CN1089160C - Method for three dimension position measurement using miniature inertia measurement combination - Google Patents

Abstract

The invention belongs to the technical field of precision measurement, and includes a measuring device composed of a three-dimensional position calibration measuring head and a computer system; a miniature inertial measurement combination composed of six micro sensors is packaged in the measuring head, and the lower end of the measuring head is a measuring probe; First use the probe to align the measurement base point P0, and then align the measured point P1, the sensor outputs the rotational angular rate and acceleration of the three axes of the measuring head; the computer system obtains the three-dimensional position of P1 point relative to the base point P0 through data processing; the present invention satisfies To meet the needs of large-scale three-dimensional measurement, the measurement system has the advantages of high reliability, low cost, and convenient operation.

Description

A Method for Three-Dimensional Position Measurement Using Miniature Inertial Measurement Unit

The invention belongs to the technical field of precision measurement, and in particular relates to the application technology of a micro-inertial measurement combination.

In industrial production and scientific experiments, three-dimensional position measurement is often required, such as the processing of workpieces, the precise installation of parts, and so on. For small workpieces, the three-dimensional position measurement can be completed with general measuring tools, but for large workpieces, ordinary measurement methods often do not work. For example, in the manufacture of aircraft wings, it is necessary to calibrate the position of each point on the wing. The aircraft wing is tens of meters long and has a complex curved surface structure. The three-dimensional position of a point is a very difficult thing. The method of laser ranging can accurately complete the measurement of large distances, but this method is only suitable for one-dimensional direction measurement and cannot meet the needs of three-dimensional measurement. The method to solve this problem in foreign countries is three-coordinate measuring machine, and through years of research, it has been developed from mechanical three-coordinate measuring machine to computer numerical control (CNC) three-coordinate measuring machine. The more successful application is in the MTU turbine engine manufacturing plant in Germany. Under the control of a measurement center, four Zeiss three-coordinate measuring machines are combined to undertake the measurement of 28 complex precision parts produced in the entire automated workshop. However, its outstanding disadvantages are bulky, complex equipment, and high cost, so it is not suitable for popularization and application.

The purpose of the present invention is to overcome the shortcomings of the above methods, and propose a brand-new three-dimensional position measurement method to meet the needs of large-scale three-dimensional measurement. The three-dimensional position measurement system designed by this method has high reliability and low cost , Easy operation and so on.

The present invention proposes a method for three-dimensional position measurement using a micro-inertial measurement combination, which is characterized in that it comprises a measuring device composed of a three-dimensional position calibration measuring head and a computer system; said three-dimensional position calibration measuring head encapsulates a micro-inertial measurement combination, The miniature inertial measurement combination consists of six microsensors, and the lower end of the measurement head is a measurement probe; the specific measurement steps are as follows:

1) First use the probe to align the measurement base point P0, then move the measuring head and use the probe to align the measured point P1, the gyroscope is sensitive and outputs the rotational angular rate of the three axes of the measuring head, the accelerometer is sensitive and outputs the three axes of the measuring head Acceleration in the axial direction;

2) The computer system samples the output of the sensor through the data line, and obtains the three-dimensional position of the P1 point relative to the base point P0 through data processing;

3) The computer system samples the output of the sensor through the data line, and obtains the three-dimensional position of P1 relative to the base point P0 through data processing:

4) After measuring point P1, the measuring head moves back and aligns with the base point P0, the computer initializes, and then moves the measuring head to align with the next measuring point P2, and the computer repeats the data processing of the above process to obtain the position of point P2, and so on. The calibration of the three-dimensional positions of multiple measuring points on any curved surface can be completed, and the results are output to the display by the computer. Said computer data processing may include the following steps;

1) Extract the angular velocity signal output by the micro-gyroscope with the second-order angular velocity, and sample the acceleration signal output by the micro-accelerometer at the same time;

2) Perform closed-loop error compensation on the signals output by the micro-gyroscope and the micro-accelerometer;

3) Using the error-compensated data, the attitude angle of the measuring head coordinate system is obtained by using the fourth-order Runge-Kutta method through the quaternion differential equation;

4) Decompose the acceleration signal along the direction of the measuring head coordinate system into acceleration components along the direction of the geographic coordinate system;

5) The three components of the acceleration vector in the geographic coordinate system are numerically integrated twice to obtain the moving velocity and three-dimensional position of the measuring head respectively.

