Ballastless track prefabricated slab fine tuning algorithm based on rigid body transformation

Abstract

The invention discloses a ballastless track prefabricated slab fine tuning algorithm based on rigid body transformation. The ballastless track prefabricated slab fine tuning algorithm comprises the following steps that S1, a track slab design coordinate system is obtained through design coordinates; s2, obtaining a track plate actual measurement coordinate system through a total station; s3, vector conversion is conducted on the track board design coordinate system and the track board actual measurement coordinate system; s4, solving a rotation vector; and S5, calculating a translation vector and performing fine adjustment. According to the method, automatic fine adjustment equipment is easier to implement, the number of tools and tools in the track fine adjustment process is reduced, the fine adjustment efficiency is improved, and the track fine adjustment precision is improved. According to the method, the manual workload of track fine adjustment is reduced, the introduction of personnel errors is reduced while the working efficiency is improved, the number of workers in the fine adjustment process can be reduced, and the fine adjustment cost is reduced. The automatic and intelligent level of track fine adjustment is improved, and full-life-cycle digital construction of track engineering construction is promoted.

Description

Technical Field

[0001] The invention relates to the technical field of high-speed railway detection, and in particular to a ballastless track prefabricated plate fine-tuning algorithm based on rigid body transformation. Background Art

[0002] The traditional track plate fine-tuning method calculates the position deviation between the actual track plate and the designed track plate into horizontal, longitudinal and vertical deviation values, and then adjusts these three directions according to the deviation values. However, when adjusting the deviations in these three directions, they will affect each other, resulting in repeated iterative adjustments, making it difficult to obtain accurate adjustment amounts. Summary of the invention

[0003] In order to solve the problems mentioned in the background technology, the present invention proposes a ballastless track precast slab fine-tuning algorithm based on rigid body transformation, which has a simple process and high fine-tuning efficiency.

[0004] To this end, the present invention adopts the following technical solutions:

[0005] A ballastless track prefabricated plate fine-tuning algorithm based on rigid body transformation includes the following steps:

[0006] S1, obtaining the track plate design coordinate system through the design coordinates of the rail support platform in the design file of the track plate to be fine-tuned;

[0007] S2, obtain the measured coordinate system of the track plate through the measured coordinates of the rail support in S1;

[0008] S3, performing vector transformation on the track plate design coordinate system and the track plate measured coordinate system, including:

[0009] The three coordinate axes in the track plate design coordinate system are converted into unit vectors relative to the geodetic coordinate system;

[0010] The three coordinate axes in the measured coordinate system of the track plate are converted into unit vectors relative to the geodetic coordinate system;

[0011] S4, rotating the three unit vectors corresponding to the coordinate axes of the measured coordinate system to make them parallel to the coordinate axes corresponding to the track plate design coordinate system, and obtaining the corresponding rotation angle and rotation matrix;

[0012] S5, calculate the translation vector P according to the rotation matrix; rotate the track plate to be fine-tuned so that its rotation angle is the same as the corresponding rotation angle, and then translate the rotated track plate to be fine-tuned according to the direction and length of the translation vector P to achieve fine adjustment of the track plate.

[0013] In step S1:

[0014] Obtain the design coordinates of the second pair and the penultimate pair of rail supports in the long mileage direction of the track plate to be fine-tuned through the design file, wherein the design coordinates of the rail supports are the coordinates of the center point of the top surface of the rail vertically above the center point of the rail supports;

[0015] Among them, the center point of the top surface of the rail corresponding to the second pair of rail support platforms, which is located on the right side of the large mileage direction, is point A, and the left side is point B. The center point of the top surface of the rail corresponding to the penultimate pair of rail support platforms, which is located on the right side of the large mileage direction, is point C, and the left side is point D. The midpoint of the line connecting point C and point D is point E;

[0016] Then, set the midpoint of the line connecting point A and point B as the origin of the track plate design coordinate system O 1 , O 1 The straight line with point E is taken as the X-axis, and the direction of the X-axis is from point O 1 Point to point E, take the straight line between point A and point B as the Y axis, and the direction of the Y axis is from O 1 Point to B;

[0017] Finally, the Z axis is obtained by multiplying the X axis by the Y axis, and the track plate design coordinate system for the track plate to be fine-tuned is constructed.

