Calibration method based on inertial navigation unit and indoor laser positioning system

Abstract

The invention discloses a calibration method based on an inertial navigation unit and an indoor laser positioning system. The method only requires the calibration personnel to arbitrarily change the posture of the calibration plate several times in space to complete the calibration. The calibration improves the calibration accuracy by optimizing the calculation and compensating for the drift of the inertial navigation unit.

Description

Technical Field

[0001] The invention relates to the field of electronic information, and in particular to a calibration method based on an inertial navigation unit and an indoor laser positioning system. Background Art

[0002] In the assembly and manufacturing of large-space workpieces, accurate dynamic positioning of workpieces is one of the key technologies for assembly. The indoor laser positioning system is a distributed coordinate measurement system developed to solve the problem of large-scale space measurement and positioning. It uses the fan-shaped laser intersection measurement principle to obtain spatial 3D coordinates. It has the characteristics of multi-target parallel positioning, full space, and high precision. However, due to the limitations of its measurement principle, the refresh frequency in the dynamic positioning process is low and is easily affected by occlusion, so it is usually necessary to introduce an inertial navigation unit for data fusion; in order to fuse, the coordinate systems of the two systems must be calibrated, and the calibration accuracy will directly affect the accuracy of the fusion. Although the calibration problem has been proposed for a long time, since its application in different fields has different requirements for the accuracy and speed of the solution, research around this issue is still very popular. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a calibration method based on an inertial navigation unit and an indoor laser positioning system.

[0004] In order to solve the above technical problems, the technical solution adopted by the present invention is a calibration method based on an inertial navigation unit and indoor laser positioning, comprising the following steps:

[0005] S1. Connect n, n≥4 photoelectric receivers and an inertial navigation unit of an indoor laser positioning system to form an integral component, namely a calibration board, and the receiving planes of the n photoelectric receivers are respectively in at least two planes;

[0006] S2, perform attitude transformation, and read the position information of n photoelectric receivers under different attitudes and the attitude information of the inertial navigation unit relative to the initial state respectively;

[0007] S3, respectively calculating the relative attitude transformation matrix from attitude i to attitude j in the inertial navigation unit coordinate system and the indoor laser positioning system coordinate system;

[0008] S4, eliminate the non-corresponding matrix;

[0009] S5. Establish the basic equations for the calibration of the inertial navigation unit and the indoor laser positioning system and optimize and solve them to obtain the preliminary calibration parameters X;

[0010] S6. Substitute X in reverse to compensate the inertial navigation unit to obtain the final calibration parameter X.

[0011] Preferably, step S2 includes: fixing the calibration plate on the bracket, and the calibration personnel arbitrarily change the calibration plate posture in the measurement space of the indoor laser positioning system. The kth transformation can obtain the position information of n photoelectric receivers through the indoor laser positioning system. The inertial navigation unit obtains the attitude information relative to the initial state, and the Euler angles of its three axes are

[0012] As a further preferred embodiment, step S3 includes:

[0013] S31, establishing a t coordinate system according to the 3D coordinates of n photoelectric receivers;

[0014] S32, assuming that the coordinate system of the indoor laser positioning system is the w coordinate system, according to Use the least squares method to calculate the rotation matrix from the w coordinate system to the t coordinate system and the translation matrix T, where is the 3D coordinate of photoelectric receiver No. i in the w coordinate system, is the 3D coordinate of photoelectric receiver No. i in the t coordinate system;

[0015] S33, set the current coordinate system of the inertial navigation unit as the b coordinate system, set the initial coordinate system of the inertial navigation unit as the g coordinate system; obtain the attitude information relative to the initial state of the inertial navigation unit, that is, the Euler angles of the three axes, and calculate the rotation matrix from the b coordinate system to the g coordinate system

[0016] S34, respectively calculate the relative posture transformation matrix from posture i to posture j in the b coordinate system and the t coordinate system, where

[0017] As a further preferred embodiment, step S4 includes:

[0018] S41. Calculate the rotation angle of different rotation matrices in the b coordinate system In t coordinate system where the symbolic computation tr(R) represents the trace of the matrix R;

[0019] S42, when |φ b -φ t |Greater than φ 0 When the reorganized data is removed, the symbol |φ| is the absolute value of φ, φ 0 The value of is calculated in a laboratory environment without human interference according to step S2 and steps S31 to S34 to obtain 100 sets of φ b ,φ t , and then calculate 100 sets of |φ b -φ tVariance of |, φ 0 is three times its variance.

[0020] As a further preferred embodiment, step S5 includes:

[0021] S51. Establish the basic equations for the calibration of inertial navigation unit and indoor laser positioning system Where X is the rotation matrix from the b coordinate system to the t coordinate system, then the objective function is The symbolic operation ||R|| means finding the F norm of the matrix R;

[0022] S52, optimization solution, first calculate and The unit axis vectors are a k =[x k ,y k ,z k ] T , b k =[u k ,v k ,w k ] T , then Xb i =a i , write X as a Rodrigues matrix representation, with Rodrigues parameters a, b, c respectively, and simplify to get After multiple measurements, multiple equations are obtained. Combined with SVD decomposition, the values ​​of a, b, and c are obtained, and the preliminary calibration parameter X is obtained.

