Method for measuring spatial pointing accuracy of panoramic camera turret

Abstract

The present application relates to panoramic camera turntable space pointing accuracy measurement method, first establish initial coordinate system to azimuth axis and pitch axis, through laser tracker to two axis rotation movement data measurement, through spherical fitting and plane fitting space circle fitting method calculates two rotation axis center coordinates and circle surface direction vector, so that the actual position relationship of two coordinate system can be obtained, then through the actual position relationship of two coordinate system, the offset and angle deviation between two coordinate system can be calculated, and the calibration parameter is obtained; then the transformation matrix between reference coordinate system and measurement coordinate system is obtained by using the actual position relationship of two coordinate system, the coordinate vector of the measured point in the reference coordinate system is obtained, and the space included angle of two vectors is obtained by calculating the space included angle of the coordinate vector of the measured point and the theoretical position coordinate vector, so as to obtain the space pointing error. The present application adopts the space coordinate calculation method of robotization method, which not only has universal significance, but also can be popularized to the accuracy measurement of other two-axis general two-dimensional space pointing mechanism.

Description

Technical Field

[0001] This invention relates to the field of aerospace payload robot pointing accuracy measurement technology, specifically a method for measuring the spatial pointing accuracy of a two-dimensional motion mechanism of an aerospace payload robot. Background Technology

[0002] As a two-dimensional spatial motion mechanism, the panoramic camera turntable adopts a two-degree-of-freedom configuration based on a robotic arm. It possesses unique advantages such as a large range of motion, high load capacity, low weight, low power consumption, and internal wiring. Its pointing accuracy is crucial for achieving scientific and engineering goals such as lunar surface scientific exploration in the harsh lunar environment, surface sampling area imaging, and image display. 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] Space two-dimensional pointing mechanisms possess wide-range dynamic pointing and motion tracking capabilities, with pointing accuracy being a crucial performance indicator. Currently, similar aerospace mechanisms have a broad range of applications, with significant demand in payloads such as space optical cameras and satellites. Due to inherent precision and errors in manufacturing, assembly, and transmission mechanisms, it is essential to develop a universal and easily implemented high-precision measurement method to provide spatial pointing accuracy measurement support for space two-dimensional pointing mechanisms, simplifying measurement steps and improving measurement efficiency. This invention utilizes a robotic approach to perform space parameter measurements on a two-dimensional panoramic camera turntable, exhibiting strong versatility, adaptability, and universality. Summary of the Invention

[0004] Based on the actual working conditions of the panoramic camera turntable, after the lander successfully lands on the lunar surface and the pyrotechnics are successfully unlocked, the turntable receives a zero-position calibration command injected from the ground. After calibration and movement to the zero-position, the turntable enters a ready-to-work state and is capable of evaluating the product's pointing accuracy characteristics. Here, pointing accuracy refers to the maximum absolute deviation between the actual spatial pointing attitude given by the turntable's azimuth and pitch joint combinations and the attitude angle theoretically generated by the position command. Therefore, this spatial pointing accuracy is measured on the ground. This invention designs a robotic measurement method to measure the spatial pointing accuracy of a robotic turntable with a two-degree-of-freedom configuration given by the azimuth and pitch joint combinations of the panoramic camera turntable. This method has universal significance and can be extended to the accuracy measurement of two-axis universal two-dimensional spatial pointing mechanisms.

[0005] The technical solution adopted by this invention to achieve the above objectives 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 and pitch joints of the panoramic camera turntable, the coordinate data set of the target measurement points set on the panoramic camera turntable collected by the laser tracker is obtained.

[0007] An azimuth coordinate system and a pitch coordinate system are established using the mean rotation axis of the azimuth axis and the mean rotation axis of the pitch axis of the panoramic camera turntable, respectively, with the azimuth coordinate system designated as the reference coordinate system. The transformation matrix T between the two coordinate systems is obtained based on the coordinate data set of the target measurement points. YP And the transformation matrix relationship T between the measurement coordinate system and the reference coordinate system. RM ;

[0008] Based on the transformation matrix relationship T between the two coordinate systems YP And the transformation matrix relationship T between the measurement coordinate system and the reference coordinate system. RM This yields the actual coordinates and ideal direction vector of 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 target point P is obtained.

