the detection light path of the large caliber mirror interferes with the robot processing position, and the mirror needs to be hoisted into the light path for detection, and then returned to the processing position, so in order to ensure the processing accuracy, the calibration needs to be re-calibrated every time the inspection-processing process is carried out, which is a large amount of work.

[0142] A single robot is used to calibrate the workpiece coordinate system, and the remaining workpiece coordinate systems are solved through the relative positions of the robots. Assuming that there are 3 robots cooperating in processing, as shown in Figure 12

[0143] For the first time positioning, the above positioning method is used to calibrate the workpiece coordinate system of the optical mirror in each robot, which is Taking the optical mirror coordinate as the intermediate reference system,

[0144] The pose transformation matrix of robot 2 relative to robot 1 is

[0145]

[0146] The pose transformation matrix of robot 3 relative to robot 1 is

[0147]

[0148] In the subsequent processing period, only the workpiece coordinate of the optical mirror in any robot needs to be calibrated, and then the pose of the mirror in other robots is solved through matrix transformation. Taking the calibration in robot 1 as an example,

[0149] The workpiece coordinate system of the optical mirror in robot 2 is

[0150]

[0151] The workpiece coordinate system of the optical mirror in robot 3 is

[0152]

[0153] ​The optical mirror to be processed in the embodiment is a circular plane mirror with a diameter of 2300 mm, and the x-axis position is marked on the cylindrical side surface. The industrial robot used is an ABB robot.

[0154] The edge finder is installed, and the probe ball center size, i.e., the position in the robot flange coordinate system, is calibrated. According to the calibration result, the tool coordinate system is set on the robot teach pendant, and is named tool_baioding, as shown in Figure 13 .

[0155] The robot is operated, and first contacts the mirror surface to obtain the coordinates of three contact points in sequence, which are read on the robot teach pendant, as shown in Figure 14 . The three contact points are separated as far as possible to cover a large area of the mirror surface. The coordinates of the three points are (2102.94, 765.45, 1079.42), (1677.69, -17.76, 1076.55), and (2288.62, -941.20, 1067.44).

[0156] The robot is operated to mark three points on the cylindrical surface. Two of the points can be selected as the x-axis marker points. These two points can be reused for the calculation of the center of the circle and the x-axis direction, reducing the workload of marking points and improving efficiency. The coordinates of the three points on the cylindrical surface are (2503.05, -1184.10, 1051.38), (2503.10, 1103.96, 1064.13), and (1493.95, -579.31, 1055.35), wherein the first two points can be reused as the x-axis positive direction (as shown in Figure 9 ) and the x-axis negative direction (as shown in Figure 10 ) calibration points.

[0157] First, the z-axis direction is solved, N = (4484.7703, -5627.3966, 871179.3453).

[0158] Then, the origin coordinates are solved, h is obtained as 4 according to Figure 6 , and the origin coordinates are (2503, -40.1307, 1067.16).

[0159] Further, the x-axis and y-axis directions are solved, X = (-0.060447021200616, -2288.0469, -14.779), and Y = (1.99338e+09, 1.36218e+04, -1.02617e+07).

[0160] The pose transformation matrix of the mirror coordinate system relative to the robot base coordinate system is obtained as

[0161]

[0162] Wherein the pose part of the transformation matrix is converted into a quaternion format readable by the ABB robot:

[0163] [q1, q2, q3, q4] = [0.707097, 0.000463684, 0.00410375, -0.707104]

[0164] Finally, the workpiece coordinate system is verified. The workpiece coordinates and tool coordinates obtained by solving are input in the robot teach pendant. The calibration ball head is moved to the theoretical origin of the workpiece coordinate system, and the deviation from the actual mirror center position is measured. The final error is about 0.2 mm, which meets the processing requirements of the system.

[0165] To sum up, the method of the application provides positioning methods in at least three working conditions, including a rotationally symmetrical mirror positioning method, a rectangular mirror positioning method, and a multi-robot cooperative positioning method, etc. The pose calibration of optical mirrors with different shapes and different specifications can be quickly and safely performed.

[0166] The above only describes the preferred embodiments of the application and is not intended to limit the application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the application shall be included in the protection scope of the application.

