Parts full-field displacement perception method based on multi-point measurement

Abstract

The present invention relates to a method for sensing full-field displacement of a part based on multi-point measurement, comprising: selecting m measurement points on the surface of a part entity, measuring the coordinates of these measurement points when the part is in a first position to obtain part coordinates #imgabs0#, and measuring the coordinates of these measurement points when the part is in a second position to obtain part coordinates #imgabs1#, where m ≥ 5; establishing a mathematical model of the part, determining m model points corresponding to the positions of these measurement points on the mathematical model, obtaining model coordinates #imgabs2# of these model points, and respectively calculating rotation and translation matrices R1T1 and R2T2 from the model coordinates #imgabs3# to the part coordinates #imgabs4# and part coordinates #imgabs5#; and obtaining the displacement of the part from the first position to the second position based on R1T1 and R2T2. The present invention is highly versatile and applicable to parts of various complex shapes and structures. It can quickly and efficiently sense the full-field displacement of the part using only a small amount of measurement and calculation.

Description

Technical Field

[0001] The present invention relates to the field of spatial measurement technology, and in particular to a method for sensing the full-field displacement of a part based on multi-point measurement. Background Art

[0002] With the rapid development of the aircraft manufacturing industry, the intelligentization of aircraft assembly processes has become an inevitable trend, and the requirements for measuring the position information and other status data of aircraft parts during assembly are becoming increasingly stringent. As the benchmark for aircraft assembly accuracy, the online, high-precision, and efficient acquisition of full-field displacement information of key parts is crucial, directly impacting the assembly accuracy and quality of the aircraft. Due to the diverse structure of aircraft tooling parts and the complex working conditions of the assembly process, the demanding measurement environment severely limits both measurement space and measurement methods, exponentially increasing the difficulty of achieving both high accuracy and effectiveness. Summary of the Invention

[0003] The object of the present invention is to provide a method for sensing the full-field displacement of a part based on multi-point measurement, wherein the part is a three-dimensional object and is rigid, and the method comprises the following steps:

[0004] Step 1: Select m measurement points on the surface of the part entity, measure the coordinates of the m measurement points when the part is in the first position, and obtain the part coordinates in, Among them, ≥5;

[0005] Step 2: Establish a mathematical model of the part, determine m model points corresponding to the positions of the m measurement points on the mathematical model, and obtain the model coordinates of the m model points in,

[0006] Step 3: Calculate the model coordinates To the part coordinates The rotation and translation matrix R1T1;

[0007] Step 4: Measure the coordinates of the m measurement points when the part is in the second position, and obtain the part coordinates in,

[0008] Step 5: Calculate the model coordinates To the part coordinates The rotation and translation matrix R2T2;

[0009] Step 6: Obtain the displacement of the part from the first position to the second position based on R1T1 and R2T2.

[0010] In one embodiment, the minimum value of m is determined by the following steps:

[0011] Step i: In the mathematical model of the part, based on the plane equations at the m model points The model coordinates Transformed into the following form:

[0012]

[0013] Among them, the plane equation Expressed as:

[0014]

[0015] Step ii: Calculate the distance vector matrix D composed of the distance vectors between every two points in the m model points M :

[0016]

[0017] Each column element Represents the distance vector between two model points, the distance vector matrix D M The total number of columns is R = (m-1) + (m-2) ... + 2 + 1 = m (m-1) / 2,

[0018] Step iii: Calculate the distance vector matrix D composed of the distance vectors between every two points in the m measurement points C :

[0019]

[0020] Step iv: The distance between every two points in the m measurement points and the distance between every two points in the m model points are equal in a one-to-one correspondence as a constraint condition for solving the following formula, and thus the minimum value of the number of measurement points m is 5 based on the following formula:

[0021]

[0022] In one embodiment, in step 1, a measurement point is selected based on the determined minimum value of m.

