Panoramic camera rotary table space pointing precision measuring method

Abstract

The invention relates to a method for measuring the spatial pointing precision of a panoramic camera turntable, which comprises the following steps of: firstly, establishing an initial coordinate system for an azimuth axis and a pitch axis, performing data measurement on the two axes during rotary motion through a laser tracker, and calculating circle center coordinates and circular surface direction vectors of the two rotary axes through a spatial circle fitting method of sphere fitting and plane fitting; the actual position relation of the two coordinate systems can be obtained, then the offset and the angular deviation between the two coordinate systems can be calculated through the actual position relation of the two coordinate systems, and calibration parameters are obtained; and solving a transformation matrix between the reference coordinate system and the measurement coordinate system by using the actual position relation of the two coordinate systems, obtaining a coordinate vector of a measured point in the reference coordinate system, and solving a space included angle between the two vectors according to the coordinate vector and a theoretical position coordinate vector of the measured point to obtain a space pointing error. The method adopts a space coordinate calculation mode of a robotization method, not only has universal significance, but also can be popularized to precision measurement of other two-axis universal two-dimensional space pointing mechanisms.

Description

Technical Field

[0001] The invention belongs to the pointing accuracy measurement technology of aerospace payload robot, in particular to a precision measurement method for the spatial pointing accuracy of a two-dimensional motion mechanism of an aerospace payload robot. Background Art

[0002] As a two-dimensional motion mechanism, the panoramic camera turntable adopts a two-degree-of-freedom configuration based on a mechanical arm. It has unique advantages such as large motion range, large load, small weight, low power consumption, and internal wiring. Its pointing accuracy is of great significance to the scientific and engineering goals such as lunar surface scientific exploration, surface sampling area imaging, and imaging display under the harsh environment of the lunar surface. Therefore, it is necessary to measure the spatial pointing accuracy of the panoramic camera turntable to ensure that it meets the specified performance indicators.

[0003] The space two-dimensional pointing mechanism has a wide range of dynamic pointing and motion tracking capabilities, among which pointing accuracy is an important indicator to measure its performance. At present, similar aerospace mechanism products have a wide range of applications, and there is a large demand for their use in space optical cameras, satellites and other payloads. Due to the accuracy and errors of the product's processing, manufacturing, assembly and transmission mechanism itself, it is extremely necessary to invent a more general and easy-to-use high-precision measurement method to provide space pointing accuracy measurement support for space two-dimensional pointing mechanism aerospace products, simplify the measurement steps, and improve product measurement efficiency. The present invention uses a two-dimensional panoramic camera turntable to carry out spatial parameter measurement in a robotized manner, which has strong versatility, adaptability and universality. Summary of the invention

[0004] According to the actual working conditions of the panoramic camera turntable, when the lander successfully lands on the lunar surface and the pyrotechnics are successfully unlocked, the turntable receives the zero-position calibration command injected from the ground. After the turntable is calibrated and moves to the zero position, it enters the working preparation state and has the characteristics of evaluating the pointing accuracy of the product. The pointing accuracy here refers to the maximum absolute deviation between the actual pointing posture in space given by the azimuth and pitch joint combination of the turntable and the posture angle theoretically generated by the position instruction. For this purpose, the spatial pointing accuracy is measured on the ground. The present invention designs a robotized measurement method to measure the spatial pointing accuracy of the robotized turntable with a two-degree-of-freedom configuration given by the azimuth and pitch joint combination of the panoramic camera turntable. It has universal significance and can be extended to the accuracy measurement of the two-axis universal two-dimensional space pointing mechanism.

[0005] The technical solution adopted by the present invention to achieve the above-mentioned purpose is: a method for measuring the spatial pointing accuracy of a panoramic camera turntable, comprising the following steps:

[0006] By controlling the rotation of the azimuth joint and the pitch joint of the panoramic camera turntable, a coordinate data set of the target measurement point set on the panoramic camera turntable collected by the laser tracker is obtained;

[0007] The azimuth axis coordinate system and the pitch axis coordinate system are established with the average rotation axis of the azimuth axis and the average rotation axis of the pitch axis of the panoramic camera turntable, respectively, where the azimuth axis coordinate system is defined as the reference coordinate system. The transformation matrix relationship T between the two axis coordinate systems is obtained based on the coordinate data set of the target measurement point. YP , and the transformation matrix relationship T between the measurement coordinate system and the reference coordinate system RM ;

[0008] According to the transformation matrix relationship T between the two axis coordinate systems YP , and the transformation matrix relationship T between the measurement coordinate system and the reference coordinate system RM , get the actual coordinates and ideal direction vector of the target point P in the pitch coordinate system Actual direction vector According to the ideal direction vector Actual direction vector The spatial pointing accuracy Δ of the target point P is obtained.

