CN101413785A - Error compensation method of positioning system based on double-rotating laser plane transmitter network - Google Patents

Abstract

The invention discloses an error compensating method for a positioning system based on a dual-rotation laser plane transmitter network. The method provides a compensating algorithm model and designs a parameter estimation algorithm, and the main implementation steps include: (1) marking the parameter; (2) collecting compensating data; (3) collecting angle data of the point to be measured; and (4) compensating measuring equation error. The step (4) includes: a) determining a compensation factor; b) compensating the measuring equation; and c) iterating until suspension condition is satisfied, so as to solve the final result. The invention relates to large scale space coordinate measuring error compensation, solves the difficulty in systemic error marking in the dual rotation laser plane space measuring positioning system, can compensate the error item of the laser plane measuring equation and improves the systemic measuring precision.

Description

Error compensation method of positioning system based on double-rotating laser plane transmitter network

Technical field

The present invention relates to the Error Compensation Technology field during 3 d space coordinate is measured on a large scale, particularly a kind of error compensation method of positioning system based on double-rotating laser plane transmitter network.

Background technology

In the manufacturing and assembling process of big machinery equipment, during machine manufacturing like flying, shipbuilding, large-scale power station and heavy-duty machine equipment were made, the problems of measurement of large-sized geometry and morpheme error was the key that affects the equipment set quality.The current large-scale metrology technology of using comparative maturity in the world mainly comprises laser transit, laser tracking measurement system and big visual field vision measurement system etc.

Carry out position measurement and positioning system is the novel no guide rail measurement of coordinates technology that grew up in recent years based on double-rotating laser plane, it adopts non-contact measurement, the location survey scope is big, precision is high, and is low to the environmental baseline requirement, has broad application prospects.Before implementing measurement, need demarcate this system, because existing measuring technique restriction, the system calibrating parameter has calibrated error, so have calibrated error in the measuring process, influences the measuring accuracy of system.For systematic error, the reference measure arm, the Error Compensation Technology of transit etc., the existing error compensation method mostly is the direct or indirect measuring system error of the more high-precision survey instrument of use, and then by setting up error compensation model, measurement result is compensated, use these methods, all need to use extra measuring equipment.

Summary of the invention

The object of the present invention is to provide a kind of error compensation method of positioning system based on double-rotating laser plane transmitter network, this method is by gathering the offset value strong point of some, based on error compensation model, with the measuring error of bucking-out system calibrated error introducing, thus the measuring accuracy of raising system.

Technical scheme of the present invention is achieved in that

Implementation step of the present invention is:

1) transmitter parameter is demarcated, and the three-dimensional travelling table of setting up the 1m * 1m * 1m that forms with line slideway and digital display height gauge is demarcated the measuring system parameter as demarcating the space;

2) offset data collection, in demarcating the space, select five known points data point by way of compensation, the coordinate and the feature angle at record offset value strong point, with these data by way of compensation, described feature angle is meant when inswept this data point of each laser plane laser plane angle that turns over of its initial position relatively;

3) the feature angle of measurement tested point according to measuring equation, is found the solution tested point volume coordinate (x ₀, y ₀, z ₀) ^T

4) according to step 2) offset data and step 3) survey the feature angle, utilize Error Compensation Algorithm that measurement result is carried out error compensation.

Described measuring system parameter calibration, concrete steps are meant:

1) set up world coordinate system, 2m～3m is apart from placing the turntable transmitter around three-dimensional is demarcated transfer table; On three-dimensional demarcation transfer table, set up world coordinate system O _W-X _WY _WZ _W, initial point O _WCan be positioned at three-dimensional travelling table optional position, X _WDirection be the horizontal direction guide rail wherein any one, Y _WDirection is horizontal direction and X _WVertical guide rail, Z _WDirection is the digital display height gauge;

2) gather nominal data, receiver is fixed in three-dimensional the demarcation on the transfer table digital display height gauge, utilize guide rail and height gauge to make receiver at X _W, Y _W900mm distance range on the direction, Z _WDirection 900mm distance range, interval 300mm on all directions, move totally 64 positions, note receiver coordinate position under described world coordinate system, and gather each transmitter and launch the laser signal of coming, import computing machine via data collecting card, described coordinate position data and characteristic time are formed nominal data;

