LOCALIZATION DEVICE USING MAGNETIC FIELD AND POSITIONING METHOD THEREOF

Abstract

A localization device using a magnetic field for positioning a moving object is provided. The localization device includes a magnetic landmark, a set of at least four tri-axes magnetic sensors mounted on the moving object, and a logic operation processing unit. The set of at least four tri-axes magnetic sensors forms four non-coplanar points in a three-dimension coordinate system. The logic operation processing unit is connected to the set of at least four tri-axes magnetic sensors. The set of at least four tri-axes magnetic sensors senses the magnetic field of the magnetic landmark and generates at least four magnetic signals transmitted to the logic operation processing unit.

Claims

1. A localization device using a magnetic field for positioning a moving object, comprising: a magnetic landmark; a set of at least four tri-axes magnetic sensors mounted on the moving object, wherein the set of at least four tri-axes magnetic sensors forms four non-coplanar points in a three-dimension coordinate system; and a logic operation processing unit connected to the set of at least four tri-axes magnetic sensors, wherein the set of at least four tri-axes magnetic sensors senses the magnetic field of the magnetic landmark and generates at least four magnetic signals transmitted to the logic operation processing unit.

2. The localization device as claimed in 1, wherein the set of at least four tri-axes magnetic sensors is positioned on three axes and an origin of the three-dimension coordinate system and the distance between any two of the four tri-axes magnetic sensors is a known distance.

3. The localization device as claimed in 2, wherein when the moving object passes through the magnetic landmark, the logic operation processing unit calculates a related-coordinate information and a distance information of the set of at least four tri-axes magnetic sensors relative to the magnetic landmark according to the at least four magnetic signals transmitted from the set of at least four tri-axes magnetic sensors to generate an identification data.

4. The localization device as claimed in 3, wherein the logic operation processing unit calculates a position vector r of the set of at least four tri-axes magnetic sensors relative to the magnetic landmark according to a magnetic moment B and a gradient tensor matrix G of the set of at least four tri-axes magnetic sensors relative to the magnetic landmark to obtain the identification data, wherein r=−3G.sup.−1B.

5. A positioning method using a magnetic field for positioning a moving object relative to a magnetic landmark, wherein the moving object has a set of at least four tri-axes magnetic sensors mounted thereon, the set of at least four tri-axes magnetic sensors forms four non-coplanar points in a three-dimension coordinate system, and the positioning method comprises: sensing the magnetic field of the magnetic landmark and generating at least four magnetic signals by the set of at least four tri-axes magnetic sensors.

6. The positioning method as claimed in 5, wherein the set of at least four tri-axes magnetic sensors is positioned on three axes and an origin of the three-dimension coordinate system and the distance between any two of the four tri-axes magnetic sensors is a known distance.

7. The positioning method as claimed in 6, wherein when the moving object passes through the magnetic landmark, the positioning method comprises calculating a related-coordinate information and a distance information of the set of at least four tri-axes magnetic sensors relative to the magnetic landmark according to the at least four magnetic signals transmitted from the set of at least four tri-axes magnetic sensors to generate an identification data.

8. The positioning method as claimed in 7, wherein a position vector r of the set of at least four tri-axes magnetic sensors relative to the magnetic landmark is calculated according to a magnetic moment B and a gradient tensor matrix G of the set of at least four tri-axes magnetic sensors relative to the magnetic landmark to obtain the identification data, wherein r=−3G.sup.−1B.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0008] FIG. 1 is a schematic diagram of a localization device using magnetic field according to an embodiment of the disclosure.

[0009] FIG. 2 is a schematic diagram of tri-axes magnetic sensors.

[0010] FIG. 3 is a schematic diagram of a magnetic landmark.

[0011] FIG. 4 is a distribution diagram of a specific locus of magnetic field in a three-dimension coordinate system.

[0012] FIG. 5 is a comparison diagram of the results obtained using the positioning method of the disclosure and the conventional energy estimation method.

DETAILED DESCRIPTION OF THE DISCLOSURE

[0013] Detailed descriptions of the disclosure are disclosed in a number of embodiments. However, the embodiments are for explanatory and exemplary purposes only, not for limiting the scope of protection of the disclosure.