[0023] In one embodiment, the model coordinates are calculated To the part coordinates The rotation and translation matrix RT includes the following steps:

[0024] Step a: Calculation and The mean matrix A C and A M :

[0025]

[0026]

[0027] Step b: Calculation and and their respective mean matrices A C and A M The difference matrix L C and

[0028] L M :

[0029]

[0030]

[0031] Step c: Calculate the difference matrix L C and L M The product H:

[0032]

[0033] Step d: Perform singular value decomposition on H to obtain H = USV:

[0034] [U,S,V]=svd(H)

[0035] Step e: Calculate the rotation and translation matrix RT:

[0036] R=VU T

[0037] T=A C -RA M

[0038] The mapping relationship from m model points to m measurement points is calculated:

[0039] P C =RP M +T

[0040] In one embodiment, the method further comprises the following steps: based on the mapping relationship obtained in step e, obtaining all points Q on the part C All points on the mathematical model of the part are Q M The mapping relationship between them:

[0041] Q C =RQ M +T

[0042] In one embodiment, obtaining the displacement of the part from the first position to the second position based on R1T1 and R2T2 includes the following steps:

[0043] Step I: Obtaining a mapping relationship between the part in the first position and the mathematical model of the part:

[0044]

[0045] in, Indicates the coordinates of all points of the part when it is in the first position,

[0046] Step II: Obtaining a mapping relationship between the part in the second position and the mathematical model of the part:

[0047]

[0048] in, represents the coordinates of all points of the part when it is in the second position,

[0049] Step III: Based on the mapping relationship in step I, the following formula is obtained:

[0050]

[0051] Step IV: Based on the mapping relationship in step II and the formula in step III, the following formula is obtained:

[0052]

[0053] According to the solution provided by the present invention, the full-field displacement of a part can be perceived quickly and efficiently through only a small amount of measurement and calculation. At the same time, this method is highly versatile and applicable to parts of various complex shapes and structures, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] To better understand the above and other objects, features, advantages, and functions of the present invention, reference may be made to the preferred embodiments shown in the accompanying drawings. Like reference numerals in the accompanying drawings refer to like components. Those skilled in the art should understand that the accompanying drawings are intended to illustrate preferred embodiments of the present invention by way of illustration and are not intended to limit the scope of the present invention. The components in the drawings are not drawn to scale.

[0055] Figure 1 This is a schematic diagram of the measurement system used in the full-field displacement sensing method of parts based on multi-point measurement.

[0056] Figure 2 It is a schematic diagram of mapping the measurement points of a part to the model points of the corresponding mathematical model.

[0057] Figure 3 It is a schematic diagram of the full-field displacement sensing results of the parts.

[0058] Where: 1-part; 2-camera; 3-measurement point; 4-mathematical model of the part; 5-coordinates Q of all points of the mathematical model of the part M ; 6-Measurement coordinates Q of all points of the part C . DETAILED DESCRIPTION

[0059] During the assembly process, for example, the spatial position and posture of a part (such as an airplane tooling) change. For example, the part undergoes translational movement and rotation at a certain angle. These displacement information are difficult to measure directly. To this end, the present invention proposes a method for sensing the full-field displacement of a part based on multi-point measurement. "Multi-point measurement" refers to measuring the coordinates of multiple points (also called points) on a part. Since the part moves (including rotation and translation), it generates displacement. The method of the present invention can determine the displacement (i.e., "displacement sensing"), and "full-field displacement of the part" refers to the displacement of the part as a whole (including all points on it). The position of the part before and after the movement can be represented by a displacement vector. The distribution of the displacement vector in three-dimensional space is called a displacement field.

[0060] In the method of the present invention, a mathematical model of a part is established. The part in the mathematical model has a fixed spatial position and posture. The position of the part is represented by coordinates (or coordinate matrix). The coordinate information of each point of the mathematical model of the part is known and constant. When the part moves from a first position to a second position, the coordinate information of its first position and second position is an unknown quantity and needs to be measured, and the displacement from the first position to the second position is also an unknown quantity and cannot be directly measured. For this purpose, the position of the mathematical model of the part as a known quantity can be used as a medium. First, the displacement vector from the first position of the part to the mathematical model is calculated, that is, the relative displacement from the first position of the part to the mathematical model is obtained. Then, the displacement vector from the second position of the part to the mathematical model is calculated, that is, the relative displacement from the second position of the part to the mathematical model is obtained. Finally, the displacement between the two positions is determined based on these two relative displacements, that is, the displacement of the part is indirectly obtained by calculation.