[0009] The conversion matrix relationship T between the two axis coordinate systems is obtained according to the coordinate data set of the target measurement point. YP , and the transformation matrix relationship T between the measurement coordinate system and the reference coordinate system RM , including the following steps:

[0010] Step 3-1: Use the space circle fitting method to calculate the center position (a, b, c) of the azimuth axis and the pitch axis and the axis rotation direction vector [A, B, C]; then obtain the azimuth axis space fitting circle direction vector [A P ,B P ,C P ], center of circle (a P ,b P ,c P );and pitch axis space fitting circle direction vector [A Y ,B Y ,C Y ], center (a Y ,b Y ,c Y );

[0011] Step 3-2: Fit the circular direction vector [A P ,B P ,C P ] and pitch axis space fitting circle direction vector [A Y ,B Y ,C Y ], and obtain the offset d of the two coordinate systems and the transformation matrix T of the pitch joint relative to the azimuth joint YP ;

[0012] Step 3-3: Calculate the transformation matrix T between the reference coordinate system and the measurement coordinate system RM .

[0013] The step 3-1 is specifically as follows:

[0014] 1) When the azimuth joint rotates or the pitch joint rotates, the coordinate data set of the target measurement point collected by the laser tracker is (x1, y1, z1), (x2, y2, z2), ..., (x n ,y n ,z n );n is the number of data; the sphere center coordinates and sphere radius are obtained by sphere fitting method;

[0015] According to the spherical equation: x 2 +y 2 +z 2 -2ax-2by-2cz+a 2 +b 2 +c 2 =R 2 , let M = 2a, N = 2b, K = 2c, Q = a 2 +b 2 +c 2 -R 2 Then there is

[0016]

[0017] By solving the above equation, we can get M, N, K, Q, and substitute a=M / 2, b=N / 2, c=K / 2, R= Get the coordinates of the sphere center (a, b, c) and the sphere radius R;

[0018] 3) Through plane fitting, the direction vector [A, B, C] of the space fitting circle is obtained:

[0019] According to the space plane equation: Ax+By+Cz+1=0, we have

[0020]

[0021] By solving the above equation to obtain coefficients A, B, and C, we get the spatial plane equation;

[0022] 3) [A, B, C] is the direction vector of the space fitting circle, the center of the circle is (a, b, c), and the space circle fitting is completed; then the azimuth axis space fitting circle direction vector [A P ,B P ,C P ], center (a P ,b P ,c P ); pitch axis space fitting circle direction vector [AY ,B Y ,C Y ], center (a Y ,b Y ,c Y ).

[0023] The step 3-2 is specifically as follows:

[0024] 1) Calculate the offset d between the azimuth axis coordinate system and the elevation axis coordinate system, that is, the distance between the non-coplanar straight lines:

[0025]

[0026] Where v1 = [A Y ,B Y ,C Y ],v2=[A P ,B P ,C P ],V=[a P -a Y ,b P -b Y ,c P -c Y ],A=[V,v1,v2] T ;

[0027] The direction vector of the common perpendicular line v3 = v1 × v2, that is

[0028] v3=[B Y C P -C Y B P ,C Y A P -A Y C P ,A Y B P -B Y A P ];

[0029] 2) The angles between the X-axis of the pitch joint zero position coordinate system and the X-axis, Y-axis, and Z-axis of the azimuth joint coordinate system are S xx , S xy , S xz ; The attitude transformation relationship between the two coordinate systems is represented by the direction cosines between the coordinate axes, and vector operations are used to obtain S xx , S xy , S xz ;

[0030] Among them, the X-axis vector of the pitch axis coordinate system is v YX =[A Y ,B Y,C Y ]; the Z-axis vector of the azimuth axis coordinate system is v PZ =[A P ,B P ,C P ], the Y-axis direction vector of the azimuth axis coordinate system is the common perpendicular vector v PY =[B Y C P -C Y B P ,C Y A P -A Y C P ,A Y B P -B Y A P ], the X-axis vector of the azimuth axis coordinate system is v PX =v PZ ×v PY =[B P (A Y B P -B Y A P )–C P (C Y A P -A Y C P ),C P (B Y C P -C Y B P )–A P (A Y B P -B Y A P ),A P (C Y A P -A Y C P )–B P (B Y C P -C Y B P )];

[0031] 3) The angles between the Y axis of the pitch joint zero position coordinate system and the X axis, Y axis, and Z axis of the azimuth joint coordinate system are S yx , S yy , S yz ;

[0032] The Y-axis vector of the pitch axis coordinate system is the common vertical vector, which is v YY =[B Y C P-C Y B P ,C Y A P -A Y C P ,A Y B P -B Y A P ]; The attitude transformation relationship between the two coordinate systems is represented by the direction cosines between the coordinate axes, and vector operations are used to obtain S yx , S yy , S yz ;

[0033] 4) The angles between the Z axis of the pitch joint zero position coordinate system and the X axis, Y axis, and Z axis of the azimuth joint coordinate system are S zx , S zy , S zz ;

[0034] The Z-axis vector of the pitch axis coordinate system is v YZ =v YX ×v YY , and use vector operations to obtain S zx , S zy , S zz ;

[0035] 5) Transformation matrix between the azimuth axis coordinate system and the elevation axis coordinate system:

[0036]

[0037] in,

[0038]

[0039] T p is the rotation matrix of the azimuth axis, T Y is the rotation matrix of the pitch axis, θ and α represent the azimuth and pitch angles respectively.