Measuring principle of the present invention is as follows:

The theoretical basis of this method is the strapdown inertial navigation principle. The core component of the inertial navigation system is the inertial measurement combination, which consists of inertial accelerometers and gyroscopes. Ordinary inertial measurement units are bulky and heavy, and can only be used for navigation of aircraft and ships. According to the working environment of the application of the present invention, draw it and strapdown inertial navigation system to have different application conditions, thereby adopted different measuring methods with strapdown inertial navigation system,:

One, the present invention selects the micro-accelerometer and the micro-gyroscope manufactured by micro-machining technology to form a micro-inertial measurement combination. Therefore, the measuring part-measuring head has the characteristics of small size and light weight, and can easily complete three-dimensional position measurement.

Its two, the working distance of the present invention is little, and time is short. The working distance of the present invention is several meters to tens of meters, and the measurement time for a point is several seconds, which is far smaller than the working range of the strapdown inertial navigation system. Therefore, the latitude change caused by the working distance can be ignored, and this condition can reduce the error differential equations from six to five. Since the working time is related to the square and the cube of the error caused, reducing the measurement time can greatly improve the measurement accuracy.

Third, the environmental interference and noise of the present invention are small. The inertial measurement combination in strapdown inertial navigation is fixed on the aircraft, and the sensor works in an environment of high-speed motion and high-frequency vibration. Random interference and noise are very large, and useful signals must be filtered before they can be used. In contrast, the interference and noise that the sensor receives when working in a common environment is very small.

Its four, the motion velocity, the acceleration and the angular velocity of rotation of the miniature inertial measuring head are small. The movement speed of the measuring head is 5m/s to 10m/s, and the acceleration is less than 2g, which are much smaller than the inertial navigation aircraft or missiles, so the error analysis is mainly based on the static base error of the system. In addition, since the measuring range of the sensor is reduced, the scale factor of the sensor can be made very small.

In order to reduce the error of the output signal of the inertial sensor, the present invention adopts a closed-loop error compensation. The error sources of inertial components include: sensor zero error, dynamic error, installation error, scale error, first-order error of specific force, and high-order error such as quadratic sensitive item error. According to the previous analysis, only those items that cause larger errors are considered, and the following inertial sensor error model formula is obtained: $\mathrm{\Δ}{A}_x={\mathrm{\θ}}_{\mathrm{xz}}^a{A}_{\mathrm{the\; y}}-{\mathrm{\θ}}_{\mathrm{xy}}^a{A}_z+k{Q}_x{A}_x^2+\mathrm{\Δ}{A}_x^{\′}$ ${\mathrm{\ΔA}}_{\mathrm{the\; y}}={\mathrm{\θ}}_{\mathrm{yx}}^a{A}_z-{\mathrm{\θ}}_{\mathrm{yz}}^a{A}_x+k{Q}_{\mathrm{the\; y}}{A}_{\mathrm{the\; y}}^2+{\mathrm{\ΔA}}_{\mathrm{the\; y}}^{\′}----\left(1\right)$ ${\mathrm{\ΔA}}_z={\mathrm{\θ}}_{\mathrm{zy}}^a{A}_x-{\mathrm{\θ}}_{\mathrm{xz}}^a{A}_{\mathrm{the\; y}}+k{Q}_z{A}_z^2+{\mathrm{\ΔA}}_z^{\′}$ ${\mathrm{\ϵ}}_x={\mathrm{\θ}}_{\mathrm{xz}}^g{\mathrm{\ω}}_{\mathrm{the\; y}}-{\mathrm{\θ}}_{\mathrm{xy}}^g{\mathrm{\ω}}_z-m^1{A}_x-q^1{A}_{\mathrm{the\; y}}+{\mathrm{no}}^1{A}_x{A}_z+{\mathrm{\ϵ}}_x^{\′}+C{\mathrm{\ω}}_x{\mathrm{\ω}}_z$ ${\mathrm{\ϵ}}_{\mathrm{the\; y}}={\mathrm{\θ}}_{\mathrm{yx}}^g{\mathrm{\ω}}_z-{\mathrm{\θ}}_{\mathrm{yz}}^g{\mathrm{\ω}}_x-m^1{A}_{\mathrm{the\; y}}+q^1{A}_x+{\mathrm{no}}^1{A}_{\mathrm{the\; y}}{A}_z+{\mathrm{\ϵ}}_{\mathrm{the\; y}}^{\′}+C{\mathrm{\ω}}_z{\mathrm{\ω}}_{\mathrm{the\; y}}----\left(2\right)$ ${\mathrm{\ϵ}}_z={\mathrm{\θ}}_{\mathrm{zy}}^g{\mathrm{\ω}}_x-{\mathrm{\θ}}_{\mathrm{zx}}^g{\mathrm{\ω}}_{\mathrm{the\; y}}-m^2{A}_z+q^2{A}_{\mathrm{the\; y}}+{\mathrm{no}}^2{A}_x{A}_z+{\mathrm{\ϵ}}_z^{\′}+C{\mathrm{\ω}}_x{\mathrm{\ω}}_z$ In the formula, ΔA _i ′(i=x, y, z) is the zero error of the accelerometer, ε _i ′ is the gyro drift rate; θ _ij ^a , θ _ij ^g (i, j=x, y, z) are respectively The installation error angle of the accelerometer and the gyro; kQ _i is the acceleration square term, m, q, n are acceleration related items; C is the gyro cross-axis coupling coefficient.