[0018] In step S2:

[0019] Measure the measured coordinates of point A, point B, point C, point D and point E in the geodetic coordinate system in step S1 by using a total station;

[0020] Set the midpoint of the line connecting point A and point B as the origin O of the track plate measured coordinate system 2 , O 2 The straight line with point E is taken as the X-axis of the measured coordinate system of the track plate, and its direction is from point O 2 Point to point E, and take the straight line between point A and point B as the Y axis of the track plate measured coordinate system, whose direction is from O 2 Point to B; the straight line where the vector obtained by multiplying the X-axis and Y-axis of the track plate measured coordinate system lies is set as the Z-axis;

[0021] The measured coordinate system of the track plate to be fine-tuned is obtained according to the measured coordinates.

[0022] When the measured coordinate system is obtained, the elevation value in the measured coordinate is adjusted by the prism elevation and the rail elevation.

[0023] Vector transformation is performed in the following way: The unit vector X pointing in the direction of the X-axis of the track plate design coordinate system 1 , the unit vector Y pointing in the Y-axis direction of the track plate design coordinate system 1 , the unit vector Z pointing in the Z-axis direction of the track plate design coordinate system 1 ;

[0024] The unit vector X pointing to the direction of the X-axis of the track plate measured coordinate system 2 , the unit vector Y pointing in the direction of the Y axis of the track plate measured coordinate system 2 , the unit vector Z pointing in the direction of the Z axis of the track plate measured coordinate system 2 .

[0025] S4 includes the following sub-steps:

[0026] S41, if Z 2 ×Z 1 =0 then Z 1 With Z 2 No need to rotate parallelly, enter S44 and set Z 2 =Z″ 2 , X 2 =X′ 2 , Y 2 =Y′ 2 ,θ x =0°,θ y =0°, otherwise go to S42; where × represents vector cross product;

[0027] S42, make Z 2 and Y 2 Around X 2 Rotate θ x Get vector Z′ 2 and vector Y′ 2 , and construct the rotation matrix

[0028] S43, Make X 2 and Z′ 2 Around Y′ 2 Rotation θ y Get vector X′ 2 and vector Z″ 2 , and construct the rotation matrix

[0029] S44, calculate X′ 2 With X 1 Angle And construct the rotation matrix

[0030] S45, solve the rotation vector R,

[0031] In S5: The translation vector P is calculated by the following formula:

[0032] P=o 1 -R·o 2 .

[0033] S42 includes the following sub-steps:

[0034] S421, calculate Z 2 In Y 2 -Z 1 Projection on a plane:

[0035]

[0036] Among them, ‖.‖ represents the modulus of the vector;

[0037] S422, calculation With Z 1 The angle is shown in the following three formulas:

[0038]

[0039] θ x = atan2(sin(θ x ),cos(θ x ));

[0040] Among them, atan2(·) is the inverse tangent function;

[0041] S423, using the θ obtained in S422 x Constructing the rotation matrix

[0042]

[0043] S424, make Z 2 and Y 2 Around X 2 Rotation θ x Get vector Z′ 2 and vector Y′ 2 , as shown in the following two formulas:

[0044]

[0045] S43 includes the following sub-steps:

[0046] S431, calculate Z′ 2 In X 2 -Z 1 Projection on a plane:

[0047]

[0048] S432, calculation With Z 1 The angle θ y , as shown below:

[0049]

[0050] θy = atan2(sin(θ y ),cos(θ y ));

[0051] S433, construct a rotation matrix using the angles obtained in S432

[0052]

[0053] S434, make X 2 and Z′ 2 Around Y′ 2 Rotation θ y Get vector X′ 1 and vector Z" 2 , as shown in the following two formulas:

[0054]

[0055] S44 comprises the following sub-steps:

[0056] S441, calculate X′ 2 With X 1 Angle

[0057]

[0058] S442, construct a rotation matrix using the angles obtained in S441

[0059]

[0060] Compared with the prior art, the present invention has the following beneficial effects:

[0061] 1. The method of the present invention is easier to implement for automated fine-tuning equipment, reduces the number of tools and machines in the track fine-tuning process, and improves the fine-tuning efficiency and track fine-tuning accuracy.

[0062] 2. The method of the present invention reduces the manual workload of track fine-tuning, improves work efficiency, reduces the introduction of human errors, and reduces the fine-tuning cost.