3) each transmitter site of bigness scale utilizes tape measure instrument rough measure transmitter at X _W, Y _WCoordinate position on the direction K is the transmitter numbering, and transmitter parameter initially is made as

4) with

Be initial value, use peg model, in conjunction with the nominal data that obtains to A _1k, B _1k, A _2k, B _2k, T _Xk, T _Yk, Tz _1k, Tz _2k, 1,2 demarcate for the laser plane label, and described peg model is

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}({(\left(R_{1k}^{\left(i\right)}{N}_{1k}\right)\·(P_i-T_{1k}))}^2+{(\left(R_{2k}^{\left(i\right)}{N}_{2k}\right)\·(P_i-T_{2k}))}^2)$

Wherein, k: transmitter numbering;

I: the numbering of calibration point;

N _1k, N _2k: the plane equation coefficient of laser plane (A, B, 1) ^T

T _1k, T _2k: the rotation center (T of laser plane _Xk, T _Yk, T _Zk) ^T

R _1k, R _2k: laser plane is to the rotation matrix of initial position;

P _i: tested point coordinate under the described world coordinate system;

Just have only 8 unknown parameters to be calibrated for each turntable transmitter this moment, given one group of initial value, and described initial value form is

, use the value that the Levenberg-Marquardt optimization searching minimizes formula, can obtain each systematic parameter.

Described measurement equation specifically refers to: according to the multi straight intersection method at world coordinate system O _W-X _WY _WZ _WThe system of equations of following simultaneous is as the model of tested point coordinate Calculation, and described world coordinate system is to set up when the parameter calibration of this measurement model, and this system of equations is:

$\left\{\begin{array}{c}\left(R_1{N}_1\right)\·(P-T_1)=0\\ \left(R_2{N}_2\right)\·(P-T_2)=0\\ \left(R_3{N}_3\right)\·(P-T_3)=0\\ \·\\ \·\\ \·\\ \left(R_k{N}_k\right)\·(P-T_k)=0\end{array}\right.$

Wherein, k: laser plane label;

P: tested point coordinate under the world coordinate system, P=(x, y, z) ^T

N _k: the initial plane normal vector of laser plane, N _k=(A _k, B _k, 1) ^T

R _k: laser plane is to the rotation matrix of initial position;

T _k: laser plane rotation center, T _k=(T _Xk, T _Yk, T _Zk); Laser plane to the rotation matrix of initial position is

$R_k=\left(\begin{array}{ccc}\cos \left({\mathrm{\θ}}_k\right)& -\sin \left({\mathrm{\θ}}_k\right)& 0\\ \sin \left({\mathrm{\θ}}_k\right)& \cos \left({\mathrm{\θ}}_k\right)& 0\\ 0& 0& 1\end{array}\right)$

Wherein, θ _k: be the feature angle of laser plane k.

Described Error Compensation Algorithm, concrete steps are as follows:

1) penalty coefficient is determined, according to the offset value strong point that collects and the measurement data of tested point, finds the solution the penalty coefficient system of equations, obtains measuring light plane surveying equation penalty coefficient c _i(i=1 ... 5), its penalty coefficient system of equations is

$\left\{\begin{array}{c}\underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k\cos {\mathrm{\θ}}_k=\cos {\mathrm{\θ}}_{\mathrm{ij}}\\ \underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k\sin {\mathrm{\θ}}_k=\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ \underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k(\cos {\mathrm{\θ}}_k{x}_k+\sin {\mathrm{\θ}}_k{y}_k)=\cos {\mathrm{\θ}}_{\mathrm{ij}}{x}_0+\sin {\mathrm{\θ}}_{\mathrm{ij}}{y}_0\\ \underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k(\cos {\mathrm{\θ}}_k{y}_k-\sin {\mathrm{\θ}}_k{x}_k)=\cos {\mathrm{\θ}}_{\mathrm{ij}}{y}_0-\sin {\mathrm{\θ}}_{\mathrm{ij}}{x}_0\\ \underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k=1\end{array}\right.$

Wherein, k: offset data piont mark (k=1,2,3,4,5);

I: the label of laser plane;

J: the label of tested point;

θ _k: corner during i laser plane over-compensation point k;

θ _Ij: corner when i laser plane crossed measurement point j;

c _k: measure the equation penalty coefficient;

x _k, y _k: k compensation point coordinate;

x ₀, y ₀: compensating measure point coordinate not;