[0061] In the calculation, the displacement between different positions is represented by a displacement vector. The displacement vector is represented by a transformation matrix between the coordinate matrices of the part at different positions and represents the displacement (including rotation and translation) between different positions. The transformation matrix is the rotation-translation matrix RT (i.e., rotation matrix R and translation matrix T) known in the art. To this end, the coordinates of the part at a first position and a second position are measured, and two rotation-translation matrices are calculated from these two sets of coordinates to the mathematical model. These two rotation-translation matrices can be used to determine the corresponding rotation and translation of the part between the first position and the second position.

[0062] In practice, this method does not necessarily require measuring all points on the part. Instead, it measures the coordinates of a limited number of points to determine the rotation and translation matrices between these points and the corresponding points on the mathematical model. This rotation and translation matrix is then applied to all points on the part and to the points on the mathematical model. Hereinafter, the points on the part to be measured are referred to as measurement points, the points on the mathematical model corresponding to the measurement points are referred to as model points, the coordinates of the measurement points are referred to as part coordinates, and the coordinates of the model points are referred to as model coordinates.

[0063] It is assumed that m measurement points need to be measured, and their coordinates are expressed as part coordinates P C or (i=(1,2,…,m)), the coordinates of the m model points of the corresponding mathematical model are expressed as model coordinates P M or Taking a three-dimensional part (i.e. a three-dimensional object) as an example, the coordinates of the m measurement points are The coordinates of the m model points are In this paper, for the convenience of expression and description, the coordinate P M or In addition to indicating specific coordinates, it can also be used to indicate the i-th model point, which also applies to P C or and Q described below C and Q M .

[0064] During measurement, since only points on the outer surface of the part entity can be measured and internal points cannot be measured, m measurement points are arranged on the surface of the part, that is, m measurement points are selected on the surface of the part entity, and correspondingly, m model points are also located on the outer surface of the mathematical model.

[0065] In summary, the method of the present invention comprises the following steps:

[0066] Step 1: Select m measurement points on the surface of the part entity, measure the coordinates of the m measurement points when the part is in the first position, and obtain the part coordinates in,

[0067] Step 2: Establish a mathematical model of the part, determine m model points corresponding to the positions of the m measurement points on the mathematical model, and obtain the model coordinates of the m model points in,

[0068] Step 3: Calculate model coordinates To the part coordinates The rotation and translation matrix R1T1;

[0069] Step 4: Measure the coordinates of the m measurement points when the part is in the second position, and obtain the coordinates of the part in,

[0070] Step 5: Calculate model coordinates To the part coordinates The rotation and translation matrix R2T2;

[0071] Step 6: Obtain the displacement of the part from the first position to the second position based on R1T1 and R2T2.

[0072] Next, we determine the minimum number of m points that need to be measured. This is based on the assumption that the part is rigid and does not deform. The distance between two points on the part is constant at all locations before and after the part is moved. Furthermore, the distance between each two points in the m measurement points corresponds to the distance between each two points in the m model points. In the calculation, the difference in the coordinates between each two points forms a distance vector, which can be used to calculate the distance between the two points. All these distance vectors form a distance vector matrix, which contains and represents the total number of distances between each two points. The following steps determine the minimum value of m.

[0073] Step i: Based on the mathematical model of the part, the model coordinates of m model points are Transform into a new coordinate form to facilitate the calculation of the distance vectors and distance vector matrices of the m model points.

[0074] In the mathematical model, as mentioned above, m model points are located on the surface of the mathematical model of the part. In one case, these surfaces are planes, then these surfaces have plane equations in the mathematical model. These equations are known and can be obtained from the mathematical model. In addition, there are also cases where the outer surface is a curved surface. In this case, the plane equations of the tangent plane of the mathematical model at the model point are taken, and these plane equations are also known in the coordinate system of the mathematical model and can be directly obtained. In the following, the plane equations in these two cases are unified as Represented, and the model points conform to these equations, that is, mathematically the following relationship exists:

[0075]

[0076] Generally speaking, it can be obtained from the mathematical model of the part It is expressed as the following formula (1):

[0077]

[0078] Among them, a k 、b k 、c k d k represents the coefficients of the plane equation,

[0079] The coordinates of m model points Substituting into formula (1), the coordinate values are transformed into the following form:

[0080]

[0081]

[0082] …

[0083]

[0084] Among them, a i→k 、b i→k 、c i→k d i→k Represents the model point position on the kth plane The coefficients of the plane equation are For example, a 2→k 、b 2→k 、c 2→k d 2→k Represents the model point position on the kth plane The coefficients of the plane equation.