[0009] The transformation matrix T between the two coordinate systems is obtained based on the set of coordinate data of the target measurement points. YP And the transformation matrix relationship T between the measurement coordinate system and the reference coordinate system. RM This includes the following steps:

[0010] Step 3-1: Using the spatial circle fitting method, calculate the center positions (a, b, c) of the azimuth and pitch axes and the axis rotation direction vectors [A, B, C]; then obtain the spatial fitting circle direction vector [A...]. P B P C P ]、,center (a P ,b P ,c P ); and pitch axis space fitted circular 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] based on the azimuth axis space. P B P C P ] and pitch axis space fitted circular direction vector [A Y B Y C Y The offset d between the two coordinate systems and the transformation matrix T of the pitch joint relative to the azimuth joint are obtained. YP ;

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

[0013] Step 3-1 is as follows:

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

[0015] Based on the equation of the sphere: 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] Solving the above equation yields M, N, K, and Q. Substituting these values ​​into a = M / 2, b = N / 2, c = K / 2, and R = ... Obtain the coordinates of the sphere's center (a, b, c) and the sphere's radius R;

[0018] 3) Obtain the direction vector [A,B,C] of the spatially fitted circle through plane fitting:

[0019] Based on the equation of the spatial plane: Ax + By + Cz + 1 = 0, then we have

[0020]

[0021] By solving the above equation, we obtain the coefficients A, B, and C, and thus the equation of the space plane.

[0022] 3) [A,B,C] is the direction vector of the spatial fitting circle, with the center at (a,b,c). The spatial circle fitting is complete; therefore, the direction vector [A] of the azimuth axis spatial fitting circle can be obtained. P B P C P ], center (a P ,b P ,c P ); pitch axis space fitting circular direction vector [AY B Y C Y ], center (a Y ,b Y ,c Y ).

[0023] Step 3-2 is as follows:

[0024] 1) Calculate the offset d between the azimuth coordinate system and the pitch coordinate system, i.e., the distance between skew 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 is 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 respectively 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 S is obtained by vector operations. xx S xy S xz ;

[0030] Wherein, the X-axis vector of the pitch axis coordinate system is v YX =[A Y B YC Y The Z-axis vector of the azimuth coordinate system is v. PZ =[A P B P C P The Y-axis direction vector of the azimuth 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 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, Y, and Z axes of the azimuth joint coordinate system are respectively S... yx S yy S yz ;

[0032] The Y-axis vector of the pitch axis coordinate system is the common perpendicular 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 S is obtained by vector operations. yx S yy S yz ;

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

[0034] The Z-axis vector of the pitch axis coordinate system is v YZ =v YX ×v YY S is obtained by using vector operations. zx S zy S zz ;

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

[0036]

[0037] in,

[0038]

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

[0040] Step 3-3 is as follows:

[0041] The Z-axis direction vector of the azimuth 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 product of the first two, denoted 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 obtained in relation to the three coordinate axis vectors v of the measurement coordinate system. MX =(1,0,0), v MY = (0,1,0) and v MZ The direction cosines of (0,0,1) are C xi C yi C zi i = x, y, z;

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

[0044]

[0045] C XX C XY C XZ Let C represent the cosines of the angles 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 YZLet C represent the cosines of the angles 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 These represent the cosines of the angles between the Z-axis of the azimuth coordinate system and the X, Y, and Z-axis of the measurement coordinate system, respectively.

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

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

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

[0049]

[0050] Among them, the coordinates P0(x) in the measurement coordinate system P0 ,y P0 ,z P0 ) Measured by a laser tracker; T YP T represents the transformation matrix relationship between the azimuth coordinate system and the pitch coordinate system. RM This represents the transformation matrix relationship between the measurement coordinate system and the azimuth axis;

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

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

[0053]

[0054] The ideal direction vector of point P

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

[0056] At a certain measurement position, i.e., azimuth angle θ and elevation angle α, the coordinates P(x) of the measurement point P in the measurement coordinate system are measured using a laser tracker. PM ,y PM ,z PM); by transforming matrix T RM Obtain 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] The ideal direction vector Actual direction vector The spatial pointing accuracy Δ of target point P is obtained as follows:

[0060] Based on the ideal direction vector of point P and actual direction vector Obtain the cosine of the angle between two vectors;

[0061] When the measurement positions are azimuth angle θ and elevation angle α, the spatial pointing accuracy of the panoramic camera turntable is:

[0062]

[0063] If the spatial pointing accuracy Δ is less than the product's accuracy technical specifications, the accuracy is considered acceptable; otherwise, it is unacceptable.