2) measure the equation compensation, utilize institute's supplement to repay coefficient c _i(i=1 ... 5) and do not compensate coordinate, each optical plane is measured equation carry out error compensation, compensation back laser plane is measured equation and is

$\left(R_i{\tilde{N}}_i\right)\·P-\left(R_i{\tilde{N}}_i\right)\·{\tilde{T}}_i=\underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k(\left(R_{\mathrm{ck}}{\tilde{N}}_i\right)\·P_{\mathrm{ck}}-\left(R_{\mathrm{ck}}{\tilde{N}}_i\right)\·T_i)$

Wherein, k: offset data piont mark (k=1,2,3,4,5);

I: the label of laser plane;

c _k: measure the equation penalty coefficient;

P: compensating measure space of points coordinate not, P=(x, y, z) ^T

P _k: compensation point volume coordinate, P _k=(x _k, y _k, z _k) ^T

Δ T _iBe the demarcation rotation center and the error thereof of i laser plane, ${\tilde{T}}_i={({\tilde{T}}_{\mathrm{xi}},{\tilde{T}}_{\mathrm{yi}},{\tilde{T}}_{\mathrm{zi}})}^T,$

ΔT _i＝(ΔT _xi，ΔT _yi，ΔT _zi) ^T；

Δ N _iBe the initial normal vector of demarcation and the error thereof of i laser plane,

${\tilde{N}}_i={({\tilde{N}}_{\mathrm{xi}},{\tilde{N}}_{\mathrm{yi}},{\tilde{N}}_{\mathrm{zi}})}^T,$ ΔN _i＝(ΔN _xi，ΔN _yi，ΔN _zi) ^T；

R _iRotation matrix for laser plane during through j tested point;

R _kRotation matrix for laser plane during through k tested point;

3) the measurement equation solution tested point volume coordinate after the utilization compensation obtains single compensation result (x ₁, y ₁, z ₁) ^T, and replace in the step 1) not compensating measure point coordinate, carry out second iteration, so circulation is until satisfying the iteration termination condition, the system calibrating error that is eliminated (Δ A, Δ B, Δ T _x, Δ T _y, Δ T _z) after measurement result (x, y, z), with this result as net result.

The present invention is only by gathering limited the known point in space point by way of compensation, by compensation model, can eliminate the systematic error that double-rotating laser plane position measurement and positioning system are measured equation, thereby improve the measuring accuracy of system, do not need extra measuring equipment, reduced the measurement cost.The present invention is applied in large corporation's assembling and positioning, parts and makes on-line measurement etc. need be determined three-dimensional coordinate in space on a large scale field.

Description of drawings

Fig. 1 is an indoor positioning measuring system running block diagram of the present invention.

Fig. 2 is an indoor positioning measuring system laser plane instrumentation plan of the present invention.

Fig. 3 is an error compensation process flow diagram of the present invention.

Below in conjunction with accompanying drawing content of the present invention is described in further detail.

Embodiment

With reference to shown in Figure 1, receiver is accepted laser signal, is transferred to computer by data collecting card and carries out data processing.

With reference to shown in Figure 2, O _w-X _wY _wZ _wBe world coordinate system, transmitter turning axle and Z axle in the same way, the some T be the laser plane rotation center, the some P be tested point, among the figure, P and T are in the same optical plane, θ is the feature angle of this laser plane.

With reference to shown in Figure 3, the compensation method process flow diagram is, do not compensate tested point coordinate and offset data → penalty coefficient → measurements equation compensation → compensation coordinate → termination differentiation, with this as an iterative loop.

The indoor positioning measuring system operates block diagram as shown in Figure 1, and the present invention needs 3 or 3 above turntable transmitters, receiver, data acquisition card and measuring systems of computing machines composition.During system works, each transmitter rotates with different rates, and outwards launches laser by the laser instrument of installing on it, sends the OZ pulse of a Fixed Time Interval simultaneously to the handling procedure of computing machine by the transmitter servomechanism.Receiver is made up of photoelectric cell and pre-amplification circuit and is used to receive the laser that described transmitter emission comes, and through processing and amplifying, imports computing machine by the data acquisition card collection again, thereby carries out computing in conjunction with the mathematical model of design.