[0085] For coordinates The transformed form consists of two coordinates x i and y i Characterization, the number of unknown quantities is reduced from the original 3 (i.e. x i 、y i 、z i ) becomes 2.

[0086] Step ii: Calculate the distance vector matrix D composed of the distance vectors between every two points in the m model points M , expressed as the following formula (2):

[0087]

[0088] Each column element Represents the distance vector between two model points. The distance vector includes the difference between the coordinate values of the two points. There are three values in total, namely the difference between the x-coordinates, the difference between the y-coordinates, and the difference between the z-coordinates. This distance vector can be used to calculate the distance between the two points.

[0089] As shown in formula (2), the distance vector matrix D M The total number of columns (ie, the total number of distance vectors or the total number of distances between points) is R = (m-1) + (m-2) ... + 2 + 1 = m (m-1) / 2.

[0090] Step iii: Similarly, calculate the distance vector between every two points in the m measurement points to form the distance vector matrix D C , expressed as the following formula (3):

[0091]

[0092] Step iv: Since the part is rigid, the distances between corresponding points between the part and its mathematical model are equal one by one, that is, as shown in the following formula (4):

[0093]

[0094] Formula (4) holds, that is, there is a solution. According to the above description, D C From the measuring point P C The coordinates of D are calculated. M The unknown quantity in (x i ,y i ), i = (1, 2, ..., m), a total of 2m unknowns, the constraint condition is R = m (m-1) / 2, so the number of constraints must be greater than or equal to the number of unknowns, as shown in the following formula (5):

[0095] m(m-1) / 2≥2m (5)

[0096] Solving formula (5), we can obtain m≥5, that is, for a three-dimensional part, at least 5 points need to be measured to implement the method of the present invention.

[0097] Similarly, for a two-dimensional part (i.e., a planar part, such as a plate), it is represented by two coordinates xy, and the coordinate information is Similarly, m≥3 is calculated using the above method, that is, for a two-dimensional part, at least three points need to be measured to implement the method of the present invention.

[0098] Calculating the rotation and translation matrix RT includes the following steps:

[0099] Step a: Calculate P C and P M The mean matrix A C and A M , where the mean matrix refers to the matrix composed of the average values of the corresponding coordinate values of these measurement points (that is, the average value of the x coordinates, the average value of the y coordinates, and the average value of the z coordinates of these measurement points), as shown in the following formulas (6) and (7):

[0100]

[0101]

[0102] Step b: Calculate P C and P M and their respective mean matrices A C and A M The difference matrix L C and L M The difference matrix is the matrix composed of the differences between the corresponding coordinate values of these measurement points and the corresponding coordinate values of their mean matrix (i.e., x-coordinate value, y-coordinate value, and z-coordinate value), as shown in the following formulas (8) and (9):

[0103] L C =P C -A C (8)

[0104] L M =P M -A M (9)

[0105] Step c: Calculate the difference matrix L C and L M The product H is shown in the following formula (10):

[0106]

[0107] Step d: Perform SVD decomposition (i.e., singular value decomposition) on H to obtain H = USV, as shown in the following formula (11):

[0108] [U,S,V]=svd(H) (11)

[0109] Step e: Based on the above SVD decomposition results, calculate the rotation and translation matrix RT, as shown in the following formulas (12) and (13):

[0110] R=VU T (12)

[0111] T=A C -RA M (13)

[0112] By obtaining the rotation and translation matrix RT, we can obtain the mapping relationship between the m model points and the m measurement points, that is, the displacement vector between the two, as shown in the following formula (14):

[0113] P C =RP M +T (14)

[0114] Expand these m points to the entire part, that is, all points Q on the part C And all points Q on the mathematical model M All satisfy formula (14), so the following formula (15) is finally obtained:

[0115] Q C =RQ M +T (15)

[0116] Formula (15) represents the full-field displacement of the part between the part and its mathematical model.

[0117] Using the above method of calculating the rotation and translation matrix RT, the rotation and translation matrices R1 and T1 between the part and the mathematical model of the part when it is in the first position are calculated, and the mapping relationship between the two is obtained, as shown in the following formula (16):

[0118]

[0119] in, Represents the coordinates of all points of the part when it is in the first position.