[0063] 3. The present invention has good economic and social benefits, provides a technical reference for intelligent railway design, improves the level of automation and intelligence of track fine-tuning, and promotes the digital construction of the entire life cycle of track engineering construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 is a flow chart of the present invention;

[0065] Figure 2It is a structural schematic diagram of the track plate to be fine-tuned;

[0066] Figure 3 Schematic diagram of the process of constructing the measured coordinate system of the track slab to be fine-tuned. DETAILED DESCRIPTION

[0067] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0068] like Figure 1 As shown, the ballastless track prefabricated slab fine-tuning algorithm based on rigid body transformation of the present invention includes the following steps:

[0069] S1, obtain the track plate design coordinate system through the design coordinates:

[0070] First, if Figure 2 As shown, the design coordinates of the second pair and the penultimate pair of rail supports in the large mileage direction on the track plate to be fine-tuned are obtained through the design file, and the design coordinates of the rail supports are the coordinates of the center point of the top surface of the rail vertically above the center point of the rail support;

[0071] Among them, the center point of the top surface of the rail corresponding to the second pair of rail support platforms is located on the right side of the large mileage direction as point A, and the left side is point B. The center point of the top surface of the rail corresponding to the penultimate pair of rail support platforms is located on the right side of the large mileage direction as point C, and the left side is point D. The midpoint of the line connecting point C and point D is point E.

[0072] Then, set the midpoint of the line connecting point A and point B as the origin of the track plate design coordinate system O 1 , O 1 The straight line with point E is taken as the X-axis, and the direction of the X-axis is from point O 1 Point to point E, take the straight line between point A and point B as the Y axis, and the direction of the Y axis is from O 1 Point to B;

[0073] Finally, the Z axis is obtained by multiplying the X axis by the Y axis, and the track plate design coordinate system for the track plate to be fine-tuned is constructed.

[0074] S2, obtain the measured coordinate system of the track plate through the total station:

[0075] First, if Figure 3 As shown, the measured coordinates of point A, point B, point C, point D and point E in the geodetic coordinate system in step S1 are measured by a prism and a total station;

[0076] Then, the midpoint of the line connecting point A and point B is set as the origin O of the track plate measured coordinate system. 2 , O 2 The straight line with point E is taken as the X-axis, and the direction of the X-axis is from O 2Point to point E, take the straight line between point A and point B as the Y axis, and the direction of the Y axis is from O 2 Point to B; set the line where the vector obtained by multiplying the X-axis by the Y-axis lies as the Z-axis.

[0077] Since the prism elevation HP is generally inconsistent with the rail elevation HR, when obtaining the measured coordinate system, the elevation value of the measured coordinate is adjusted by (HP-HR)·SINθ; where θ is the inward inclination angle of the rail.

[0078] After adjusting the measured coordinates, the measured coordinate system of the track plate to be fine-tuned is obtained.

[0079] S3, perform vector transformation between the track slab design coordinate system and the track slab measured coordinate system:

[0080] Transform the three coordinate axes in the track plate design coordinate system relative to the geodetic coordinate system into:

[0081] The unit vector X pointing in the direction of the X-axis of the track plate design coordinate system 1 , the unit vector Y pointing in the Y-axis direction of the track plate design coordinate system 1 , the unit vector Z pointing in the Z-axis direction of the track plate design coordinate system 1 ;

[0082] The three coordinate axes in the measured coordinate system of the track plate are transformed relative to the geodetic coordinate system into:

[0083] The unit vector X pointing to the direction of the X-axis of the track plate measured coordinate system 2 , the unit vector Y pointing in the direction of the Y axis of the track plate measured coordinate system 2 , the unit vector Z pointing in the direction of the Z axis of the track plate measured coordinate system 2 ;

[0084] S4, solve the rotation vector R:

[0085] S41, if Z 2 ×Z 1 =0 then Z 1 With Z 2 No need to rotate parallelly, enter S44 and set Z 2 =Z″ 2 , X 2 =X′ 2 , Y 2 =Y′ 2 ,θ x =0°,θ y =0°, otherwise go to S42; where × represents vector cross product.

[0086] S42, make Z 2 and Y 2 Around X2 Rotation:

[0087] S421, calculate Z 2 In Y 2 -Z 1 Projection on a plane:

[0088]

[0089] Among them, ‖.‖ represents the modulus of the vector.