1. measurement model is described

Indoor positioning measuring system laser plane instrumentation plan as shown in Figure 2, at world coordinate system O _w-X _wY _wz _wDown, described transmitter turning axle and OZ _wAxle parallels.When initial position, the rotation center of a laser plane L1 is (T on the transmitter _x, T _y, T _z), its initial normal vector is N=(A, B, 1) ^TWhen transmitter rotates, drive the laser plane rotation.Optical plane is after the relative initial position of its turning axle turns over angle θ, and its relative world coordinate system OZ axle also turns over angle θ.Optical plane normal vector in this position is:

N _θ＝R _θN

Wherein, wherein, R _θBe rotation matrix, $R_{\mathrm{\θ}}=\left[\begin{array}{ccc}\cos \mathrm{\θ}& -\sin \mathrm{\θ}& 0\\ \sin \mathrm{\θ}& \cos \mathrm{\θ}& 0\\ 0& 0& 1\end{array}\right].$

If the space tested point is that (z), the angle that the relative initial position of optical plane turns over during L1 process P point is made as θ to P for x, y ₁, at this moment, P point and T point all are among the optical plane L1.Vector PT and N _{θ 1}Following relation is arranged, and we are called the measurement equation.

PT·N _θ1＝0

Wherein, PT=(x-T _x, y-T _y, z-T _z) ^T

If space distribution has n generating laser, then the number on rotary laser plane is 2n.Tested point P satisfies:

$\left\{\begin{array}{c}\left(R_{11}{N}_{11}\right)\·(P-T_{11})=0\\ \left(R_{12}{N}_{12}\right)\·(P-T_{12})=0\\ \left(R_{21}{N}_{21}\right)\·(P-T_{21})=0\\ \left(R_{22}{N}_{22}\right)\·(P-T_{22})=0\\ \·\\ \·\\ \·\\ \left(R_{k1}{N}_{k1}\right)\·(P-T_{k1})=0\\ \left(R_{k2}{N}_{k2}\right)\·(P-T_{k2})=0\end{array}\right.$

Wherein, k: the laser plane label, k=1,2 ..., n;

P: tested point coordinate under the world coordinate system, P=(x, y, z) ^T

N _K1, N _K2: the initial plane normal vector of laser plane, N=(A, B, 1) ^T

R _K1, R _K2: laser plane is respectively the laser plane rotational angle theta to the rotation matrix of initial position _K1, θ _K2Function;

T _K1, T _K2: laser plane rotation center, T=(T _x, T _y, T _z);

When the transmitter number greater than 2 the time, this is an overdetermined equation group, at Model parameter N _K1, N _K2And T _K1, T _K2After deciding by demarcation, according to the characteristic time θ that obtains _K1, θ _K2Just can solve above-mentioned system of equations with least square method, obtain tested point P at O _W-X _WY _WZ _WFollowing coordinate position X _W

2. backoff algorithm model

Five of the systematic parameter light that needs in the coordinate Calculation process, i.e. planar process vector parameter A _i, B _i, and optical plane rotation center coordinate parameters T _Xi, T _Yi, T _Zi, establish its calibration value and be respectively:

Its calibrated error is: Δ A _i, Δ B _i, Δ T _Xi, Δ T _Yi, Δ T _Zi, therefore following result is arranged:

$N_i={\tilde{N}}_i+\mathrm{\Δ}{N}_i$

$T_i={\tilde{T}}_i+\mathrm{\Δ}{T}_i$

Wherein,

Be calibration value, Δ N _i, Δ T _iBe error between calibration value and the true value.

Optical plane of above-mentioned formula substitution is measured equation, can have

$\left(R_i({\tilde{N}}_i+\mathrm{\Δ}{N}_i)\right)\·(P-({\tilde{T}}_i+\mathrm{\Δ}{T}_i))=0$

It is launched arrangement, have

$\left(R_i{\tilde{N}}_i\right)\·P-\left(R_i{\tilde{N}}_i\right)\·{\tilde{T}}_i=\left(R_i{\tilde{N}}_i\right)\·\mathrm{\Δ}{\tilde{T}}_i-\left(R_i\mathrm{\Δ}{N}_i\right)\·P+\left(R_i\mathrm{\Δ}{N}_i\right)\·{\tilde{T}}_i+\left(R_i\mathrm{\Δ}{N}_i\right)\·\mathrm{\Δ}{T}_i$