[0040] The step 3-3 is specifically as follows:

[0041] The Z-axis direction vector of the azimuth axis coordinate system is v PZ =[A P ,B P ,C P ], the Y-axis direction vector is v PY =[B Y C P -C Y B P ,C Y A P -A Y C P ,AY B P -B Y A P ], the X-axis direction vector is the vector product of the first two, expressed as v PX =v PZ ×v PY =[B P (A Y B P -B Y A P )–C P (C Y A P -A Y C P ),C P (B Y C P -C Y B P )–A P (A Y B P -B Y A P ),A P (C Y A P -A Y C P )–B P (B Y C P -C Y B P )];

[0042] Therefore, each of these three vectors is related to the three coordinate axis vectors v of the measurement coordinate system MX =(1,0,0),v MY =(0,1,0) and v MZ =(0,0,1) direction cosines, respectively C xi , C yi , C zi ; i = x, y, z;

[0043] Then the transformation matrix between the measurement coordinate system and the reference coordinate system is:

[0044]

[0045] C XX , C XY , C XZ They represent the cosine of the angle between the X axis of the azimuth coordinate system and the X, Y, and Z axes of the measurement coordinate system, respectively. YX , C YY , C YZThey represent the cosine of the angle between the Y axis of the azimuth coordinate system and the X, Y, and Z axes of the measurement coordinate system, respectively. ZX , C ZY , C ZZ They represent the cosine of the angles between the Z axis of the orientation coordinate system and the X, Y, and Z axes of the measurement coordinate system.

[0046] The azimuth axis coordinate system and the pitch axis coordinate system are respectively established with the average rotation axis of the azimuth axis and the average rotation axis of the pitch axis of the panoramic camera turntable, and the azimuth axis coordinate system in the zero initial state is used as the reference coordinate system.

[0047] The actual coordinates and ideal direction vector of the target point P in the pitch coordinate system Actual direction vector The details are as follows:

[0048] (1) Calculate the actual coordinate P of the target point P in the pitch coordinate system py (x PY ,y PY ,z PY ), through homogeneous coordinate transformation we get:

[0049]

[0050] Among them, the coordinate P0(x P0 ,y P0 ,z P0 ) is measured by laser tracker; T YP Represents the transformation matrix relationship between the azimuth axis coordinate system and the pitch axis coordinate system, T RM Represents the transformation matrix relationship between the measurement coordinate system and the orientation axis;

[0051] (2) Calculate the ideal direction vector of the target point P

[0052] At a certain measurement position, i.e., azimuth angle θ and elevation angle α, the ideal coordinate value of point P in the reference coordinate system is obtained by homogeneous coordinate transformation:

[0053]

[0054] The ideal direction vector of point P

[0055] (3) Calculate the actual direction vector of the target point P

[0056] At a certain measurement position, i.e., azimuth angle θ and elevation angle α, the coordinates P (x PM ,y PM ,z PM); by transforming the matrix T RM Get the coordinates P′(x′) of point P in the reference coordinate system PR ,y′ PR ,z′ PR )

[0057] [x′ PR ,y′ PR ,z′ PR ] T =T RM [x PM ,y PM ,z PM ] T

[0058] Then the actual direction vector of point P is

[0059] According to the ideal direction vector Actual direction vector The spatial pointing accuracy Δ of the target point P is obtained as follows:

[0060] According to the ideal direction vector of point P and the actual direction vector Get the cosine of the angle between two vectors;

[0061] The spatial pointing accuracy of the panoramic camera turntable at the measurement position, i.e., azimuth angle θ and elevation angle α, is:

[0062]

[0063] If the spatial pointing accuracy Δ is less than the product accuracy technical index, the accuracy is considered qualified; otherwise, it is unqualified.

[0064] The present invention has the following beneficial effects and advantages:

[0065] 1. The present invention adopts a robotized theoretical calculation method, which can inherit the theoretical knowledge of robot kinematics and has a certain degree of versatility;

[0066] 2. The present invention uses a laser tracker to measure the sampling points more accurately. When the sampling sample is not large, the spatial pointing accuracy of the mechanism can be calculated and solved, which is more efficient and accurate.

[0067] 3. Although the present invention is a panoramic camera turntable measurement method, it can be extended to a general measurement method for a two-dimensional pointing mechanism and has universal significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 A measurement system constructed by the laser tracker and panoramic camera turntable of the present invention and its control system;

[0069] Figure 2 Schematic diagram of the azimuth and elevation axis coordinate systems Figure 1 ;

[0070] Figure 3 Schematic diagram of the azimuth and elevation axis coordinate systems Figure 2 ;

[0071] Figure 4 The figure is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0072] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0073] The present invention first establishes an initial coordinate system for the azimuth axis and the pitch axis of the panoramic camera turntable, measures data when the two axes rotate by a laser tracker, and then calculates the center coordinates and circular surface direction vectors of the two rotating axes by a spatial circle fitting method of sphere fitting and plane fitting, thereby obtaining the actual position relationship of the two coordinate systems, and then calculates the offset and angular deviation between the two coordinate systems by the actual position relationship of the two coordinate systems to obtain calibration parameters; then, the actual position relationship of the two coordinate systems is used to obtain the transformation matrix between the reference coordinate system and the measurement coordinate system, and the coordinates of the measured point under any posture are transformed to obtain the coordinate vector of the measured point in the reference coordinate system, and the spatial angle between the two vectors is calculated by using the position coordinate vector of the measured point under the robotization theory, thereby obtaining the spatial pointing error, such as Figure 4 shown.