Claims

1. A rapid and high-precision positioning method suitable for optical polishing systems of industrial robots, characterized in that, An edge finder is installed on the rotating spindle of the polishing head in an industrial robot optical polishing system. The probe end of the edge finder is a standard ball head with a radius of r. By determining the robot's calibration tool coordinate system, the robot tool center point TCP is fixed at the center position of the ball head of the edge finder probe. The dimensions of the tool coordinate system are measured and input into the robot controller. The calibration ball head contacts the target position, and the corresponding TCP coordinates on the robot teach pendant are read. Using the geometric principles of three points determining a plane and three points determining a circle, the workpiece coordinate system of the optical mirror to be processed is solved. The optical mirror to be processed is a rotationally symmetric near-circular workpiece, and its positioning method specifically includes the following steps: 1) Calibrate the z-axis of the workpiece coordinate system; calculate the z-axis vector by determining the plane with the z-axis as the normal vector; select a target plane perpendicular to the z-axis, control the robot so that the calibration ball head contacts the plane in any pose, and read the TCP coordinates on the robot teach pendant, that is, the position of the center of the calibration ball head in the robot base coordinate system; under any contact pose, the line connecting the center of the ball and the corresponding contact point is perpendicular to the target plane, then the plane formed by the three center positions is parallel to the target contact plane, and the distance between the two planes is the radius r of the ball head; 2) If the robot obtains the coordinates of any three non-collinear points P1(x1,y1,z1), P2(x2,y2,z2), and P3(x3,y3,z3), then: ； P1P3=[(x3-x1),(y3-y1),(z3-z1)]; The equation of the plane formed by the centers of the three spheres is: ; 3) Based on the geometric principle that three points determine a circle, control the robot so that the calibration ball head contacts the cylindrical surface in any pose, and read the TCP coordinates on the robot teach pendant; 4) Control the robot to obtain the coordinate values ​​P4(x4,y4,z4), P5(x5,y5,z5), and P6(x6,y6,z6) of any three points on the cylindrical surface. Based on the principle of planar projection, project the coordinates of the sphere's center onto the auxiliary calculation plane L. On the auxiliary calculation plane L, the coordinates of the center of the circle formed by the three projected points can be calculated using the following formula, where the center coordinates are (x0,y0,z0). ； 5) Based on the actual geometric position of the dotting contact plane, calculate the distance h from the auxiliary calculation plane L to the origin of the workpiece coordinate system; 6) Calculate the coordinates of the origin (x_work, y_work, z_work). The calculation formula is as follows: ； Choose the correct solution based on the positional relationship between the auxiliary calculation plane L and the origin; 7) Calculate the directions of the x-axis and y-axis; determine the direction of one of the x or y axes, and then solve for the other axis through vector cross product operation; make the contact point of the probe ball tangent to the marking line of the previous process; 8) Let the workpiece coordinate system of the optical mirror be T_work. By calculating the coordinates of the origin and the vectors of each coordinate axis, we can obtain: ； in ; ； ； ； ； ； ； ； 。 2. The rapid and high-precision positioning method for an industrial robot optical polishing system according to claim 1, characterized in that, The calibration method used in step 7) is as follows: Directly target two points on the target axis, P7(x7,y7,z7) and P8(x8,y8,z8); use the projection method to project the target points onto the auxiliary calculation plane L, obtaining the coordinates of the projected points (x7_p,y7_p,z7_p) and (x8_p,y8_p,z8_p). When the target axis is the x-axis ； ； According to the right-hand rule, the cross product operation can be used to solve for: 。 3. The rapid and high-precision positioning method for industrial robot optical polishing systems according to claim 1, characterized in that, The calibration method used in step 7) is as follows: When there is only one marker point or the calibration probe in another direction is difficult to move, hit a point P7 on the x-axis of the target and project it onto the auxiliary calculation plane L. Calculate the x-axis direction from the coordinates of the center of the circle obtained from the projection point and the center coordinates of the circle obtained from the hitting plane. When the target point is positive on the x-axis, then: ； When the target point is negative on the x-axis, then: ； The y-axis direction can be obtained by using the right-hand rule and the cross product operation.

4. A rapid and high-precision positioning method suitable for optical polishing systems of industrial robots, characterized in that, An edge finder is installed on the rotating spindle of the polishing head in an industrial robot optical polishing system. The probe end of the edge finder is a standard ball head with a radius of r. By determining the robot's calibration tool coordinate system, the robot tool center point TCP is fixed at the center position of the ball head of the edge finder probe. The dimensions of the tool coordinate system are measured and input into the robot controller. The calibration ball head contacts the target position, and the corresponding TCP coordinates on the robot teach pendant are read. Using the geometric principles of three points determining a plane and three points determining a circle, the workpiece coordinate system of the optical mirror to be processed is solved. The optical mirror to be processed is a rectangular workpiece, and its positioning method specifically includes the following steps: 1) Calibrate the z-axis of the workpiece coordinate system and solve for the auxiliary calibration plane M; the z-axis vector is... The z-axis calibration method is as follows: Calculate the z-axis vector by determining a plane with the z-axis as the normal vector; select a target plane perpendicular to the z-axis, control the robot so that the calibration ball head contacts the plane in any pose, and read the TCP coordinates on the robot teach pendant, i.e., the position of the calibration ball head's center in the robot's base coordinate system; under any contact pose, the line connecting the ball center and the corresponding contact point is perpendicular to the target plane, then the plane formed by the three ball center positions is parallel to the target contact plane, and the distance between the two planes is the ball head radius r. 2) Select any two adjacent right-angled sides, mark two points on each side, and project them onto plane M to obtain two projected sides; the distance from projection side 1 (parallel to the x-axis) to the x-axis is dy+r, and the distance from projection side 2 (parallel to the y-axis) to the x-axis is dx+r; the equations of the lines of the projected sides can be expressed as: ； ； The directions of the x-axis and y-axis are calculated based on the actual orientation of the coordinate axes: ； ； 3) Offset the projected edge until it coincides with the origin and the target axis. The coordinates (x0, y0, z0) of the projection point of the origin on the auxiliary calculation plane M can be obtained by the following formula: ； The system of equations has four solutions. Based on the positive and negative relationship between the projected edge and the actual x-axis and y-axis, the correct origin projection coordinates are selected. 4) Based on the actual distance between the auxiliary calculation plane M and the origin, solve for the coordinates of the origin using the above method, and solve for the workpiece coordinate pose transformation matrix.

5. The rapid and high-precision positioning method for an industrial robot optical polishing system according to claim 1 or 4, characterized in that, The localization method employing multi-robot collaboration includes the following specific steps: 1) Use a single robot to calibrate the workpiece coordinate system, and solve the coordinate system of the remaining workpieces by using the relative positions between the robots; 2) During the initial positioning, the optical mirrors are calibrated sequentially, followed by the workpiece coordinate system in each robot; 3) In subsequent processing cycles, it is only necessary to calibrate the workpiece coordinates of the optical mirror in any robot, and then solve the pose of the mirror in other robots through matrix transformation.

Images