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

[0065] 1. This invention employs a robotic theoretical calculation method, which can inherit the theoretical knowledge of robot kinematics and has a certain degree of versatility;

[0066] 2. This invention uses a laser tracker to measure sampling points more accurately, and can calculate the spatial pointing accuracy of the mechanism even with a small sample size, making it more efficient and accurate;

[0067] 3. Although this invention is a measurement method for a panoramic camera turntable, it can be extended to a general measurement method for two-dimensional pointing mechanisms and has universal significance. Attached Figure Description

[0068] Figure 1 The measurement system built upon the laser tracker, panoramic camera turntable, and their control system of the present invention;

[0069] Figure 2 Schematic diagram of azimuth and pitch coordinate systems Figure 1 ;

[0070] Figure 3 Schematic diagram of azimuth and pitch coordinate systems Figure 2 ;

[0071] Figure 4 This is a flowchart of the method of the present invention. Detailed Implementation

[0072] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0073] This invention first establishes initial coordinate systems for the azimuth and pitch axes of a panoramic camera turntable. Data is measured during the rotational motion of these two axes using a laser tracker. Then, the center coordinates and direction vectors of the two rotation axes are calculated using spatial circle fitting methods (sphere fitting and plane fitting), thus obtaining the actual positional relationship between the two coordinate systems. The offset and angular deviation between the two coordinate systems are then calculated based on this actual positional relationship, yielding calibration parameters. Next, the transformation matrix between the reference coordinate system and the measurement coordinate system is obtained using the actual positional relationship. Coordinate transformation is performed on the coordinates of the measured point under any orientation to obtain the coordinate vector of the measured point in the reference coordinate system. The spatial angle between the two vectors is calculated using the position coordinate vector of the measured point under robotic theory, thus obtaining the spatial pointing error. Figure 4 As shown.

[0074] The pointing accuracy measurement system consists of a laser tracker and a panoramic camera turntable (hereinafter referred to as the turntable), as shown in the attached diagram. Figure 1 The laser tracker's measurement sensor is mounted on the camera plate of the turntable's pitch joint. When the turntable's azimuth and pitch joints are driven by the control system, the sensor will report the spatial position point P(X, Y, Z) of the turntable under the position command (azimuth angle θ, pitch angle α). The laser tracker's measurement computer can record the value of point P under the corresponding command.

[0075] Establish a reference coordinate system for the turntable. Use the mean rotation axes of the azimuth and pitch axes to establish azimuth and pitch axis coordinate systems, and use the azimuth axis coordinate system at the initial zero position as the reference coordinate system. (See attached...) Figure 2 .

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

[0077] Calculate the calibration parameters, which are the offset and angular deviation between the two coordinate systems. (See appendix) Figure 3 The length of the common perpendicular segment 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 It is the x-axis of the pitch coordinate system baseYaw The three-term angular position error between the axis vector and the axes of the azimuth coordinate system (y-axis of the pitch coordinate system) baseYaw Axis vectors and z baseYaw The six angular position errors between the axis vectors and the axes of the three-coordinate system of the azimuth coordinate system are not shown in the figure.

[0078] Based on the measured two-axis direction vector parameters, the coordinate transformation between the laser tracker's measurement coordinate system and the reference coordinate system is determined, as is the coordinate transformation between the reference coordinate system and the pitch coordinate system.

[0079] After obtaining the calibration parameters, the coordinates of the measured target point (target) P in the pitch axis coordinate system can be calculated based on the 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 θ, elevation angle α), the ideal coordinates of the target point (target mount) P in the reference coordinate system can be calculated, thus obtaining the ideal direction vector of point P.

[0081] At a given measurement position (azimuth angle θ, elevation angle α), the coordinates of the target measurement point (target mount) P in the measurement coordinate system can be measured using a laser tracker. The measured coordinates can then be transformed back to the reference coordinate system using a transformation matrix between the reference and measurement coordinate systems to obtain the actual direction vector.