[0074] Among them, a laser tracker and a panoramic camera turntable (hereinafter referred to as the turntable) are used to form a pointing accuracy measurement system. Figure 1 The laser tracker measurement sensor is installed on the turntable pitch joint camera board. When the turntable azimuth joint and pitch joint are driven by the control system to move, the sensor will feedback the spatial position point P (X, Y, Z) corresponding to the turntable under the position instruction (azimuth angle is θ, pitch angle is α), and the laser tracker measurement computer can record the point P value under the corresponding instruction;

[0075] The reference coordinate system of the turntable is established. The azimuth axis and pitch axis coordinate systems are established with the average rotation axis of the azimuth axis and pitch axis, and the azimuth axis coordinate system at the zero initial state is used as the reference coordinate system. Figure 2 .

[0076] The equation of a space circle can be expressed by a set of equations consisting of a space sphere and a space plane. Therefore, the actual operation of space circle fitting can be divided into two steps: first, sphere fitting is performed to obtain the coordinates of the center of the space circle, and then plane fitting is performed to obtain the direction vector of the space circle surface.

[0077] Calculate the calibration parameters, which are the offset and angular deviation between the two coordinate systems. Figure 3 The length of the common perpendicular line segment in is the offset d of the origin of the pitch joint zero position coordinate system relative to the origin of the azimuth joint coordinate system; S xx , S xy and S xz is the x of the pitch axis coordinate system baseYaw The three angular position errors between the axis vector and the three coordinate system axes of the azimuth axis coordinate system (y baseYaw Axis vector and z baseYaw The six angular position errors between the axis vector and the three coordinate axes of the azimuth axis coordinate system are not shown in the figure).

[0078] According to the measured two-axis direction vector parameters, the coordinate transformation between the laser tracker measurement coordinate system and the reference coordinate system is obtained, and the coordinate transformation between the reference coordinate system and the pitch coordinate system is obtained.

[0079] After obtaining the calibration parameters, the coordinates of the measured target point (target seat) P in the pitch axis coordinate system can be calculated based on the obtained coordinate transformation matrix between the pitch coordinate system and the reference coordinate system, and the coordinate transformation matrix between the reference coordinate system and the measurement coordinate system.

[0080] At a certain measurement position (azimuth angle is θ, elevation angle is α), the ideal coordinate value of the target point (target seat) point P in the reference coordinate system can be calculated to obtain the ideal direction vector of point P

[0081] At a certain measurement position (azimuth angle is θ, pitch angle is α), the laser tracker can be used to measure the coordinate value of the target measurement point (target seat) P in the measurement coordinate system. The measured coordinate value can be converted to the reference coordinate system through the transformation matrix between the reference coordinate system and the measurement coordinate system, and the actual direction vector can be obtained.

[0082] The ideal direction vector of point P is obtained respectively and the actual direction vector Afterwards, the spatial pointing error of the two vectors can be calculated using the cosine formula of the angle between the two vectors.

[0083] Step 1: Refer to the attached Figure 1 , the laser tracker and the panoramic camera turntable and its control system are built into a measurement system, the target measurement point P of the laser tracker is placed on the pitch joint camera plate of the panoramic camera turntable, and glued firmly. The panoramic camera turntable is an existing technology, and the following technical solutions can also be adopted: CN108870034A A robotized panoramic camera turntable adapted to the lunar environment.

[0084] Step 2: After the panoramic camera turntable control system is powered on, the azimuth joint and pitch joint are respectively controlled by position instructions (azimuth angle is θ, pitch angle is α), and the coordinate data set {x 1-n ,y 1-n ,z 1-n}, n = 75; the coordinate data set when the pitch axis rotates {x 1-n ,y 1-n ,z 1-n}, n=50.

[0085] Step 3: Establish a two-axis coordinate system, refer to the attached Figure 2 Based on the above data set obtained by measurement, the following theoretical calculation process is carried out to complete the calibration parameter calculation of the two-axis coordinate system, and obtain the relative matrix relationship of the two-axis coordinate system and the transformation matrix relationship between the measurement coordinate system and the two axes of the turntable.

[0086] Step 3-1: Use the space circle fitting method to calculate the center position (a, b, c) of the azimuth axis and pitch axis and the axis rotation direction vector [A, B, C].

[0087] Space circle fitting method:

[0088] The spatial circle fitting is performed by first performing spherical fitting and then performing plane fitting.

[0089] Through spherical fitting, the coordinates of the sphere center and the sphere radius are obtained:

[0090] The coordinate data measured by the laser tracker is a set of (x1, y1, z1), (x2, y2, z2), ..., (x n ,y n ,z n ).

[0091] When the research object is the azimuth axis, n=75; when the research object is the elevation axis, n=50.