If there is a known point C in the space, its coordinate is P _c(x _c, y _c, z _c), its corner is measured as θ during laser plane i is inswept C point _cCan get by following formula

$\left(R_c{\tilde{N}}_i\right)\·P_c-\left(R_c{\tilde{N}}_i\right)\·{\tilde{T}}_i=\left(R_c{\tilde{N}}_i\right)\·\mathrm{\Δ}{\tilde{T}}_i-\left(R_c\mathrm{\Δ}{N}_i\right)\·P_c+\left(R_c\mathrm{\Δ}{N}_i\right)\·{\tilde{T}}_i+\left(R_c\mathrm{\Δ}{N}_i\right)\·\mathrm{\Δ}{T}_i$

Therefore, can consider that an item on the C measurement equation left side compensates measuring point error term formula.

For same laser plane, it is measured equation and has identical calibrating parameters and calibrated error, and different has only tested point coordinate figure and corner.Measuring point is measured the error in equation item

(R _iΔ N _i) Δ T _iCan be along with matrix of coefficients R _iCompensation and eliminate.Therefore, for these three, can only consider R _iCompensation get final product.

$R_i=\left[\begin{array}{ccc}\cos {\mathrm{\θ}}_i& -\sin {\mathrm{\θ}}_i& 0\\ \sin {\mathrm{\θ}}_i& \cos {\mathrm{\θ}}_i& 0\\ 0& 0& 1\end{array}\right]$

Further, compensate R _i, only need compensation cos θ _i, sin θ _i, 1 gets final product.

For (R _iΔ N _i) P, we launch it, and observe its rule, and its expansion is:

(cosθ _ix+sinθ _iy)ΔA _i+(cosθ _iy-sinθ _ix)ΔB _i+1

Eliminate error delta A _i, Δ B _i, need only eliminate its coefficient (cos θ _iX+sin θ _iY), (cos θ _iY-sin θ _iX), 1 get final product.

Therefore, the error term of ultimate demand compensation is: cos θ _i, sin θ _i, (cos θ _iX+sin θ _iY), (cos θ _iY-sin θ _iX), 1.So need five known points point by way of compensation, above-mentioned five compensated.Therefore, desirable five compensation points are formed the compensation system of equations, find the solution penalty coefficient.

If compensation point is respectively C ₁(x ₁, y ₁, z ₁, θ ₁), C ₂(x ₂, y ₂, z ₂, θ ₂), C ₃(x ₃, y ₃, z ₃, θ ₃), C ₄(x ₄, y ₄, z ₄, θ ₄), C ₅(x ₅, y ₅, z ₅, θ ₅), the penalty coefficient system of equations is:

$\left\{\begin{array}{c}\underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k\cos {\mathrm{\θ}}_k=\cos {\mathrm{\θ}}_{\mathrm{ij}}\\ \underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k\sin {\mathrm{\θ}}_k=\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ \underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k(\cos {\mathrm{\θ}}_k{x}_k+\sin {\mathrm{\θ}}_k{y}_k)=\cos {\mathrm{\θ}}_{\mathrm{ij}}{x}_0+\sin {\mathrm{\θ}}_{\mathrm{ij}}{y}_0\\ \underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k(\cos {\mathrm{\θ}}_k{y}_k-\sin {\mathrm{\θ}}_k{x}_k)=\cos {\mathrm{\θ}}_{\mathrm{ij}}{y}_0-\sin {\mathrm{\θ}}_{\mathrm{ij}}{x}_0\\ \underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k=1\end{array}\right.$

The c that finds the solution wherein undetermined _i(i=1,2,3,4,5) is penalty coefficient.

Behind the penalty coefficient that the method for undetermined coefficients is asked, have following result:

$\left\{\begin{array}{c}\underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k\left(R_{\mathrm{ck}}{\tilde{N}}_i\right)\·\mathrm{\Δ}{T}_i=\left(R_i{\tilde{N}}_i\right)\·\mathrm{\Δ}{T}_i\\ \underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k\left(R_{\mathrm{ck}}\mathrm{\Δ}{\tilde{N}}_i\right)\·P_{\mathrm{ck}}=\left(R_i\mathrm{\Δ}{\tilde{N}}_i\right)\·P\\ \underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k\left(R_{\mathrm{ck}}\mathrm{\Δ}{N}_i\right)\·{\tilde{T}}_i=\left(R_i\mathrm{\Δ}{N}_i\right)\·{\tilde{T}}_i\\ \underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k\left(R_{\mathrm{ck}}\mathrm{\Δ}{N}_i\right)\·\mathrm{\Δ}{T}_i=\left(R_i\mathrm{\Δ}{N}_i\right)\·\mathrm{\Δ}{T}_i\end{array}\right.$