[0120] Similarly, the rotation and translation matrices R2 and T2 between the part and the mathematical model of the part when the part is in the first position are calculated, and the mapping relationship between the two is obtained, as shown in the following formula (17):

[0121]

[0122] in, Indicates the coordinates of all points of the part when it is in the second position.

[0123] The following formula (18) is obtained from formula (16):

[0124]

[0125] Among them, (R1) -1 Represents the inverse matrix of R1.

[0126] Substituting formula (18) into formula (17), we obtain formula (19):

[0127]

[0128] From formula (19), we can get all the points of the part: and The mapping relationship between them is that the displacement of the part from the first position to the second position is obtained based on R1T1 and R2T2.

[0129] By analogy, when the part moves to the third position, the displacement between the third position of the part and the first position or the second position can be calculated, that is, the displacement between the various positions of the part is sensed to obtain the displacement field of the part.

[0130] The specific embodiments of the present invention are described in detail below with reference to specific parts and drawings. Figure 1 A three-dimensional solid part 1 is shown, which is in a certain position. The part is L-shaped as a whole and includes ribs. Its outer contour includes multiple planes, but this is only a simple example of the present invention. The part can also be various other shapes and structures and its outer contour can also include curved surfaces of various shapes, such as quadratic surfaces, including spheres, ellipsoids, cylindrical surfaces, hyperboloids, etc.

[0131] Figure 1 The measurement system includes a camera 2, which is used to capture and measure the spatial coordinates of various points on part 1 at that location. Measurement points 3 of part 1 are located on the surface of the part; that is, camera 2 measures the coordinates of points on the surface of the part; and these measurement points 3 are within the camera's field of view. To this end, before measurement, the position of the camera or part can be adjusted so that the area or location on the part where the measurement points are located is captured by the camera. The location of the measurement points can be selected arbitrarily, as long as they are within the camera's field of view. Once the measurement points are located, their relative position to the part is fixed and does not change.

[0132] The measurement point can be selected at a position with obvious characteristics. For example, the measurement point can be located on the edge of the part, on the intersection line between two planes, or at the intersection of lines. In this way, the positional relationship between the measurement point and the part can be quickly and easily determined. Correspondingly, the position of the model point corresponding to the measurement point on the mathematical model of the part can be determined accordingly. However, the present invention is not limited to this. The measurement point can be selected at various positions and characterized by the distance between it and the reference element of the part (for example, a plane, a line, an intersection). Figure 1Points in For example, it is located on the left vertical plane of the part, a certain distance away from the top plane of the part, and a certain distance away from the left and right edges of the left vertical plane. By using the top plane and the two edges as reference elements, the position of the point can be easily selected and located. Correspondingly, on the mathematical model of the part, Figure 2 As shown, the corresponding model points can also be located based on the above reference elements and distances. The position of all measurement points and model points can be determined by analogy, and then the subsequent steps can be carried out.

[0133] According to the displacement sensing method described above, for a three-dimensional part, at least five points need to be measured, but more than five points can also be measured. Figure 1 As shown, there are 5 points on the part In order to fully reflect the overall shape of the part, these points are evenly distributed on multiple planes of the part. and Located on the same plane. It is more preferred that these points can be arranged so that one point is correspondingly arranged on one plane. In the extreme case, these points can be arranged on the same plane. Note that, Figure 1 The embodiment in which the outer surfaces of the parts are all planes and the measurement points are arranged on these planes is shown. However, as mentioned above, this is not limited to this. The parts can also include curved surfaces and the measurement points can be arranged on the curved surfaces. According to the above method, the positions of these measurement points are represented by reference elements, and correspondingly, the positions of the model points are determined on the mathematical model of the part, such as Figure 2 As shown, the measuring point The model point corresponding to the position in the mathematical model is

[0134] The following five points are used to verify the minimum value of m obtained by the above method. The mathematical model of the part establishes an xyz coordinate system and the coordinate information of its outer surface is known. The coordinate information of the five model points is These 5 model points are located on the 4 surfaces of the part model Above, among them and Located on the same surface On, therefore, The following relationships exist with the surface of the model:

[0135]

[0136] like Figure 2 As shown, according to the coordinate information of the mathematical model, the plane equations of these four surfaces are obtained as follows:

[0137]

[0138]

[0139]

[0140]

[0141] So we have the following:

[0142]

[0143]

[0144]

[0145]

[0146]

[0147] It should be noted here that in this embodiment, the surface of the part where the measurement points are arranged is a plane, so the coordinates of the points conform to the equation of the plane; when the measurement points are arranged on a curved surface, the equation of the tangent plane of the curved surface at the point is used, that is, the measurement point is located on the tangent plane, and its coordinates conform to the equation of the tangent plane.