[0090] S422, calculation With Z 1 The angle between 2 and Y 2 Around X 2 The angle of rotation is shown in the following three formulas:

[0091]

[0092] θ x = atan2(sin(θ x ),cos(θ x )).

[0093] Among them, atan2(·) is the inverse tangent function, which can be used to obtain the angle value and determine the rotation direction.

[0094] S423, using the θ obtained in S422 x Constructing the rotation matrix

[0095]

[0096] S424, make Z 2 and Y 2 Around X 2 Rotation θ x Get vector Z′ 2 and vector Y′ 2 , as shown in the following two formulas:

[0097]

[0098] S43, Make X 2 and Z′ 2 Around Y′ 2 Rotation, including the following steps:

[0099] S431, calculate Z′ 2 In X 2 -Z 1 Projection on a plane:

[0100]

[0101] S432, calculation With Z 1 The angle θ y , as shown in the following three formulas:

[0102]

[0103] θ y = atan2(sin(θ y ),cos(θ y )).

[0104] S433, construct a rotation matrix using the angles obtained in S432

[0105]

[0106] S434, make X 2 and Z′ 2 Around Y′ 2 Rotation θ y Get vector X′ 1 and vector Z" 2 , as shown in the following two formulas:

[0107]

[0108] S44, make X′ 2 and Y ′ 2 Along Z" 2 The rotation is performed, including the following sub-steps:

[0109] S441, calculate X′ 2 With X 1 Angle As shown in the following three formulas:

[0110]

[0111] S442, construct a rotation matrix using the angles obtained in S441

[0112]

[0113] S45, solve the rotation vector R,

[0114] S5, calculate the translation vector P and make fine adjustments:

[0115] S51, calculate the translation vector P, as shown in the following formula:

[0116] P=o 1 -R·o2 ;

[0117] S52, move the track plate to be fine-tuned along X 2 Rotation θ x , and then along Y′ 2 Rotation θ y , and finally along Z″ 2 Rotation The rotated track plate is obtained, and the rotated track plate is translated along the direction and length of P to achieve fine adjustment of the track plate.

Claims

1. A ballastless track precast slab fine-tuning algorithm based on rigid body transformation, characterized in that: The following steps are involved: S1, obtaining the track plate design coordinate system through the design coordinates of the rail support platform in the design file of the track plate to be fine-tuned; S2, obtain the measured coordinate system of the track plate through the measured coordinates of the rail support in S1; S3, performing vector transformation on the track plate design coordinate system and the track plate measured coordinate system, including: The three coordinate axes in the track plate design coordinate system are converted into unit vectors relative to the geodetic coordinate system; The three coordinate axes in the measured coordinate system of the track plate are converted into unit vectors relative to the geodetic coordinate system; S4, rotating the three unit vectors corresponding to the coordinate axes of the measured coordinate system to make them parallel to the coordinate axes corresponding to the track plate design coordinate system, and obtaining the corresponding rotation angle and rotation matrix; S5, calculate the translation vector P according to the rotation matrix; rotate the track plate to be fine-tuned so that its rotation angle is the same as the corresponding rotation angle, and then translate the rotated track plate to be fine-tuned according to the direction and length of the translation vector P to achieve fine adjustment of the track plate.

2. According to the rigid body transformation based ballastless track precast slab fine tuning algorithm of claim 1, it is characterized by: In step S1: Obtain the design coordinates of the second pair and the penultimate pair of rail supports in the long mileage direction of the track plate to be fine-tuned through the design file, wherein the design coordinates of the rail supports are the coordinates of the center point of the top surface of the rail vertically above the center point of the rail supports; Among them, the center point of the top surface of the rail corresponding to the second pair of rail support platforms, which is located on the right side of the large mileage direction, is point A, and the left side is point B. The center point of the top surface of the rail corresponding to the penultimate pair of rail support platforms, which is located on the right side of the large mileage direction, is point C, and the left side is point D. The midpoint of the line connecting point C and point D is point E; Then, the midpoint of the line connecting point A and point B is set as the origin O1 of the track plate design coordinate system, the straight line between O1 and point E is set as the X-axis, and the direction of the X-axis is from point O1 to point E, and the straight line between point A and point B is set as the Y-axis, and the direction of the Y-axis is from O1 to point B; Finally, the Z axis is obtained by multiplying the X axis by the Y axis, and the track plate design coordinate system for the track plate to be fine-tuned is constructed.