With the item addition of the above-mentioned system of equations left side, be optical plane and measure the equation compensation term, the compensation back is measured equation and is

$\left(R_i{\tilde{N}}_i\right)\·P-\left(R_i{\tilde{N}}_i\right)\·{\tilde{T}}_i=\underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k(\left(R_{\mathrm{ck}}{\tilde{N}}_i\right)\·P_{\mathrm{ck}}-\left(R_{\mathrm{ck}}{\tilde{N}}_i\right)\·T_i)$

Wherein, k: offset data piont mark (k=1,2,3,4,5);

I: the label of laser plane;

c _k: measure the equation penalty coefficient;

P: compensating measure space of points coordinate not, P=(x, y, z) ^T

P _k: compensation point volume coordinate, P _k=(x _k, y _k, z _k) ^T

Δ T _iBe the demarcation rotation center and the error thereof of i laser plane, ${\tilde{T}}_i={({\tilde{T}}_{\mathrm{xi}},{\tilde{T}}_{\mathrm{yi}},{\tilde{T}}_{\mathrm{zi}})}^T,$

ΔT _i＝(ΔT _xi，ΔT _yi，ΔT _zi) ^T；

Δ N _iBe the initial normal vector of demarcation and the error thereof of i laser plane,

${\tilde{N}}_i={({\tilde{N}}_{\mathrm{xi}},{\tilde{N}}_{\mathrm{yi}},{\tilde{N}}_{\mathrm{zi}})}^T,$ ΔN _i＝(ΔN _xi，ΔN _yi，ΔN _zi) ^T；

R _iRotation matrix for laser plane during through j tested point;

R _kRotation matrix for laser plane during through k tested point.

In the actual mechanical process, when carrying out an iteration, will measure (x for compensation point ₀, y ₀, z ₀) as initial point, the substitution said process.Until satisfying the iteration termination condition, the system calibrating error that is eliminated (Δ A, Δ B, Δ T _x, Δ T _y, Δ T _z) after measurement result (x, y, z), with this result as net result.

3. compensation implementation step

(1) parameter calibration.Foundation is set up world coordinate system O with the demarcation space of the 1m * 1m * 1m of line slideway and digital display height gauge composition on three-dimensional travelling table _W-X _WY _WZ _W, measuring system is demarcated;

(2) offset data collection.In demarcating the space, select five offset value strong points equably, should be evenly arranged in the measurement space as far as possible between the data point.For an offset value strong point, the information that gather has the world coordinate system coordinate of this point, and optical plane inswept this time the relative angle that turns over of its initial position.For the homogenizing stochastic error, system can take multiple measurements to gather and average when carrying out the angle information collection.

(3) measure the tested point angle-data,, calculate tested point volume coordinate (x according to measurement model ₀, y ₀, z ₀) ^T

(4) error compensation process flow diagram such as Fig. 3 compensate measuring error in equation, the steps include:

A) penalty coefficient is determined.According to the measurement result of offset data that collects and tested point, adopt the penalty coefficient system of equations of design to find the solution, obtain measuring light plane surveying equation penalty coefficient c _i(i=1 ... 5);

B) measure the equation compensation.Utilize the penalty coefficient c that separates _i(i=1 ... 5) and do not compensate coordinate, adopt the compensation system of equations of design, each optical plane is measured equation carry out error compensation, and utilize the measurement equation of single compensation to form system of equations.

C) find the solution the compensation system of equations, obtain single compensation result (x ₁, y ₁, z ₁) ^TUtilize single compensation tested point coordinate, replace in the step (1) not compensating measure point coordinate, carry out second iteration, so circulation is until satisfying the iteration termination condition, the system calibrating error that is eliminated (Δ A, Δ B, Δ T _x, Δ T _y, Δ T _z) after measurement result (x, y, z), with this result as net result.