[0148] According to the relationship between the model points on the mathematical model of the part, The distance vector matrix D composed of the distance vectors between each two points M It can be expressed as:

[0149]

[0150] Then the matrix D M The total number of columns represents the total number of distances between points, which is R = (5-1) + (5-2)... + 2 + 1 = 5 (5-1) / 2 = 10.

[0151] In the actual measurement of the part, the 5 model points P M The corresponding 5 measurement points P C The measured coordinate values are shown in Table 1 below.

[0152] Table 1

[0153]

[0154] The distance vector matrix D between the model points in the mathematical model M Correspondingly, the measuring point P C The distance vector matrix D composed of the distance vectors between each two pointsC It can be calculated according to Table 1:

[0155]

[0156] Since the part is rigid, the distance between every two points is constant, and the distances between corresponding points in the part and its mathematical model are equal one by one, then

[0157]

[0158] This formula is valid. According to the above derivation, D M There are 10 unknown quantities in D C From the five measurement points P in Table 1 C Calculation shows that the number of constraints is 10. It can be seen that the number of unknown quantities is equal to the number of constraints, so the formula has a solution, thereby verifying that the method of the present invention requires at least m=5 points to be measured.

[0159] Next, determine the part Figure 2 In the position shown, the measuring point P C To model point P M The mapping relationship between the two coordinate matrices is determined, that is, the transformation matrix between them, that is, the rotation and translation matrix RT.

[0160] According to the coordinate information of the mathematical model, the five model points P M The coordinate values are shown in Table 2 below:

[0161] Table 2

[0162]

[0163]

[0164] First, calculate P C and P M The mean matrix A C and A M ,as follows:

[0165]

[0166]

[0167] Then, calculate P C and P M and their respective mean matrices A C and A M The difference matrix l C and l M ,as follows:

[0168]

[0169]

[0170] Next, calculate L C and L M The product H of

[0171]

[0172] Then, perform SVD decomposition (i.e. singular value decomposition) on H, i.e. H = USV, and we get the following

[0173]

[0174]

[0175]

[0176] According to the above calculation results, the rotation and translation matrix RT is calculated as follows:

[0177]

[0178] T=A C -RA M =[-1815.161 -1611.369 1293.901] T

[0179] Finally, the model point P is obtained M To measuring point P C The mapping relationship is expressed as:

[0180] P C =RP M +T

[0181] Its mathematical meaning is that the model point P M Transform to the measurement point P through the rotation vector (i.e., rotation matrix R) and translation vector (i.e., translation matrix T) C Specific to the parts, its physical meaning is that the point P on the mathematical model of the part M Move to the measurement point P after the rotation associated with the rotation matrix R and the translation associated with the translation matrix T C , and the rotation angle and translation distance experienced can be represented and determined by the rotation matrix R and the translation matrix T respectively. The specific calculation method is well known in the art and will not be repeated here.

[0182] Expand these limited 5 discrete points to the entire part. As mentioned above, all points of the part are Q C All points Q of its mathematical model M The above relationship is satisfied, that is,

[0183] Q C =RQ M +T

[0184] Specific as Figure 3 As shown, the number 5 on the left represents all the points Q of the mathematical model of the part M The coordinates of the part are shown in Figure 6, and the number 6 on the right represents all the points Q of the part. C The two have different coordinate values, different positions and postures, and the displacement between them (including rotation and translation) is represented and determined by the rotation matrix R and the translation matrix T.

[0185] Figures 1 to 3 The method specifically describes how to determine the positional mapping relationship between a part at a certain position and its mathematical model. Each time the part moves, for example, the position before the part moves is defined as the first position, and the position after the part moves is defined as the second position. Using the method described above, the displacement represented by formula (19) can be ultimately obtained simply by measuring the coordinates of five points on the part entity before and after the movement. This determines the displacement of the part each time it moves, enabling perception of the full-field displacement of the part.