[0014] Refer to FIG. 1. The localization device according to an embodiment of the disclosure is used for positioning a moving object 100, such as an automatic guided vehicle (AGV). The localization device includes a magnetic landmark 110, a set of at least four tri-axes magnetic sensors 120, and a logic operation processing unit 130. The magnetic landmark 110 is positioned at a positioning point of a workstation for the moving object 100. The set of four tri-axes magnetic sensors 120 is mounted on the moving object 100. When the moving object 100 reaches a workstation, a magnetic landmark 110 is disposed on the ground of the workstation, and at least four tri-axes magnetic sensors 120 are mounted on the moving object 100 to sense a magnetic field of the magnetic landmark 110.

[0015] The magnetic landmark 110 is for generating a predetermined magnetic field. The magnetic landmark 110 can be a magnet or an electromagnet. Refer to FIG. 3. The magnetic landmark 110 can have an N-pole magnetic source 112 and an S-pole magnetic source 114 or can have multiple N-pole magnetic sources and multiple S-pole magnetic sources. The magnetic intensity of the magnetic landmark 110 is determined according to the quantity of magnetic sources.

[0016] Refer to FIGS. 1 and 2. The four tri-axes magnetic sensors 120 form four non-coplanar points (No. 0-3) in a three-dimension coordinate system. The four tri-axes magnetic sensors 120 correspondingly generate four magnetic signals transmitted to the logic operation processing unit 130. The logic operation processing unit 130 can be a computer or a micro-processor of a computer. Before receiving the magnetic field information, the logic operation processing unit 130 can reduce the noise contained in the magnetic field information to increase the signal-to-noise ratio using a low-pass filter. Then, the magnetic field information can be converted into digitalized magnetic field information by an analog/digital converter. As indicated in FIG. 2, the four tri-axes magnetic sensors 120 are respectively mounted on three orthogonal support frames 140 and relative positions between the four tri-axes magnetic sensors 120 can be adjusted through the sliding chute 142 and the slider 144 mounted on each axis (that is, the slider 144 is positioned on the sliding chute 142 and can be locked at a predetermined position). Therefore, the distance between any two tri-axes magnetic sensors 120 can be increased or decreased.

[0017] In an embodiment, tri-axes magnetic sensors 120 can be a three-dimensional electronic compass composed of a three-dimensional magneto-resistive sensor (or magnetometer), a biaxial inclination sensor and a micro-processor. The three-dimensional magneto-resistive sensor is for measuring an external magnetic field. The inclination sensor performs compensation when the magnetometer is in a non-horizontal state. The micro-processor is for processing the signals and data output of the magnetometer and the inclination sensor and the hard/soft iron compensation. The magnetometer is formed of three orthogonal magneto-resistive sensors. The magneto-resistive sensor mounted on each axis detects the magnetic intensity on the same axis. The magneto-resistive sensor in the X direction (forward direction) detects the vector value of the external magnetic field in the X direction. The magneto-resistive sensor in the Y direction (left direction) detects the vector value of the external magnetic field in the Y direction. The magneto-resistive sensor in the Z direction (upward direction) detects the vector value of the external magnetic field in the Z direction. The analog output signal generated by magneto-resistive sensor is further amplified and transmitted to the micro-processor for subsequent processing. Since the electronic compass of the magneto-resistive sensor advantageously has smaller volume and faster response rate, the magneto-resistive sensor significantly outdoes the Hall sensor in terms of sensitivity and linearity.

[0018] The logic operation processing unit 130 calculates the related-coordinate information and the distance information of at least four tri-axes magnetic sensors 120 relative to the magnetic landmark 110 according to at least four magnetic signals to generate an identification data.

[0019] In FIG. 1, p represents a landmark magnetic moment; the coordinate system of the magnetic landmark is expressed as [Ox Oy Oz]; the four tri-axes magnetic sensors 120 in the three-dimension coordinate system is expressed as [bx by bz]; the four tri-axes magnetic sensors 120 are four non-coplanar points. The No. 0 sensor is positioned at the origin. The No. 1, No, 2 and No. 3 sensors are respectively disposed on the X-axis, the Y-axis and the Z-axis of the sensor coordinate system. The distance between each of the No. 1, No, 2 and No. 3 sensors and the origin is a known distance (such as length d). The position of each of the No. 0, No, 2 and No. 3 sensors relative to the landmark coordinate system is expressed as r.sub.i.Math.n.sub.i, wherein i is a numbering parameter between 0˜3; r is the distance of the four tri-axes magnetic sensors 120 relative to the magnetic landmark 110; n is a directional vector.