Claims (4)

1, a kind of error compensation method of positioning system based on double-rotating laser plane transmitter network is characterized in that, the implementation step of compensation is:

1) transmitter parameter is demarcated, and the three-dimensional travelling table of setting up the 1m * 1m * 1m that forms with line slideway and digital display height gauge is demarcated the measuring system parameter as demarcating the space;

2) offset data collection, in demarcating the space, select five known points data point by way of compensation, the coordinate and the feature angle at record offset value strong point, with these data by way of compensation, described feature angle is meant when inswept this data point of each laser plane laser plane angle that turns over of its initial position relatively;

3) the feature angle of measurement tested point according to measuring equation, is found the solution tested point volume coordinate (x ₀, y ₀, z ₀) ^T

4) according to step 2) offset data and step 3) survey the feature angle, utilize Error Compensation Algorithm that measurement result is carried out error compensation.

2, the error compensation method of positioning system based on double-rotating laser plane transmitter network according to claim 1 is characterized in that, described measuring system parameter calibration, and concrete steps are meant:

1) set up world coordinate system, 2m～3m is apart from placing the turntable transmitter around three-dimensional is demarcated transfer table; On three-dimensional demarcation transfer table, set up world coordinate system O _W-X _WY _WZ _W, initial point O _WCan be positioned at three-dimensional travelling table optional position, X _WDirection be the horizontal direction guide rail wherein any one, Y _WDirection is horizontal direction and X _WVertical guide rail, Z _WDirection is the digital display height gauge;

2) gather nominal data, receiver is fixed in three-dimensional the demarcation on the transfer table digital display height gauge, utilize guide rail and height gauge to make receiver at X _W, Y _W900mm distance range on the direction, Z _WDirection 900mm distance range, interval 300mm on all directions, move totally 64 positions, note receiver coordinate position under described world coordinate system, and gather each transmitter and launch the laser signal of coming, import computing machine via data collecting card, described coordinate position data and characteristic time are formed nominal data;

3) each transmitter site of bigness scale utilizes tape measure instrument rough measure transmitter at X _W, Y _WCoordinate position on the direction

K is the transmitter numbering, and transmitter parameter initially is made as

4) with

Be initial value, use peg model, in conjunction with the nominal data that obtains to A _1k, B _1k, A _2k, B _2k, T _Xk, T _Yk, T _Z1k, T _Z2k, 1,2 demarcate for the laser plane label, and described peg model is

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}({(\left(R_{1k}^{\left(i\right)}{N}_{1k}\right)\·(P_i-T_{1k}))}^2+{(\left(R_{2k}^{\left(i\right)}{N}_{2k}\right)\·(P_i-T_{2k}))}^2)$

Wherein, k: transmitter numbering;

I: the numbering of calibration point;

N _1k, N _2k: the plane equation coefficient of laser plane (A, B, 1) ^T

T _1k, T _2k: the rotation center (T of laser plane _Xk, T _Yk, T _Zk) ^T

R _1k, R _2k: laser plane is to the rotation matrix of initial position;

P _i: tested point coordinate under the described world coordinate system;

Just have only 8 unknown parameters to be calibrated for each turntable transmitter this moment, given one group of initial value, and described initial value form is

Use the value that the Levenberg-Marquardt optimization searching minimizes formula, can obtain each systematic parameter.

3, the error compensation method of positioning system based on double-rotating laser plane transmitter network according to claim 1 is characterized in that, described measurement equation specifically refers to: according to the multi straight intersection method at world coordinate system O _W-X _WY _WZ _WThe system of equations of following simultaneous is as the model of tested point coordinate Calculation, and described world coordinate system is to set up when the parameter calibration of this measurement model, and this system of equations is:

$\left\{\begin{array}{c}\left(R_1{N}_1\right)\·(P-T_1)=0\\ \left(R_2{N}_2\right)\·(P-T_2)=0\\ \left(R_3{N}_3\right)\·(P-T_3)=0\\ \·\\ \·\\ \·\\ \left(R_k{N}_k\right)\·(P-T_k)=0\end{array}\right.$

Wherein, k: laser plane label;

P: tested point coordinate under the world coordinate system, P=(x, y, z) ^T

N _k: the initial plane normal vector of laser plane, N _k=(A _k, B _k, 1) ^T

R _k: laser plane is to the rotation matrix of initial position;

T _k: laser plane rotation center, T _k=(T _Xk, T _Yk, T _Zk);

Laser plane to the rotation matrix of initial position is

$R_k=\left(\begin{array}{ccc}\cos \left({\mathrm{\θ}}_k\right)& -\sin \left({\mathrm{\θ}}_k\right)& 0\\ \sin \left({\mathrm{\θ}}_k\right)& \cos \left({\mathrm{\θ}}_k\right)& 0\\ 0& 0& 1\end{array}\right)$

Wherein, θ _k: be the feature angle of laser plane k.