According to formulas (1) and (2), the closed-loop error compensation of the inertial sensor is carried out. As shown in Figure 1 and Figure 2, since the closed-loop compensation uses the compensated signal to obtain the error compensation amount and compensate the output of the inertial element, the output accuracy of this error compensation method is relatively high. In Figure 2, ε _ax , ε _ay , and ε _az are expressed as follows: ε _ax = -m ¹ A _x -q ¹ A _y +n ¹ A _x A _zz ε _ay = -m ¹ A _y +q ¹ A _x + n ¹ A _y A _z (3)ε _az ＝-m ² A _z +q ² A _y +n ² A _x A _z After analysis, the following conclusions can be drawn: this method can fully compensate the static error caused by constant acceleration input ; The dynamic error caused by constant angular velocity input can be compensated to an order of magnitude less than 10 ^-7 . The error after compensation is: ΔA _x = ΔA _y = ΔA ₂ = 10 ^-7 g, ε _x = ε _y = ε _z = 10 ^-6 rad/s, α ₀ = β ₀ = γ ₀ = 10 ^-5 rad.

微分方程的个数由六个减到五个是由于在测量中纬度的变化可以忽略，即δ＝0。上式1中参数分别取地球半径R＝6367.65km，地球自转角速度ω_e＝15.04107°/h，当地(北京)纬度＝39.933°，当地加速度g＝9.80065m/s²，测量时间t＝3s。用四阶龙格-库塔法求解(4)式，再用位置误差方程： $\mathrm{\δ}\stackrel{\·}{Y}=-\mathrm{\δ}{V}_v----\left(5\right)$ $\mathrm{\δ}\stackrel{\·}{Z}=-\mathrm{\δ}{V}_z$ 求出系统的三维测量误差，误差曲线如图3所示。可以看出该系统的测量误差小于1mm，对应的测量范围是二十米，这个精度可以满足一般大型工件的加工制造。According to the above applicable conditions, the error equation under the static base is obtained, which is five first-order differential equations, and its matrix form is as follows:

The reason for reducing the number of differential equations from six to five is that the change of latitude  can be neglected in the measurement, that is, δ=0. The parameters in the above formula 1 are respectively taken as the radius of the earth R=6367.65km, the angular velocity of the earth’s rotation ω _e =15.04107°/h, the local (Beijing) latitude =39.933°, the local acceleration g=9.80065m/s ² , and the measurement time t=3s . Use the fourth-order Runge-Kutta method to solve equation (4), and then use the position error equation: $\mathrm{\δ}\stackrel{\&Center\; Dot;}{Y}=-\mathrm{\δ}{V}_v----\left(5\right)$ $\mathrm{\δ}\stackrel{\·}{Z}=-\mathrm{\δ}{V}_z$ Calculate the three-dimensional measurement error of the system, and the error curve is shown in Figure 3. It can be seen that the measurement error of the system is less than 1 mm, and the corresponding measurement range is 20 meters. This accuracy can meet the processing and manufacturing of general large workpieces.

The present invention has following characteristics:

First, this method firstly applies the inertial navigation theory to precision measurement, combined with the new achievements of micro/nano technology, creates a new application field of micro-inertial measurement combination. Second, through theoretical analysis, it is confirmed that the method has high measurement accuracy. Within the measurement range of 20m, the measurement error is less than 1mm.