[0082] The ideal direction vectors of point P are obtained respectively. and actual direction vector Then, 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 appendix Figure 1 A measurement system is constructed by integrating a laser tracker, a panoramic camera turntable, and their control 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 in place. The panoramic camera turntable is existing technology, but the following technical solution can also be adopted: CN108870034A A robotic panoramic camera turntable adapted to the lunar environment.

[0084] Step 2: After the panoramic camera turntable control system is powered on, it implements rotation control of the azimuth and pitch joints respectively through position commands (azimuth angle θ, pitch angle α). The coordinate data set {x} during azimuth axis rotation is measured and recorded using a laser tracker. 1-n ,y 1-n ,z 1-n}, n = 75; the set of coordinate data for pitch axis rotation {x 1-n ,y 1-n ,z 1-n}, n = 50.

[0085] Step 3: Establish a two-axis coordinate system, refer to the appendix. Figure 2 Based on the data set obtained from the measurement, the following theoretical calculation process is carried out to complete the calculation of the calibration parameters of the two-axis coordinate system, and to 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 spatial circle fitting method to calculate the center positions (a,b,c) of the azimuth axis and pitch axis and the axis rotation direction vector [A,B,C].

[0087] Spatial circle fitting method:

[0088] Spatial circle fitting first involves sphere fitting, followed by plane fitting.

[0089] By fitting the sphere, the coordinates of the sphere's center and the sphere's radius can be obtained:

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

[0091] When the object of study is the azimuth axis, n = 75; when the object of study is the pitch axis, n = 50.

[0092] Let the equation of the sphere be (xa). 2 +(yb) 2 +(z–c) 2 =R 2 Where a, b, and c are the centers of the sphere, and R is the radius of the sphere, the result after expansion is:

[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 We can obtain:

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

[0096] Rewritten in matrix form, we can obtain

[0097]

[0098] We can obtain this through matrix transformation.

[0099]

[0100] Solving for M, N, K, and Q, and substituting them into a = M / 2, b = N / 2, and c = K / 2, This gives us the coordinates of the sphere's center (a, b, c) and the sphere's radius R.

[0101] The direction vector of the spatially fitted circle is obtained through plane fitting.

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

[0103]

[0104] After matrix transformation, we can obtain

[0105]

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

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

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

[0109] 2. Pitch axis spatial fitting circular 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 mean rotation axis of the azimuth axis is:

[0114]

[0115] The equation of the mean gyration axis of the pitch axis is:

[0116]

[0117] Using spatial geometry, we know that the offset d between two coordinate systems is the distance between skew lines, and the length d of the common perpendicular 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 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) 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

[0123] The direction cosines between coordinate axes can characterize the attitude transformation relationship between two coordinate systems. Let S be 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. 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, Y, and Z axes of the azimuth joint coordinate system, are shown in the attached figure. Figure 3 As shown.

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

[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 coordinate system is v. PZ =[A P B P C P The Y-axis direction vector of the azimuth coordinate system is the common perpendicular vector (Equation 010) as 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 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, using vector operations, we can obtain the following results respectively.

[0127]

[0128]

[0129]

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

[0131] Let 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 be Syx, Syy, and Syz, respectively. First, determine the expression for each vector.

[0132] The Y-axis vector of the pitch axis coordinate system is the common perpendicular 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 azimuth coordinate system's axis vectors were given in the previous section. Then, using vector operations, we obtain...

[0133]

[0134]

[0135]

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

[0137] Let 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 be Szx, Szy, and Szz, respectively. First, determine the expression for each vector.

[0138] The Z-axis vector of the pitch axis coordinate system is v YZ =v YX ×v YY The azimuth coordinate system's axis vectors were given in the previous section. Then, using vector operations, we 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 and pitch coordinate systems can be obtained. The nine 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 robotics theory. YP

[0144]

[0145] in

[0146]

[0147] T p T is the rotation matrix for the azimuth axis. Y Let be the rotation matrix of the pitch axis, and θ and α be the azimuth and pitch angles of the two axes, respectively. If a point P(x) in the pitch coordinate system is known... PY ,y PY ,z PY If ), then its coordinates P(x) in the azimuth coordinate system are... 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] Based on the previous data processing results, 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 previous two, denoted 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 obtained in relation to the three coordinate axis vectors v of the measurement coordinate system. MX =(1,0,0), v MY = (0,1,0) and v MZThe direction cosine of (0,0,1) has 9 terms, which are respectively

[0155]

[0156]

[0157]

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

[0159]

[0160] Step 4: Calculate the actual coordinates of target point P in the elevation coordinate system as follows.