[0092] Let the equation of the ball be (xa) 2 +(yb) 2 +(z–c) 2 =R 2 , where a, b, c are the center of the sphere, and R is the radius of the sphere. After expansion, we can get:

[0093] x 2 + y 2 + z 2 - 2ax - 2by - 2cz + a 2 + b 2 + c 2 = R 2 (001)

[0094] Let M = 2a, N = 2b, K = 2c, Q = a 2 +b 2 +c 2 -R 2 You can get:

[0095] x 2 + y 2 + z 2 - Mx – Ny – Kz +Q = 0 (002)

[0096] Written in matrix form, we get

[0097]

[0098] After matrix transformation, we can get

[0099]

[0100] Solve for M, N, K, Q, and substitute a=M / 2, b=N / 2, c=K / 2, You can get the coordinates of the center of the sphere (a, b, c) and the radius R of the sphere.

[0101] By plane fitting, the direction vector of the space fitting circle is obtained

[0102] The spatial plane equation can usually be expressed as Ax+By+Cz+1=0, which can be written in matrix form as:

[0103]

[0104] After matrix transformation, we can get

[0105]

[0106] By solving the coefficients A, B, and C, we can get the equation of the space plane.

[0107] Then [A, B, C] is the direction vector of the space fitting circle, the center of the circle is (a, b, c), and the space circle fitting is completed. The symbols of the obtained space fitting circle parameters of the azimuth axis and pitch axis are given below:

[0108] 1. Azimuth axis space fitting circle direction vector [A P ,B P ,C P ], center (a P ,b P ,c P );

[0109] 2. Pitch axis space fitting circle direction vector [A Y ,BY ,C Y ], center (a Y ,b Y ,c Y ).

[0110] Step 3-2: Calculate the calibration parameters of the two-axis coordinate system, and obtain the offset d of the two coordinate systems and the transformation matrix T of the pitch joint relative to the azimuth joint YP .

[0111] Calibration parameter calculation

[0112] 1) Calculate the offset d between the two coordinate systems

[0113] After obtaining the parameters of the spatial fitting circle, the equation of the average rotation axis of the azimuth axis is:

[0114]

[0115] The mean rotation axis equation of the pitch axis is

[0116]

[0117] Using the knowledge of spatial geometry, we know that the offset d between the two coordinate systems is the distance between the non-coplanar straight lines, and the length of the common perpendicular line d is

[0118]

[0119] Where v1 = [A Y ,B Y ,C Y ],v2=[A P ,B P ,C P ],V=[a P -a Y ,b P -b Y ,c P -c Y ],A=[V,v1,v2] T .

[0120] At the same time, the direction vector of the common perpendicular line is equal to v3 = v1 × v2, that is

[0121] v3=[B Y C P -C Y B P ,C Y A P -A Y C P ,A Y B P -B Y AP ] (010)

[0122] 2) The angle between the X-axis of the pitch joint zero position coordinate system and the X-axis, Y-axis, and Z-axis of the azimuth joint coordinate system

[0123] The direction cosines between the coordinate axes can characterize the attitude transformation relationship between the two coordinate systems. Suppose the angles between the X-axis of the pitch joint zero-position coordinate system and the X-axis, Y-axis, and Z-axis of the azimuth joint coordinate system are S xx , S xy , S xz The relationship between the two coordinate systems and the angles between the X-axis of the pitch joint zero position coordinate system and the X-axis, Y-axis, and Z-axis of the azimuth joint coordinate system are shown in the attached figure. Figure 3 shown.

[0124] First, determine the vector expression where the coordinate axes of each coordinate system lie.

[0125] The X-axis vector of the pitch axis coordinate system is v YX =[A Y ,B Y ,C Y ], the Z-axis vector of the azimuth axis coordinate system is v PZ =[A P ,B P ,C P ], the Y-axis direction vector of the azimuth axis coordinate system is the common vertical vector (Formula 010) v PY =[B Y C P -C Y B P ,C Y A P -A Y C P ,A Y B P -B Y A P ], the X-axis vector of the azimuth axis coordinate system is v PX =v PZ ×v PY =[B P (A Y B P -B Y A P )–C P (C Y A P -A Y C P ),C P (B Y C P -C Y B P )–A P(A Y B P -B Y A P ),A P (C Y A P -A Y C P )–B P (B Y C P -C Y B P )].

[0126] Then we use vector operations to get

[0127]

[0128]

[0129]

[0130] 3) The angle between the Y axis of the pitch joint zero position coordinate system and the X axis, Y axis, and Z axis of the azimuth joint coordinate system

[0131] Assume that the angles between the X-axis of the pitch joint zero position coordinate system and the X-axis, Y-axis, and Z-axis of the azimuth joint coordinate system are Syx, Syy, and Syz respectively. First, determine the expression of each vector.