Third, the method for three-dimensional position measurement using a miniature inertial measurement combination proposed by the present invention is suitable for three-dimensional measurement and position calibration of large and complex workpieces. The three-dimensional position measurement system designed by this method has high reliability, low cost, Easy to operate and other advantages, the measurement range can reach 5 meters to 20 meters. The method can be used in the processing and manufacturing of large workpieces, such as the manufacturing of heavy mechanical equipment, ships, aerospace equipment and large power generation equipment, and thus has a broad application market.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a schematic diagram of the inertial accelerometer closed-loop error compensation method of the present invention. FIG. 2 is a schematic diagram of an inertial gyro closed-loop error compensation method according to the present invention. FIG. 3 is a schematic diagram of a position error curve after error compensation in the present invention. Fig. 4 is a schematic diagram of the three-dimensional position measuring device of the present invention. Fig. 5 is a schematic diagram of the coordinate system of the measuring head of the present invention. Fig. 6 is a working diagram of the three-dimensional position measuring device of the present invention; Fig. 7 is a schematic diagram of the three-dimensional position measuring method of the present invention.

The present invention proposes an embodiment of a three-dimensional position measurement device based on inertial measurement combination, as shown in Figures 4 to 7, and the measurement methods are described in detail in conjunction with each figure as follows:

This embodiment consists of a three-dimensional position calibration measuring head and a computer system. The three-dimensional position calibration measurement head encapsulates a miniature inertial measurement combination, which consists of six microsensors, including three single-degree-of-freedom microgyroscopes A ₁ , A ₂ , A ₃ , and three micro-accelerometers G ₁ , G ₂ , _G3 . These six sensors are installed on three orthogonal surfaces of the cube, and their sensitive axes are perpendicular to each other to form a three-dimensional coordinate system of the measuring body, as shown in Figure 5, Gx, Gy, and Gz are the micro-gyroscopes G ₁ , G _2. The three sensitive axes of G ₃ , Ax, Ay, Az are the three sensitive axes of the micro-accelerometers A ₁ , A ₂ , A ₃ , the coordinate origin O is located at the geometric center of the measuring head, and the lower end of the measuring head is a measuring The probe, with endpoint P, is located on the reverse extension of the Gz axis. The final size of the probe head is 5×5×5 cm ³ and weighs about 480 g. The movement speed of the measuring head is 5m/s to 10m/s, and the acceleration is less than 2g. It can accurately measure the three-dimensional coordinates of many points on any surface and their relative positions.

When this embodiment is working, as shown in FIG. 6 , the probe is first aligned with the measurement base point P0, and then the measuring head is moved to align the probe with the measured point P1. In this process, the gyroscope is sensitive and outputs the rotational angular rate of the three axes of the measuring head, and the accelerometer is sensitive and outputs the acceleration of the three axes of the measuring head; the computer system samples the output of the sensor through the data line, and calculates the P1 point through calculation The three-dimensional position relative to the base point P0. After measuring point P1, the measuring head moves back and aligns with the base point P0, the computer initializes, and then moves the measuring head to align with the next measuring point P2, and the computer calculates the position of point P2. By repeating the above process, the calibration of the three-dimensional positions of multiple measurement points on any curved surface can be completed.

The function of the computer system is to process the output signal of the sensor and calculate the measurement result. As shown in Figure 7, the computer first samples the angular rate signal output by the gyroscope and the acceleration signal output by the accelerometer and performs error compensation; then calculates the attitude matrix of the measuring head, which is also the most important in the three-dimensional position calibration calculation method Then the computer decomposes the sampled acceleration signal along the direction of the measuring head coordinate system according to the direction cosine matrix obtained in the previous step to obtain the acceleration component along the direction of the geographical coordinate system; Velocity and position in a geographic coordinate system. Specific steps are as follows:

1. Use the second-order angular velocity extraction to obtain the angular velocity signal. The gyroscope works in the force feedback state, and the output in the form of digital quantity is the angular increment. Therefore, the relationship between the angular increment and the angular velocity must be obtained. If the output of the gyro is Δθ _i1 ′ from t _i to t _i +T/2, and the output is Δθ _t2 ′ from t _i +T/2 to t _i +T, T is the sampling period. Using the second-order angular velocity extraction, the angular velocity measured by the gyro is as follows: $\mathrm{\ω}\left(t_1\right)=\frac{1}{T}(3\mathrm{\Δ}{\mathrm{\θ}}_{i1}^{\′}-\mathrm{\Δ}{\mathrm{\θ}}_{i2}^{\′})$ $\mathrm{\ω}(t_i+\frac{T}{2})=\frac{1}{T}({\mathrm{\Δ\θ}}_{i1}^{\′}+{\mathrm{\Δ\θ}}_{i2}^{\′})----\left(7\right)$ $\mathrm{\ω}(t_i+T)=\frac{1}{T}(3{\mathrm{\Δ\θ}}_{i2}^{\′}-{\mathrm{\Δ\θ}}_{i1}^{\′})$

2. Error compensation of inertial components. According to the error model shown in (1) and (2), use the method shown in Figure 1 and Figure 2 to perform closed-loop compensation.