4, the Positioning System Error backoff algorithm based on double-rotating laser plane transmitter network according to claim 1 is characterized in that, described Error Compensation Algorithm, and concrete steps are as follows:

1) penalty coefficient is determined, according to the offset value strong point that collects and the measurement data of tested point, finds the solution the penalty coefficient system of equations, obtains measuring light plane surveying equation penalty coefficient c _i(i=1 ... 5), its penalty coefficient system of equations is

$\left\{\begin{array}{c}\underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k\cos {\mathrm{\θ}}_k=\cos {\mathrm{\θ}}_{\mathrm{ij}}\\ \underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k\sin {\mathrm{\θ}}_k=\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ \underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k(\cos {\mathrm{\θ}}_k{x}_k+\sin {\mathrm{\θ}}_k{y}_k)=\cos {\mathrm{\θ}}_{\mathrm{ij}}{x}_0+\sin {\mathrm{\θ}}_{\mathrm{ij}}{y}_0\\ \underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k(\cos {\mathrm{\θ}}_k{y}_k-\sin {\mathrm{\θ}}_k{x}_k)=\cos {\mathrm{\θ}}_{\mathrm{ij}}{y}_0-\sin {\mathrm{\θ}}_{\mathrm{ij}}{x}_0\\ \underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k=1\end{array}\right.$

Wherein, k: offset data piont mark (k=1,2,3,4,5);

I: the label of laser plane;

J: the label of tested point;

θ _k: corner during i laser plane over-compensation point k;

θ _Ij: corner when i laser plane crossed measurement point j;

c _k: measure the equation penalty coefficient;

x _k, y _k: k compensation point coordinate;

x ₀, y ₀: compensating measure point coordinate not;

2) measure the equation compensation, utilize institute's supplement to repay coefficient c _i(i=1 ... 5) and do not compensate coordinate, each optical plane is measured equation carry out error compensation, compensation back laser plane is measured equation and is

$\left(R_i{\tilde{N}}_i\right)\·P-\left(R_i{\tilde{N}}_i\right)\·{\tilde{T}}_i=\underset{k=1}{\overset{5}{\mathrm{\Σ}}}{c}_k(\left(R_{\mathrm{ck}}{\tilde{N}}_i\right)\·P_{\mathrm{ck}}-\left(R_{\mathrm{ck}}{\tilde{N}}_i\right)\·T_i)$

Wherein, k: offset data piont mark (k=1,2,3,4,5);

I: the label of laser plane;

c _k: measure the equation penalty coefficient;

P: compensating measure space of points coordinate not, P=(x, y, z) ^T

P _k: compensation point volume coordinate, P _k=(x _k, y _k, z _k) ^T

Δ T _iBe the demarcation rotation center and the error thereof of i laser plane, ${\tilde{T}}_i={({\tilde{T}}_{\mathrm{xi}},{\tilde{T}}_{\mathrm{yi}},{\tilde{T}}_{\mathrm{zi}})}^T,$

ΔT _i＝(ΔT _xi，ΔT _yi，ΔT _zi) ^T；

Δ N _iBe the initial normal vector of demarcation and the error thereof of i laser plane,

${\tilde{N}}_i={({\tilde{N}}_{\mathrm{xi}},{\tilde{N}}_{\mathrm{yi}},{\tilde{N}}_{\mathrm{zi}})}^T,$ ΔN _i＝(ΔN _xi，ΔN _yi，ΔN _zi) ^T；

R _iRotation matrix for laser plane during through j tested point;

R _kRotation matrix for laser plane during through k tested point;

3) the measurement equation solution tested point volume coordinate after the utilization compensation obtains single compensation result (x ₁, y ₁, z ₁) ^T, and replace in the step 1) not compensating measure point coordinate, carry out second iteration, so circulation is until satisfying the iteration termination condition, the system calibrating error that is eliminated (Δ A, Δ B, Δ T _x, Δ T _y, Δ T _z) after measurement result (x, y, z), with this result as net result.

Images