[0132] The Y-axis vector of the pitch axis coordinate system is the common vertical vector, which is v YY =[B Y C P -C Y B P ,C Y A P -A Y C P ,A Y B P -B Y A P ], the axis vectors of the azimuth axis coordinate system have been given in the previous section. Then, using vector operations, we can obtain

[0133]

[0134]

[0135]

[0136] 4) The angle between the Z axis of the pitch joint zero position coordinate system and the X axis, Y axis, and Z axis of the azimuth joint coordinate system

[0137] Assume that the angles between the Z axis of the pitch joint zero position coordinate system and the X axis, Y axis, and Z axis of the azimuth joint coordinate system are Szx, Szy, and Szz respectively. First, determine the expression of each vector.

[0138] The Z-axis vector of the pitch axis coordinate system is v YZ =v YX ×v YY , the axis vectors of the azimuth axis coordinate system have been given in the previous section. Then, using vector operations, we can obtain

[0139]

[0140]

[0141]

[0142] 5) Transformation matrix between the reference coordinate system (azimuth axis coordinate system) and the pitch axis coordinate system

[0143] After obtaining the calibration parameters, the transformation matrix between the azimuth axis coordinate system and the pitch axis coordinate system can be obtained. The 9 direction cosines obtained in 2), 3) and 4) can be used to characterize the attitude transformation between the two coordinate systems. Combined with the offset between the two coordinate systems obtained in 1), the complete transformation matrix T between the two coordinate systems can be obtained using the theoretical knowledge of robotics. YP

[0144]

[0145] in

[0146]

[0147] T p is the rotation matrix of the azimuth axis, T Y is the rotation matrix of the pitch axis, θ and α are the azimuth and pitch angles of the two axes respectively. If we know a point P(x PY ,y PY ,z PY ), then its coordinate P(x PP ,y PP ,z PP )for

[0148]

[0149] Step 3-3: Calculate the transformation matrix T between the reference coordinate system and the measurement coordinate system as follows: RM

[0150] Calculate the coordinate transformation matrix T between the reference coordinate system and the measurement coordinate system RM .

[0151] From the previous data processing results, we know that the Z-axis direction vector of the reference coordinate system is v PZ =[A P ,B P ,C P ],

[0152] The Y-axis direction vector is v PY =[B Y C P -C Y B P ,C Y A P -A Y C P ,A Y B P -B Y A P ],

[0153] The X-axis direction vector is the vector product of the first two, expressed as v PX =v PZ ×v PY =[B P (A Y B P -B Y A P )–C P (C Y A P -A Y C P ),C P (B Y C P -C Y B P )–A P (A Y B P -B Y A P ),A P (C Y A P -A Y C P )–B P (B Y C P -C Y B P )].

[0154] Therefore, each of these three vectors is related to the three coordinate axis vectors v of the measurement coordinate system MX =(1,0,0),v MY =(0,1,0) and v MZ=(0,0,1) direction cosine, there are 9 items, they are

[0155]

[0156]

[0157]

[0158] Then the transformation matrix T between the measurement coordinate system and the reference coordinate system is RM for

[0159]

[0160] Step 4: Calculate the actual coordinate value of the target point P in the pitch coordinate system as follows:

[0161] Calculate the coordinates of point P in the pitch coordinate system

[0162] Select a certain initial state, the measured target point (target base) P, the coordinates P0 (x P0 ,y P0 ,z P0 ) can be measured by a laser tracker, then its coordinate P in the pitch axis coordinate system is py (x PY ,y PY ,z PY ), can be obtained by homogeneous coordinate transformation:

[0163]

[0164] Step 5: Calculate the ideal direction vector of target point P as follows

[0165] Calculate the ideal direction vector of point P

[0166] At a certain measurement position (azimuth angle is θ, elevation angle is α), the ideal coordinate value of point P in the reference coordinate system is (obtained using homogeneous coordinate transformation)

[0167]

[0168] At this time, the ideal direction vector of point P (from the origin to point P) is

[0169] Step 6: Calculate the actual direction vector of the target point P as follows

[0170] Calculate the actual direction vector of point P

[0171] At a certain measurement position (azimuth angle is θ, elevation angle is α), the laser tracker can be used to measure the coordinates P (x PM ,y PM ,z PM ). Then by transforming the matrix T RM The coordinates of point P in the reference coordinate system can be obtained as P′(x′ PR ,y′ PR ,z′ PR )

[0172] [x′ PR ,y′ PR ,z′ PR ] T =T RM [x PM ,y PM ,z PM ] T (028) Then the actual direction vector of point P is

[0173] Step 7: Calculate the spatial pointing accuracy Δ of the target point P as follows

[0174] Calculate the pointing accuracy Δ at the measurement position (azimuth angle is θ, elevation angle is α)

[0175] The ideal direction vector of point P is obtained respectively and the actual direction vector After that, the cosine of the angle between the two vectors can be obtained using the following formula:

[0176]

[0177] Then the spatial pointing accuracy of the panoramic camera turntable at the measurement position (azimuth angle is θ, pitch angle is α) is:

[0178]

[0179] The accuracy measurement result is obtained by comparing the pointing accuracy with the product accuracy technical indicators.