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

[0162] Choose a certain initial state, the target point (target base) P to be measured, and its coordinates P0(x) in the measurement coordinate system. P0 ,y P0 ,z P0 The coordinates P of the object in the pitch axis coordinate system can be measured by a laser tracker. py (x PY ,y PY ,z PY This can be obtained through 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 θ, elevation angle α), the ideal coordinates of point P in the reference coordinate system are (obtained using homogeneous coordinate transformation).

[0167]

[0168] Then, at this point, the ideal direction vector of point P (pointing from the origin to point P) is:

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

[0170] Calculate the actual direction vector of point P.

[0171] At a certain measurement position (azimuth angle θ, elevation angle α), the coordinates P(x, y) of the measurement point (target) P in the measurement coordinate system can be measured using a laser tracker. PM ,y PM ,z PM Then, by transforming matrix T... RM We can obtain the coordinates P′(x′) of point P in the reference coordinate system. 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 target point P using the following method.

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

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

[0176]

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

[0178]

[0179] The accuracy measurement results are obtained by comparing the pointing accuracy with the product's accuracy technical specifications.

Claims

1. A method for measuring the spatial pointing accuracy of a panoramic camera turntable, characterized in that, Includes the following steps: By controlling the rotation of the azimuth and pitch joints of the panoramic camera turntable, the coordinate data set of the target measurement points set on the panoramic camera turntable collected by the laser tracker is obtained. Establish azimuth and pitch coordinate systems using the mean rotation axes of the azimuth and pitch axes of the panoramic camera turntable, respectively, with the azimuth coordinate system designated as the reference coordinate system. Obtain the transformation matrix T between the two coordinate systems based on the target measurement point coordinate data set. YP And the transformation matrix relationship T between the measurement coordinate system and the reference coordinate system. RM ; Based on the transformation matrix relationship T between the two coordinate systems YP And the transformation matrix relationship T between the measurement coordinate system and the reference coordinate system. RM This yields the actual coordinates and ideal direction vector of 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 target point P is obtained; The transformation matrix T between the two coordinate systems is obtained based on the set of coordinate data of the target measurement points. YP And the transformation matrix relationship T between the measurement coordinate system and the reference coordinate system. RM This includes the following steps: Step 3-1: Using the spatial circle fitting method, calculate the center positions (a, b, c) of the azimuth and pitch axes and the axis rotation direction vectors [A, B, C]; thus obtaining the spatial fitting circle direction vector of the azimuth axis. center ; and the pitch axis spatial fitting circular direction vector center ; Step 3-2: Fit a circular direction vector based on the azimuth axis space Fitting circular direction vectors to pitch axis space The offset d between the two coordinate systems and the transformation matrix T of the pitch joint relative to the azimuth joint are obtained. YP ; Step 3-3: Calculate the transformation matrix T between the reference coordinate system and the measurement coordinate system. RM .

2. The method for measuring the spatial pointing accuracy of a panoramic camera turntable according to claim 1, characterized in that, Step 3-1 is as follows: 1) When the azimuth joint rotates or the pitch joint rotates, the set of coordinate data of the target measurement points collected by the laser tracker is ( x 1, y 1, z 1), ( x 2, y 2, z 2), ..., ( x n , y n , z n ); n is the number of data points; the coordinates of the sphere's center and the radius of the sphere are obtained using a sphere fitting method; Based on the equation of the sphere: 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 ； Solving the above equation yields M, N, K, and Q. Substituting these values ​​into the equations a = M / 2, b = N / 2, c = K / 2, and R = ... This gives us the coordinates of the sphere's center (a, b, c) and the sphere's radius R. 2) Obtain the direction vectors [A, B, C] of the spatially fitted circle through plane fitting; According to the equation of the spatial plane: Ax + By + Cz + 1 = 0, then we have ； By solving the above equation, we obtain the coefficients A, B, and C, and thus the equation of the space plane. 3) [A, B, C] are the direction vectors of the spatial fitting circle, with the center at (a, b, c). Once the spatial circle fitting is complete, the direction vectors of the azimuth axis spatial fitting circle can be obtained. center ; pitch axis space fitting circular direction vector center .