[0023] As a further preferred embodiment, step S6 includes: according to steps S51-S52, it can be known that after m, m ≥ 3 posture transformations, the preliminary calibration parameter X can be obtained, and the transformations after m times can be obtained by reversely substituting the previously calculated preliminary calibration parameter X according to the methods of steps S31-S34, steps S41-S42 and steps S51-S52. Solve for its drift error When e is greater than a certain threshold σ, let Among them, σ is related to the accuracy of the inertial navigation unit and the indoor laser positioning system, and is generally taken as 0.01~0.1; then continue to calculate according to the methods of steps S31~S34 and steps S51~S52 until all the measured postures are calculated, that is, i=N, and the final calibration parameter X is obtained.

[0024] The beneficial effects of the present invention are:

[0025] This method only requires the calibration personnel to change the calibration plate posture several times in space to complete the calibration. The calibration accuracy is improved by optimizing the calculation and compensating for the drift of the inertial navigation unit. DETAILED DESCRIPTION

[0026] A calibration method based on an inertial navigation unit and an indoor laser positioning system is implemented according to the following steps:

[0027] 1. Assemble the calibration plate, fix the 4 photoelectric receivers and the inertial navigation measurement unit (IMU) of the indoor laser positioning system on the same rectangular aluminum alloy plate, where the IMU is installed in the middle of the aluminum alloy plate, and the 4 photoelectric receivers are fixed at the four corners of the aluminum alloy plate. In order to better establish the t coordinate system and prevent the occurrence of a singular matrix, one of the photoelectric receivers should be higher than the other three by more than 40mm.

[0028] 2. Perform posture change. Fix the calibration plate on the bracket. The calibration personnel can change the posture of the calibration plate arbitrarily in the measurement space of the indoor laser positioning system. The kth transformation can obtain the position information of the four photoelectric receivers through the indoor laser positioning system. The inertial navigation unit obtains the attitude information relative to the initial state, and the Euler angles of its three axes are

[0029] 3. Calculate the attitude transfer matrix. Let the coordinate systems g, w, b, and t be the initial coordinate system of the inertial navigation unit, the indoor laser positioning system coordinate system, the inertial navigation unit coordinate system, and the coordinate system composed of the photoelectric receiver on the calibration board. The w coordinate system and the g coordinate system are fixed during the calibration process. Since the b coordinate system and the t coordinate system are rigidly connected, the transformation matrix X between the two coordinate systems does not change with the attitude transformation. First, calculate the attitude transfer matrix from attitude i to attitude j (i≠j) in the indoor laser positioning system coordinates. in is the attitude transfer matrix from the w coordinate system to the t coordinate system attitude j; then calculate the attitude transfer matrix from attitude i to attitude j (i≠j) under the initial coordinates of the inertial navigation unit in It can be obtained by the formula of Euler angle to rotation matrix. The calculation order is x, y, z. In this example, 15 groups of transformations are performed, and there are a total of 105 combinations, that is, 105 groups are obtained. and

[0030] 4. Calculate the rotation angle of different rotation matrices in the b coordinate system In t coordinate system The symbolic computation tr(R) represents the trace of the matrix R; when |φ b -φ t |Greater than φ 0 The data set is removed when |φ| is taken as the absolute value of φ.0 The value of is calculated in a laboratory environment without human interference according to steps 2 and 3 to obtain 100 sets of φ b ,φ t , and then calculate 100 sets of |φ b -φ t Variance of |, φ 0 is three times its variance. In this example, φ 0 =0.1.

[0031] 5. Build the model and calculate. According to steps 2, 3 and 4, the model is: Where X is the transformation matrix from coordinate system b to t, that is, the calibration parameters to be solved;

[0032] According to the matrix solution, we have Xb i =a i ,in Symbolic Operations Where 1+2cosφ=tr(C), tr(C) is the trace of the matrix C, and the symbolic operation v=[V]∧ means that the matrix V is stretched into a vector v=[v 1 ,v 2 ,v 3 ] T , where the matrix

[0033] Assume a k =[k k ,y k ,z k ] T , b k =[u k ,v k ,w k ] T , then G=l, where s=[a,b,c] T ,

[0034] l 3n×1 =[u 1 -x 1 ,v 1 -y 1 ,w 1 -z 1 ,…,u n -x n ,v n -y n ,w n -z n ] T

[0035]

[0036] Perform SVD decomposition on the augmented matrix [G, l] to obtain [G, l] = USD T ,but Where D(1:3,4) represents the 4th column and 1st to 3rd rows of matrix D, and D(4,4) represents the 4th row and 4th column; finally, we get X = (I + S) (IS) -1 , where I represents the three-dimensional identity matrix,

[0037] 6. Compensate for the drift of the inertial navigation unit. According to step 5, the initial calibration parameter X can be obtained after m and m ≥ 3 attitude changes. The changes after m times can be obtained by substituting the previously calculated initial calibration parameter X according to steps 3 and 5. Solve for its drift error The symbolic operation ||R|| represents the F-norm of the matrix R; when e is greater than a certain threshold σ, let Wherein σ is related to the accuracy of the inertial navigation unit and the indoor laser positioning system, and is taken as 0.02 in this example; then continue to calculate according to the method of steps S31-S34, steps S41-S42, and steps S51-S52 until all the measured postures are calculated, that is, i=15, and the calibration parameter X is obtained.