[0186]

[0187] By sensing the displacement of the part each time it moves, the displacement field of the part is obtained. After the displacement field is established, the position of the part in space can be represented by the coordinate information of the displacement field, realizing the digital modeling of the entire part, which is convenient for carrying out the measurement of the spatial coordinates and vector displacement (including translation and rotation) of the part.

[0188] The method of the present invention is simple, easy to implement, and consumes few resources. It can quickly and efficiently complete the perception of the full-field displacement of a part through only a small amount of measurement and calculation. At the same time, the method is highly versatile and applicable to parts of various complex shapes and structures, and has broad application prospects.

[0189] The above description of various embodiments of the present invention is provided for the purpose of description to one of ordinary skill in the relevant art. It is not intended to exclude or limit the present invention to a single disclosed embodiment. As mentioned above, a person of ordinary skill in the field of the above teachings will understand the various substitutions and variations of the present invention. Therefore, although some alternative embodiments are specifically described, a person of ordinary skill in the art will understand or relatively easily develop other embodiments. The present invention is intended to include all substitutions, modifications and variations of the present invention described herein, as well as other embodiments that fall within the spirit and scope of the present invention described above.

Claims

1. A method for sensing full-field displacement of parts based on multi-point measurement, characterized in that: The part is a three-dimensional object and is rigid, and the method comprises the following steps: Step 1: Select m measurement points on the surface of the part entity, measure the coordinates of the m measurement points when the part is in the first position, and obtain the part coordinates in, Where m≥5; Step 2: Establish a mathematical model of the part, determine m model points corresponding to the positions of the m measurement points on the mathematical model, and obtain the model coordinates of the m model points in, Step 3: Calculate the model coordinates To the part coordinates The rotation and translation matrix R1T1; Step 4: Measure the coordinates of the m measurement points when the part is in the second position, and obtain the part coordinates in, Step 5: Calculate the model coordinates To the part coordinates The rotation and translation matrix R2T2; Step 6: Obtain the displacement of the part from the first position to the second position based on R1T1 and R2T2, The minimum value of m is determined by the following steps: Step i: In the mathematical model of the part, based on the plane equations at the m model points The model coordinates Transformed into the following form: Among them, the plane equation Expressed as: Step ii: Calculate the distance vector matrix D composed of the distance vectors between every two points in the m model points M : Among them, each column element Represents the distance vector between two model points, the distance vector matrix D M The total number of columns is R = (m-1) + (m-2) ... + 2 + 1 = m (m-1) / 2, Step iii: Calculate the distance vector matrix D composed of the distance vectors between every two points in the m measurement points C : Step iv: The distance between every two points in the m measurement points and the distance between every two points in the m model points are equal in a one-to-one correspondence as a constraint condition for solving the following formula, and thus the minimum value of the number of measurement points m is 5 based on the following formula:

2. The method according to claim 1, characterized in that In the step 1, a measurement point is selected based on the determined minimum value of m.

3. The method according to claim 1, characterized in that Calculate the model coordinates To the part coordinate P i C The rotation and translation matrix RT includes the following steps: Step a: Calculate P i C and P i M The mean matrix A C and A M : Step b: Calculation and and their respective mean matrices A C and A M The difference matrix L C and L M : Step c: Calculate the difference matrix L C and L M The product H: Step d: Perform singular value decomposition on H to obtain H = USV: [U,S,V]=svd(H) Step e: Calculate the rotation and translation matrix RT: R=VU T T=A C -UK M The mapping relationship from m model points to m measurement points is calculated: P C =RP M +T。 4. The method according to claim 3, characterized in that The method further comprises the following steps: based on the mapping relationship obtained in step e, obtaining all points Q on the part C All points on the mathematical model of the part are Q M The mapping relationship between them: Q C =RQ M +T。 5. The method according to claim 4, characterized in that Obtaining the displacement of the part from the first position to the second position based on R1T1 and R2T2 includes the following steps: Step I: Obtaining a mapping relationship between the part in the first position and the mathematical model of the part: in, Indicates the coordinates of all points of the part when it is in the first position, Step II: Obtaining a mapping relationship between the part in the second position and the mathematical model of the part: in, represents the coordinates of all points of the part when it is in the second position, Step III: Based on the mapping relationship in step I, the following formula is obtained: Step IV: Based on the mapping relationship in step II and the formula in step III, the following formula is obtained:

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