Claims

1. A method for measuring the spatial pointing accuracy of a panoramic camera turntable, characterized in that: The following steps are involved: By controlling the rotation of the azimuth joint and the pitch joint of the panoramic camera turntable, a coordinate data set of the target measurement point set on the panoramic camera turntable collected by the laser tracker is obtained; The azimuth axis coordinate system and the pitch axis coordinate system are established with the average rotation axis of the azimuth axis and the average rotation axis of the pitch axis of the panoramic camera turntable, respectively, where the azimuth axis coordinate system is defined as the reference coordinate system. The transformation matrix relationship T between the two axis coordinate systems is obtained based on the coordinate data set of the target measurement point. YP , and the transformation matrix relationship T between the measurement coordinate system and the reference coordinate system RM ; According to the transformation matrix relationship T between the two axis coordinate systems YP , and the transformation matrix relationship T between the measurement coordinate system and the reference coordinate system RM , get the actual coordinates and ideal direction vector of the target point P in the pitch coordinate system Actual direction vector According to the ideal direction vector Actual direction vector The spatial pointing accuracy Δ of the target point P is obtained.

2. The method for measuring the spatial pointing accuracy of a panoramic camera turntable according to claim 1, characterized in that: The conversion matrix relationship T between the two axis coordinate systems is obtained according to the coordinate data set of the target measurement point. YP , and the transformation matrix relationship T between the measurement coordinate system and the reference coordinate system RM , including the following steps: Step 3-1: Use the space circle fitting method to calculate the center position (a, b, c) of the azimuth axis and the pitch axis and the axis rotation direction vector [A, B, C]; then obtain the azimuth axis space fitting circle direction vector [A P ,B P ,C P ], center of circle (a P ,b P ,c P );and pitch axis space fitting circle direction vector [A Y ,B Y ,C Y ], center (a Y ,b Y ,c Y ); Step 3-2: Fit the circular direction vector [A P ,B P ,C P ] and pitch axis space fitting circle direction vector [A Y ,B Y ,C Y ], and obtain the offset d of the two coordinate systems and the transformation matrix T of the pitch joint relative to the azimuth joint YP ; Step 3-3: Calculate the transformation matrix T between the reference coordinate system and the measurement coordinate system RM .

3. The method for measuring spatial pointing accuracy of a panoramic camera turntable according to claim 2, characterized in that: The step 3-1 is specifically as follows: 1) When the azimuth joint rotates or the pitch joint rotates, the coordinate data set of the target measurement point collected by the laser tracker is (x1, y1, z1), (x2, y2, z2), ..., (x n ,y n ,z n );n is the number of data; the sphere center coordinates and sphere radius are obtained by sphere fitting method; According to the spherical equation: x 2 +y 2 +z 2 -2ax-2by-2cz+a 2 +b 2 +c 2 =R 2 , let M = 2a, N = 2b, K = 2c, Q = a 2 +b 2 +c 2 -R 2 Then there is By solving the above equation, we can get M, N, K, Q, and substitute a=M / 2, b=N / 2, c=K / 2. Get the coordinates of the sphere center (a, b, c) and the sphere radius R; 2) Obtain the direction vector [A, B, C] of the space fitting circle through plane fitting; According to the space plane equation: Ax+By+Cz+1=0, we have By solving the above equation to obtain coefficients A, B, and C, we get the spatial plane equation; 3) [A, B, C] is the direction vector of the space fitting circle, the center of the circle is (a, b, c), and the space circle fitting is completed; then the azimuth axis space fitting circle direction vector [A P ,B P ,C P ], center (a P ,b P ,c P ); pitch axis space fitting circle direction vector [A Y ,B Y ,C Y ], center (a Y ,b Y ,c Y ).

4. The method for measuring the spatial pointing accuracy of a panoramic camera turntable according to claim 2, characterized in that: The step 3-2 is specifically as follows: 1) Calculate the offset d between the azimuth axis coordinate system and the elevation axis coordinate system, that is, the distance between the non-coplanar straight lines: where, v1 = [A Y , B Y , C Y , v2 = [A P , B P , C P , V = [a P -a Y , b P -b Y , c P -c Y , A = [V, v1, v2] T ; The direction vector of the common perpendicular line v3 = v1 × v2, that is v3=[B Y C P -C Y B P ,C Y A P -A Y C P ,A Y B P -B Y A P ]; 2) The angles between the X-axis of the pitch joint zero position coordinate system and the X-axis, Y-axis, and Z-axis of the azimuth joint coordinate system are S xx , S xy , S xz ; The attitude transformation relationship between the two coordinate systems is represented by the direction cosines between the coordinate axes, and vector operations are used to obtain S xx , S xy , S xz ; Among them, the X-axis vector of the pitch axis coordinate system is v YX =[A Y ,B Y ,C Y ]; the Z-axis vector of the azimuth axis coordinate system is v PZ =[A P ,B P ,C P ], the Y-axis direction vector of the azimuth axis coordinate system is the common perpendicular vector v PY =[B Y C P -C Y B P ,C Y A P -A Y C P ,A Y B P -B Y A P ], the X-axis vector of the azimuth axis coordinate system is v PX =v PZ ×v PY =[B P (A Y B P -B Y A P )–C P (C Y A P -A Y C P ),C P (B Y C P -C Y B P )–A P (A Y B P -B Y A P ),A P (C Y A P -A Y C P )–B P (B Y C P -C Y B P )]; 3) The angles between the Y axis of the pitch joint zero position coordinate system and the X axis, Y axis, and Z axis of the azimuth joint coordinate system are S yx , S yy , S yz ; The Y-axis vector of the pitch axis coordinate system is the common vertical vector, which is v YY =[B Y C P -C Y B P ,C Y A P -A Y C P ,A Y B P -B Y A P ]; The attitude transformation relationship between the two coordinate systems is represented by the direction cosines between the coordinate axes, and vector operations are used to obtain S yx , S yy , S yz ; 4) The angles between the Z axis of the pitch joint zero position coordinate system and the X axis, Y axis, and Z axis of the azimuth joint coordinate system are S zx , S zy , S zz ; The Z-axis vector of the pitch axis coordinate system is v YZ =v YX ×v YY , and use vector operations to obtain S zx , S zy , S zz ; 5) Transformation matrix between the azimuth axis coordinate system and the elevation axis coordinate system: in, T p is the rotation matrix of the azimuth axis, T Y is the rotation matrix of the pitch axis, θ and α represent the azimuth and pitch angles respectively.