[0020] In the following formulas, B represents a vector of magnetic moment detected by each tri-axes magnetic sensor 120 at distance r; B′ represents a vector of magnetic moment detected by each tri-axes magnetic sensor 120 at distance r+ndr; μ.sub.0 represents a spatial medium parameter. The difference of the magnetic moments B and B′ can be obtained from formulas (1) and (2) and expressed as formula (3).

[00001]$\begin{array}{cc}B=\frac{{\mu }_0}{4.Math.\pi }.Math.\frac{3.Math.\left(p.Math.n\right).Math.n-p}{r^3}={\left[\begin{array}{ccc}{B}_x& B_y& B_z\end{array}\right]}^T& \left(1\right)\\ B^{\prime }=\frac{{\mu }_0}{4.Math.\pi }.Math.\frac{3.Math.\left(p.Math.n\right).Math.n-p}{{\left(r^3+\mathrm{dr}\right)}^2}={\left[\begin{array}{ccc}{B}_x^{\prime }& B_y^{\prime }& B_z^{\prime }\end{array}\right]}^T& \left(2\right)\\ B-B^{\prime }=\frac{{\mu }_0}{4.Math.\pi }.Math.\left(3.Math.\left(p.Math.n\right).Math.n-p\right).Math.\frac{\partial }{\partial r}.Math.\frac{1}{r^3}.Math.\mathrm{dr}\cong -\frac{3}{r}.Math.\mathrm{Bdr}& \left(3\right)\end{array}$

[0021] The vector of magnetic flux difference can be expressed using the gradient tensor matrix G, and formula (4) can be obtained from formula (3).

[00002]$\begin{array}{cc}G=\left[\begin{array}{ccc}{\partial }_x.Math.B_x& {\partial }_y.Math.B_x& {\partial }_z.Math.B_x\\ {\partial }_x.Math.B_y& {\partial }_y.Math.B_y& {\partial }_z.Math.B_y\\ {\partial }_x.Math.B_z& {\partial }_y.Math.B_z& {\partial }_z.Math.B_z\end{array}\right],r=-3.Math.G^{-1}.Math.B& \left(4\right)\end{array}$

[0022] It can be known from the above formulas that the coordinate and distance information of each tri-axes magnetic sensor 120 can be obtained from the magnetic moment B detected and the gradient tensor matrix G by each tri-axes magnetic sensor 120 in the space. Details of solving the simultaneous equations using the gradient tensor matrix G are disclosed below. Suppose the magnetic field signal received by each tri-axes magnetic sensor 120 can be expressed as:

{circumflex over (z)}.sub.i,m(k)B.sub.E(k)+R.sub.landmark.sup.body(k)B.sub.i(k)+O+N.sub.i,m(k)  (5)

Wherein B.sub.E represents a geomagnetic vector; R.sub.landmark.sup.body represents a rotation matrix between the landmark coordinate and the sensor coordinate; O represents the hard iron effect in the environment; N represents a noise vector. If the magnetic sensor system contains gyro information, then the gyro information can be added to the system to obtain better estimation results.

[0023] The gyro sensing signal can be expressed as:

{circumflex over (z)}.sub.i,gyro(k)=[ω.sub.i,x(k) ω.sub.i,y(k) ω.sub.i,z(k)].sup.T+N.sub.i,gyro(k)  (6)

Wherein, ω represents an angular speed of the sensor coordinate; N represents a noise vector.

[0024] Based on formulas (1), (4) and (5), the gradient tensor matrix G can be obtained using approximation method:

[00003]$\begin{array}{cc}{\left[\begin{array}{ccc}{\partial }_x.Math.B_x& {\partial }_x.Math.B_y& {\partial }_x.Math.B_z\end{array}\right]}^T.Math.\left(k\right)\approx \left(\frac{B_1\left(k\right)-B_0\left(k\right)}{d}\right)=R_{\mathrm{body}}^{\mathrm{landmark}}\left(k\right).Math.\left(\frac{{\hat{z}}_{1,m}\left(k\right)-{\hat{z}}_{0,m}\left(k\right)}{d}\right)+N_{0,1}\left(k\right)& \left(7\right)\\ {\left[\begin{array}{ccc}{\partial }_y.Math.B_x& {\partial }_y.Math.B_y& {\partial }_y.Math.B_z\end{array}\right]}^T.Math.\left(k\right)\approx \left(\frac{B_2\left(k\right)-B_0\left(k\right)}{d}\right)=R_{\mathrm{body}}^{\mathrm{landmark}}\left(k\right).Math.\left(\frac{{\hat{z}}_{2,m}\left(k\right)-{\hat{z}}_{0,m}\left(k\right)}{d}\right)+N_{0,2}\left(k\right)& \left(8\right)\\ {\left[\begin{array}{ccc}{\partial }_z.Math.B_x& {\partial }_z.Math.B_y& {\partial }_z.Math.B_z\end{array}\right]}^T.Math.\left(k\right)\approx \left(\frac{B_3\left(k\right)-B_0\left(k\right)}{d}\right)=R_{\mathrm{body}}^{\mathrm{landmark}}\left(k\right).Math.\left(\frac{{\hat{z}}_{3,m}\left(k\right)-{\hat{z}}_{0,m}\left(k\right)}{d}\right)+N_{0,3}\left(k\right)& \left(9\right)\end{array}$