3. The method for measuring the spatial pointing accuracy of a panoramic camera turntable according to claim 1, characterized in that, Step 3-2 is as follows: 1) Calculate the offset d between the azimuth coordinate system and the pitch coordinate system, i.e., the distance between skew lines: ； wherein v1 = [A Y , B Y , C Y , v2 = [A P , B P , C P , V = , A = [V, v1,v2] T ; The direction vector of the common perpendicular, v3 = ,Right now 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 respectively... 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 ; Wherein, the X-axis vector of the pitch axis coordinate system is = [A Y B Y C Y The Z-axis vector of the azimuth coordinate system is... =[A P B P C P The Y-axis direction vector of the azimuth coordinate system is the common perpendicular vector. = [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 coordinate system is... = = [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, Y, and Z axes of the azimuth joint coordinate system are respectively S... yx S yy S yz ; The Y-axis vector of the pitch axis coordinate system is the common perpendicular 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 S is obtained by vector operations. yx S yy S yz ; 4) The angles between the Z-axis of the pitch joint zero-position coordinate system and the X, Y, and Z-axis of the azimuth joint coordinate system are respectively S... zx S zy S zz ; The Z-axis vector of the pitch axis coordinate system is = S is obtained by using vector operations. zx S zy S zz ; 5) Transformation matrix between the azimuth coordinate system and the pitch coordinate system: ； in, ； ； T p T is the rotation matrix for the azimuth axis. Y Let θ be the rotation matrix of the pitch axis, and α be the azimuth and pitch angles, respectively.

4. The method for measuring the spatial pointing accuracy of a panoramic camera turntable according to claim 1, characterized in that, Step 3-3 is as follows: The Z-axis direction vector of the azimuth 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 product of the first two, denoted as v. PX = =[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 obtained in relation to the three coordinate axis vectors v of the measurement coordinate system. MX = (1, 0, 0), v MY = (0, 1, 0) and v MZ The direction cosines of (0, 0, 1) are C xi C yi C zi i = x, y, z; The transformation matrix between the measurement coordinate system and the reference coordinate system is: ； C XX C XY C XZ Let C represent the cosines of the angles 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 Let C represent the cosines of the angles 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 These represent the cosines of the angles between the Z-axis of the azimuth coordinate system and the X, Y, and Z-axis of the measurement coordinate system, respectively.

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

6. The method for measuring the 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 elevation coordinate system Actual direction vector The details are as follows: (1) Calculate the actual coordinates P of the target point P in the pitch coordinate system. py ( x PY , y PY , z PY ), obtained through homogeneous coordinate transformation: ； Among them, the coordinates P0 in the measurement coordinate system ( x P0 , y P0 , z P0 ) Measured by a laser tracker; T YP T represents the transformation matrix relationship between the azimuth coordinate system and the pitch coordinate system. RM This represents the transformation matrix relationship between the measurement coordinate system and the azimuth axis; (2) Calculate the ideal direction vector of target point P. : At a certain measurement position, i.e., azimuth angle θ and elevation angle α, the ideal coordinates of point P in the reference coordinate system are obtained using homogeneous coordinate transformation: ； The ideal direction vector of point P [ , , ] T ; (3) Calculate the actual direction vector of target point P. : At a certain measurement position, i.e., azimuth angle θ and elevation angle α, the coordinates P(θ) of the measurement point P in the measurement coordinate system are measured using a laser tracker. x PM , y PM , z PM ); by transforming matrix T RM Obtain the coordinates of point P in the reference coordinate system. ; ； Then the actual direction vector of point P is .

7. The method for measuring the spatial pointing accuracy of a panoramic camera turntable according to claim 1, characterized in that, The ideal direction vector Actual direction vector The spatial pointing accuracy Δ of target point P is obtained as follows: Based on the ideal direction vector of point P and actual direction vector Obtain the cosine of the angle between two vectors; When the measurement positions are azimuth angle θ and elevation angle α, the spatial pointing accuracy of the panoramic camera turntable is: 。 8. The method for measuring the spatial pointing accuracy of a panoramic camera turntable according to claim 7, characterized in that, If the spatial pointing accuracy Δ is less than the product's accuracy technical specifications, the accuracy is considered acceptable; otherwise, it is unacceptable.

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