3. The ballastless track precast slab fine-tuning algorithm based on rigid body transformation according to claim 2 is characterized in that: In step S2: Measure the measured coordinates of point A, point B, point C, point D and point E in the geodetic coordinate system in step S1 by using a total station; The midpoint of the line connecting point A and point B is set as the origin O2 of the track plate measured coordinate system, the straight line between O2 and point E is set as the X-axis of the track plate measured coordinate system, and its direction is from point O2 to point E, the straight line between point A and point B is set as the Y-axis of the track plate measured coordinate system, and its direction is from O2 to B; the straight line where the vector obtained by cross-multiplying the X-axis and Y-axis of the track plate measured coordinate system is set as the Z-axis; The measured coordinate system of the track plate to be fine-tuned is obtained according to the measured coordinates.

4. The ballastless track precast slab fine-tuning algorithm based on rigid body transformation according to claim 3 is characterized in that: When the measured coordinate system is obtained, the elevation value in the measured coordinate is adjusted by the prism elevation and the rail elevation.

5. The ballastless track precast slab fine-tuning algorithm based on rigid body transformation according to claim 1 is characterized in that: The vector conversion is performed in the following manner: the unit vector X1 pointing in the direction of the X-axis of the track plate design coordinate system, the unit vector Y1 pointing in the direction of the Y-axis of the track plate design coordinate system, and the unit vector Z1 pointing in the direction of the Z-axis of the track plate design coordinate system; The unit vector X2 points to the direction of the X-axis of the track plate's measured coordinate system, the unit vector Y2 points to the direction of the Y-axis of the track plate's measured coordinate system, and the unit vector Z2 points to the direction of the Z-axis of the track plate's measured coordinate system.

6. The ballastless track precast slab fine-tuning algorithm based on rigid body transformation according to claim 5 is characterized in that: S4 includes the following sub-steps: S41, if Z2×Z1=0, then Z1 and Z2 are parallel and no rotation is required, enter S44 and set Z2=Z″2, X2=X′2, Y2=Y′2, θ x =0°,θ y =0°, otherwise go to S42; where × represents vector cross product; S42, rotate Z2 and Y2 around X2 by θ x Get vector Z′2 and vector Y′2, and construct the rotation matrix S43, rotate X2 and Z′2 around Y′2 by θ y Get vector X′2 and vector Z″2, and construct the rotation matrix S44, calculate the angle between X′2 and X1 And construct the rotation matrix S45, solve the rotation vector R, 7. The ballastless track precast slab fine-tuning algorithm based on rigid body transformation according to claim 6 is characterized in that: In S5: The translation vector P is calculated by the following formula: P=o1-R·o2.

8. The ballastless track precast slab fine-tuning algorithm based on rigid body transformation according to claim 6 is characterized in that: S42 includes the following sub-steps: S421, calculate the projection of Z2 on the Y2-Z1 plane: Among them, ‖.‖ represents the modulus of the vector; S422, calculation The angle with Z1 is shown in the following three equations: i x =atan2(sin(θ x ),cos(θ x )); Among them, atan2(·) is the inverse tangent function; S423, using the θ obtained in S422 x Constructing the rotation matrix S424, rotate Z2 and Y2 around X2 by θ x The vector Z′2 and vector Y′2 are obtained as shown in the following two equations:

9. The ballastless track precast slab fine-tuning algorithm based on rigid body transformation according to claim 8 is characterized in that: S43 includes the following sub-steps: S431, calculate the projection of Z′2 on the X2-Z1 plane: S432, calculation Angle θ with Z1 y , as shown below: i y =atan2(sin(θ y ),cos(θ y )); S433, construct a rotation matrix using the angles obtained in S432 S434, rotate X2 and Z′2 around Y′2 by θ y The vector X′2 and vector Z″2 are obtained as shown in the following two equations:

10. The ballastless track precast slab fine-tuning algorithm based on rigid body transformation according to claim 9 is characterized in that: S44 comprises the following sub-steps: S441, calculate the angle between X′2 and X1 S442, construct a rotation matrix using the angles obtained in S441

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