Wherein R.sub.landmark.sup.body can be expressed as:

R.sub.body.sup.landmark=[n.sub.1−n.sub.0 n.sub.2−n.sub.0 n.sub.3−n.sub.0]  (10)

[0025] {dot over (R)}.sub.body.sup.landmark can be obtained by differentiating R.sub.body.sup.landmark:

[00004]$\begin{array}{cc}{\stackrel{.}{R}}_{\mathrm{body}}^{\mathrm{landmark}}\approx \Omega .Math..Math.R_{\mathrm{body}}^{\mathrm{landmark}}=\left[\begin{array}{ccc}0& -{\omega }_z& {\omega }_y\\ {\omega }_z& 0& -{\omega }_x\\ -{\omega }_y& {\omega }_x& 0\end{array}\right].Math.R_{\mathrm{body}}^{\mathrm{landmark}}& \left(11\right)\end{array}$

Formula (12) can be obtained through the rearrangement of formulas (7)-(9), wherein u.sub.i=n.sub.i−n.sub.0, i=1˜3.

[00005]$\begin{array}{cc}{B}_0\left(k\right)=\frac{-1}{3}.Math.G\left(k\right).Math.r_0\left(k\right)=\frac{-1}{3.Math.d}\left[\begin{array}{c}{u_1\left(k\right)}^T\\ {u_2\left(k\right)}^T\\ {u_3\left(k\right)}^T\end{array}\right].Math.{\left[\begin{array}{c}{\left({\hat{z}}_{1,m}\left(k\right)-{\hat{z}}_{0,m}\left(k\right)\right)}^T\\ {\left({\hat{z}}_{2,m}\left(k\right)-{\hat{z}}_{0,m}\left(k\right)\right)}^T\\ {\left({\hat{z}}_{3,m}\left(k\right)-{\hat{z}}_{0,m}\left(k\right)\right)}^T\end{array}\right]}^T.Math.r_0\left(k\right)& \left(12\right)\end{array}$

[0026] If x=[u.sub.1 u.sub.2 u.sub.3 r.sub.0],εR.sup.12, then the linear system matrix A can be expressed as formula (13), wherein w represents a vector of system noises.

[00006]$\begin{array}{cc}x\left(k+1\right)=A\left(k\right).Math.x\left(k\right)+w\left(k\right),.Math.A=\left[\begin{array}{cccc}{I}_3+\mathrm{\Omega \Delta }.Math..Math.t& 0& 0& 0\\ 0& I_3+\mathrm{\Omega \Delta }.Math..Math.t& 0& 0\\ 0& 0& I_3+\mathrm{\Omega \Delta }.Math..Math.t& 0\\ 0& 0& 0& I_3\end{array}\right]& \left(13\right)\end{array}$

Based on the features of rotation matrix, the following constraints can be obtained:

u.sub.1.sup.Tu.sub.2=0

u.sub.2.sup.Tu.sub.3=0

u.sub.3.sup.Tu.sub.1=0

u.sub.1.sup.Tu.sub.1=1

u.sub.2.sup.Tu.sub.2=1

u.sub.3.sup.Tu.sub.3=1  (14)

[0027] Lastly, following formula is obtained using constrained Kalman filter. Refer to FIG. 4 and FIG. 5. FIG. 4 is a distribution diagram of a specific locus of magnetic field in a three-dimension coordinate system. FIG. 5 is a comparison diagram of the results obtained using the positioning method of the disclosure and the conventional energy estimation method. The accuracy and efficiency of the algorithm are verified according to the simulation results of FIGS. 4 and 5. The procedures of the algorithm are as follows:

x(k+1)=A(k)x(k)+w(k)

y(k)=h(x(k))+v(k)

st. G.sub.hard(x(k))=h  (15)