用四阶龙格-库塔法求解(8)式得到转动四元数q，再将q代入下式：α＝-sin^-1(T₁₃) $\mathrm{\β}={\mathrm{tg}}^{-1}\left(\frac{T_{23}}{T_{33}}\right)----\left(9\right)$ $\mathrm{\γ}={\mathrm{tg}}^{-1}\left(\frac{T_{12}}{T_{11}}\right)$ 求出测量头坐标系的姿态角。3. Solving of quaternion differential equations and attitude angles. Substitute the result of step 2 into the quaternion differential equation:

Use the fourth-order Runge-Kutta method to solve equation (8) to obtain the rotation quaternion q, and then substitute q into the following equation: α=-sin ^-1 (T ₁₃ ) $\mathrm{\β}={\mathrm{tg}}^{-1}\left(\frac{T_{\mathrm{twenty\; three}}}{T_{33}}\right)----\left(9\right)$ $\mathrm{\γ}={\mathrm{tg}}^{-1}\left(\frac{T_{12}}{T_{11}}\right)$ Find the attitude angle of the measuring head coordinate system.

4. Decompose acceleration. The computer samples the output signal of the micro-accelerometer, and uses the q obtained in step 3 to decompose the acceleration signal along the direction of the measuring head coordinate system into acceleration components along the direction of the geographic coordinate system:

_RE ＝qR _b q ^-1 (10) where R _b is the acceleration vector output by the accelerometer, and _RE is the acceleration vector in the geographic coordinate system, the expression is:

R _b ＝A _xb i+A _yb j+A _zb k (11)

R _ε =A _xE i+A _yE j+A _zE k (12)

5. Output the measurement result. The three components of R _E are numerically integrated twice to obtain the moving velocity and three-dimensional position of the measuring head respectively. The result is output to the display by the computer, and the result can also include the attitude angle in step 3.

Claims (2)

1, a kind of method of three dimension position measurement using miniature inertia measurement combination is characterized in that, comprises by three-dimensional position calibration measurements head and computer system composition measuring apparatus; Encapsulation MIMU (Micro Inertial Measurement Unit) in the said three-dimensional position calibration measurements head, MIMU (Micro Inertial Measurement Unit) is made up of six microsensors, these six microsensors adopt three single-degree-of-freedom gyroscopes and three micro-acceleration gauge aggregate erections on hexahedral three normal surfaces, its sensitive axes is vertical mutually, the three-dimensional system of coordinate of forming measuring body, the lower end of this measuring head is a measuring probe, the concrete measurement

Step is as follows:

1) earlier measure basic point P0 with probe alignment, the traverse measurement head is with measured some P1 of probe alignment then, and gyroscope is responsive and export the angle of rotation speed of three axles of measuring head, and accelerometer sensitive is also exported three axial acceleration of measuring head;

2) computer system obtains the three-dimensional position of the relative basic point P0 of P1 point by the output of data line sampling sensor by data processing;

3) measure the P1 point after, basic point P0 is retracted and aimed to measuring head, computer initialization, the traverse measurement head is aimed at next measurement point P2 again, the data processing of computer repeats processing obtains the position that P2 is ordered, can finish the demarcation of the three-dimensional position of a plurality of measurement points on the arbitrary surface by that analogy, its result is outputed on the display by computing machine.

Such as claim 1 the method for three-dimensional position measuring of art, it is characterized in that said computer data is handled and be may further comprise the steps:

1) extracts the angular velocity signal that little gyro is exported with second order angular velocity, the acceleration signal of the micro-acceleration gauge of sampling simultaneously output;

2) signal to little gyro and micro-acceleration gauge output carries out closed loop error compensation;

3) employing is obtained the attitude angle of measuring head coordinate system through the data of error compensation with fourth-order Runge-Kutta method by the hypercomplex number differential equation;

4) acceleration signal along measuring head coordinate system direction is resolved into along the component of acceleration of geographic coordinate system direction;

5) three components to the acceleration in the geographic coordinate system carry out numerical integration twice, obtain the movement velocity and the three-dimensional position of measuring head respectively.

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