5. The method for measuring the spatial pointing accuracy of a panoramic camera turntable according to claim 2, characterized in that: The step 3-3 is specifically as follows: The Z-axis direction vector of the azimuth axis coordinate system is v PZ =[A P ,B P ,C P ], the Y-axis direction vector is v PY =[B Y C P -C Y B P ,C Y A P -A Y C P ,A Y B P -B Y A P ], the X-axis direction vector is the vector product of the first two, expressed as v PX =v PZ ×v PY =[B P (A Y B P -B Y A P )–C P (C Y A P -A Y C P ),C P (B Y C P -C Y B P )–A P (A Y B P -B Y A P ),A P (C Y A P -A Y C P )–B P (B Y C P -C Y B P )]; Therefore, each of these three vectors is related to the three coordinate axis vectors v of the measurement coordinate system MX =(1,0,0),v MY =(0,1,0) and v MZ =(0,0,1) direction cosines, respectively C xi , C yi , C zi ; i = x, y, z; Then the transformation matrix between the measurement coordinate system and the reference coordinate system is: C XX , C XY , C XZ They represent the cosine of the angle between the X axis of the azimuth coordinate system and the X, Y, and Z axes of the measurement coordinate system, respectively. YX , C YY , C YZ They represent the cosine of the angle between the Y axis of the azimuth coordinate system and the X, Y, and Z axes of the measurement coordinate system, respectively. ZX , C ZY , C ZZ They represent the cosine of the angles between the Z axis of the orientation coordinate system and the X, Y, and Z axes of the measurement coordinate system.

6. The method for measuring spatial pointing accuracy of a panoramic camera turntable according to claim 1, characterized in that: The azimuth axis coordinate system and the pitch axis coordinate system are respectively established with the average rotation axis of the azimuth axis and the average rotation axis of the pitch axis of the panoramic camera turntable, and the azimuth axis coordinate system in the zero initial state is used as the reference coordinate system.

7. The method for measuring spatial pointing accuracy of a panoramic camera turntable according to claim 1, characterized in that: The actual coordinates and ideal direction vector of the target point P in the pitch coordinate system Actual direction vector The details are as follows: (1) Calculate the actual coordinate P of the target point P in the pitch coordinate system py (x PY ,y PY ,z PY ), through homogeneous coordinate transformation we get: Among them, the coordinate P0(x P0 ,y P0 ,z P0 ) is measured by laser tracker; T YP Represents the transformation matrix relationship between the azimuth axis coordinate system and the pitch axis coordinate system, T RM Represents the transformation matrix relationship between the measurement coordinate system and the orientation axis; (2) Calculate the ideal direction vector of the target point P At a certain measurement position, i.e., azimuth angle θ and elevation angle α, the ideal coordinate value of point P in the reference coordinate system is obtained by homogeneous coordinate transformation: The ideal direction vector of point P (3) Calculate the actual direction vector of the target point P At a certain measurement position, i.e., azimuth angle θ and elevation angle α, the coordinates P (x PM ,y PM ,z PM ); by transforming the matrix T RM Get the coordinates P′(x′) of point P in the reference coordinate system PR ,y′ PR ,z′ PR ) [x′ PR ,y′ PR ,z′ PR ] T =T RM [x PM ,y PM ,z PM ] T Then the actual direction vector of point P is 8. The method for measuring spatial pointing accuracy of a panoramic camera turntable according to claim 1, characterized in that: According to the ideal direction vector Actual direction vector The spatial pointing accuracy Δ of the target point P is obtained as follows: According to the ideal direction vector of point P and the actual direction vector Get the cosine of the angle between two vectors; The spatial pointing accuracy of the panoramic camera turntable at the measurement position, i.e., azimuth angle θ and elevation angle α, is:

9. The method for measuring spatial pointing accuracy of a panoramic camera turntable according to claim 8, characterized in that: If the spatial pointing accuracy Δ is less than the product accuracy technical index, the accuracy is considered qualified; otherwise, it is unqualified.

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