Measurement update:

H(k)=∇.sup.Th({circumflex over (x)}.sup.−(k))

P.sup.+(k)=(P.sup.−(k).sup.−1+H(k).sup.TR.sup.−1H(k)).sup.−1

F(k)=∇.sup.TG.sub.Hard({circumflex over (x)}.sup.−(k))

f(k)=h−G.sub.Hard({circumflex over (x)}.sup.−(k))+F(k){circumflex over (x)}.sup.−(k)

{circumflex over (x)}.sup.U(k)={circumflex over (x)}.sup.−(k)+P.sup.+(k)H(k).sup.TR.sup.−1(y(k)−h({circumflex over (x)}.sup.−(k)))

{circumflex over (x)}.sup.+(k)={circumflex over (x)}.sup.U(k)−P.sup.+(k)F(k).sup.T.Math.[F(k)P.sup.+(k)F(k).sup.T].sup.−1[F(k){circumflex over (x)}.sup.U(k)−f(k)]

Time update:

{circumflex over (x)}.sup.−(k+1)=A(k){circumflex over (x)}.sup.+(k)

P.sup.−(k)=A(k)P.sup.+(k)A(k).sup.T+Q

Wherein, x and y represent a state vector and a measurement vector respectively; k represents a time parameter; A represents a linear system matrix; P represents magnetic moment; r represent a distance from each sensor to the origin; P− and P+ represent state error covariance matrix; h represents a measurement equation; H represents a Jacobian matrix of h; Q and R represent noise covariance matrixes; w and v respectively represent a vector of zero mean white Gaussian noises.

[0028] FIG. 4 shows a simulation result. A magnetic landmark is positioned at the origin of a virtual coordinate system, and a spiral upward path is composed in the space. The direction and length of an arrow represent the direction and intensity of the magnetic field detected at each point on the path. The thick dashed line represents actual reference positions. The thin dashed line represents estimated positions obtained using the algorithm of the present application. As indicated in FIG. 4, the errors of estimation maintain within a minimum value without diverging, therefore the convergence property of the algorithm of the present application can be verified.

[0029] FIG. 5 is a comparison diagram of the results obtained using the positioning method of the present application and the conventional energy estimation method. FIG. 5 shows that the positioning method of the present application is superior to the conventional energy estimation method. Curve 1 denotes reference positions; curve 2 denotes estimated positions obtained using the algorithm of the present application; curve 3 denotes the positions calculated according to a relationship formula that energy is inversely proportional to the square of the distance. The three curves are equalized to the same starting points. Along with the increase in distance and signal-to-noise ratio, error starts to increase. The comparison clearly shows that the positioning method of the present application is superior to the conventional energy estimation method.

[0030] The above disclosure shows that when the moving object 100 passes through the magnetic landmark 110, the logic operation processing unit 130 calculates the position vector r of the at least four tri-axes magnetic sensors 120 relative to the magnetic landmark 110 according to the magnetic moment B and the gradient tensor matrix G of the at least four tri-axes magnetic sensors 120 relative to the magnetic landmark to obtain an identification data, wherein r=−3G.sup.−1B and the identification data is the positioning data of the moving object 100.

[0031] A localization device using magnetic field and a positioning method thereof are disclosed in above embodiments of the disclosure. The localization device is capable of detecting the coordinates of a moving object in the space and requires only one magnetic landmark. Therefore, the disclosure does not require prior arrangement of the environment or multiple magnetic landmarks. Besides, the known technologies which estimate the distance using magnetic intensity are nonlinear (inversely proportional to the square of the distance) and have low resistance against noises. The localization device using magnetic field and the positioning method of the present disclosure employ at least four non-coplanar tri-axes magnetic sensors, such that the estimation system becomes a linear system and achieves millimeter (mm) level precision, and the information of the three-dimension coordinate system can be calculated.

[0032] While the disclosure has been described by way of example and in terms of the embodiment(s), it is to be understood that the disclosure is not limited thereto. On the contrary, it is intended to cover various modifications and similar arrangements and procedures, and the scope of the appended claims therefore should be accorded the broadest interpretation so as to encompass all such modifications and similar arrangements and procedures.