[0038] The above-described embodiments of the present invention do not constitute a limitation on the protection scope of the present invention. Any modification, equivalent substitution and improvement made within the spirit and principle of the present invention shall be included in the protection scope of the claims of the present invention.

Claims

1. Calibration method based on inertial navigation unit and indoor laser positioning system, The following steps are involved: S1. Connect n, n≥4 photoelectric receivers and an inertial navigation unit of an indoor laser positioning system to form an integral component, namely a calibration board, and the receiving planes of the n photoelectric receivers are respectively in at least two different planes; S2, perform attitude transformation, and read the position information of n photoelectric receivers under different attitudes and the attitude information of the inertial navigation unit relative to the initial state respectively; S3, respectively calculating the relative attitude transformation matrix from attitude i to attitude j in the inertial navigation unit coordinate system and the indoor laser positioning system coordinate system; S4, eliminate the non-corresponding matrix; S5. Establish the basic equations for the calibration of the inertial navigation unit and the indoor laser positioning system and optimize and solve them to obtain the preliminary calibration parameters X; S6. Substitute X in reverse to compensate the inertial navigation unit to obtain the final calibration parameter X 1 ; The step S2 further comprises the following steps: S21. Fix the calibration board on the bracket. The calibrator arbitrarily changes the attitude of the calibration board within the measurement space of the indoor laser positioning system. For the k-th change, the position information of n optoelectronic receivers can be obtained through the indoor laser positioning system, which are respectively i = 1, 2, …, n, k = 1, 2, …, N. The inertial navigation unit obtains the attitude information relative to the initial state, and the Euler angles of its three axes are The step S3 further includes the following steps: S31, establishing a t coordinate system according to the 3D coordinates of n photoelectric receivers; S32, assuming that the coordinate system of the indoor laser positioning system is the w coordinate system, according to i=1,2,…,n, use the least squares method to calculate the rotation matrix from the w coordinate system to the t coordinate system and the translation matrix T, where is the 3D coordinate of photoelectric receiver No. i in the w coordinate system, is the 3D coordinate of photoelectric receiver No. i in the t coordinate system; S33, set the current coordinate system of the inertial navigation unit as the b coordinate system, set the initial coordinate system of the inertial navigation unit as the g coordinate system; obtain the attitude information relative to the initial state of the inertial navigation unit, that is, the Euler angles of the three axes, and calculate the rotation matrix from the b coordinate system to the g coordinate system S34, respectively calculate the relative posture transformation matrix from posture i to posture j in the b coordinate system and the t coordinate system, where The step S4 also includes the following steps: S41. Calculate the rotation angle of different rotation matrices in the b coordinate system In t coordinate system where the symbolic computation tr(R) represents the trace of the matrix R; S42, when |φ b -φ t |Greater than φ 0 The data set is removed when |φ| is taken as the absolute value of φ. 0 The value of is calculated in a laboratory environment without human interference according to step S21 and steps S31-S34 to obtain 100 sets of φ b ,φ t , and then calculate 100 sets of |φ b -φ t Variance of |, φ 0 is three times its variance; The step S5 further comprises the following steps: S51. Establish the basic equations for the calibration of inertial navigation unit and indoor laser positioning system Then the objective function is The symbolic operation ||R|| means finding the F norm of the matrix R; S52, optimization solution, first calculate and The unit axis vectors are a k =[x k ,y k ,z k ] T , b k =[u k ,v k ,w k ] T , then Xb k =a k , write X as a Rodrigues matrix representation, with Rodrigues parameters a, b, c respectively, and simplify to get After multiple measurements, multiple equations are obtained, and the values ​​of a, b, and c are obtained by combining SVD decomposition, and the preliminary calibration parameter X is obtained; The step S6 also includes the following steps: S61. According to steps S51 - S52, it can be known that the preliminary calibration parameter X can be obtained after m attitude transformations where m ≥ 3. The transformations after m times can all be obtained by substituting the previously calculated preliminary calibration parameter X back into the steps of steps S31 - S34, steps S41 - S42, and steps S51 - S52 in reverse order. Solve its drift error When e is greater than a certain threshold value σ, let where σ is related to the accuracy of the inertial navigation unit and the indoor laser positioning system, taking 0.01 - 0.1; then continue to calculate according to the methods of steps S31 - S34 and steps S51 - S52 until all the measured attitudes are calculated, that is, i = n, to obtain the final calibration parameter X. 1 .

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