Rapid electromagnetic tracking method based on plane rotating magnetic field

Abstract

The invention belongs to the technical field of electromagnetic tracking, and particularly relates to a rapid electromagnetic tracking method based on a plane rotating magnetic field. A system related to the method comprises two magnetic field sources with fixed positions and a three-axis magnetic sensor (tracking a target), wherein each magnetic field source consists of two mutually orthogonal coils. According to the invention, two coils of each magnetic field source are respectively subjected to orthogonal constant current excitation once, and two rotating magnetic fields are generated in space; performing phase analysis and module value analysis on the magnetic induction intensities of the two rotating magnetic fields acquired by the three-axis magnetic sensor to obtain position coordinates of a tracking target; and the attitude angle of the tracking target can be obtained through simple matrix linear operation. The method is simple in system, low in calculation complexity and high in tracking speed. The method is suitable for multiple fields of surgical navigation, virtual reality and the like, and has a wide application prospect.

Description

Technical Field

[0001] The invention belongs to the technical field of electromagnetic tracking, and in particular relates to a fast electromagnetic tracking method based on a plane rotating magnetic field. Background Art

[0002] Electromagnetic tracking is a technology that uses electromagnetic technology to determine the position and posture of an object. It determines the position coordinates of an object by measuring the magnetic induction intensity signal at the location of the object. Electromagnetic positioning systems are usually composed of magnetic field sources, magnetic sensors, signal processors, and positioning algorithms; through the collaboration of these modules, accurate identification and tracking of the object's position can be achieved. With the widespread application of electromagnetic positioning systems in many fields such as indoor navigation, virtual reality, and minimally invasive surgery, the real-time requirements for positioning are increasing.

[0003] Traditional electromagnetic tracking systems usually use sensors to receive magnetic induction intensity signals after exciting a magnetic field source to generate a magnetic field, and then calculate the position and posture of the target by iteratively solving a set of nonlinear equations. The time consumption of its calculation cannot fully meet the high real-time requirements of practical applications, and it is possible to fall into a local optimal solution and cause a large positioning error. In response to the above technical problems, the present invention proposes an electromagnetic tracking method based on a plane rotating magnetic field, which can achieve target tracking with only two exciting magnetic field sources and simple linear operations, thereby improving the response speed of the system, and has significant advantages and broad application prospects. Summary of the invention

[0004] The object of the present invention is to provide a fast electromagnetic tracking method based on a plane rotating magnetic field with fast response speed and small calculation amount.

[0005] The present invention provides a rapid electromagnetic tracking method based on a planar rotating magnetic field, and the system involved includes at least two magnetic field sources and a three-axis magnetic sensor (tracking target); each magnetic field source is composed of two mutually orthogonal coils, and the three-axis magnetic sensor is used to sense the magnetic induction intensity in three mutually orthogonal directions; it only takes two excitations of the magnetic field source to generate a planar rotating magnetic field, and the three-axis magnetic sensor collects the signal, and its position and posture information can be obtained through linear calculations.

[0006] For ease of explanation, three coordinate systems S1, S2 and S3 are defined; S1 is a global coordinate system, whose coordinate axes X1 and Y1 coincide with the axes of the two orthogonal coils constituting magnetic field source 1 (S1), and coordinate axis Z1 is the cross product of X1 and Y1; the center point of the two orthogonal coils constituting S1, i.e., the origin of coordinate system S1, is (0,0,0); coordinate system S2 is a coordinate system corresponding to magnetic field source 2 (S2), whose coordinate axes X2 and Y2 coincide with the axes of the two orthogonal coils constituting S2, and the direction of coordinate axis Z2 is opposite to the cross product of X2 and Y2; the center point of the two orthogonal coils constituting S2 is located at the origin of coordinate system S2; the origin of coordinate system S2 is located at (d,0,0) of the global coordinate system, i.e., the distance between the center points of the two magnetic field sources is d; in addition, X1 and X2 coincide but are in opposite directions; Y1 and Y2, Z1 and Z2 are parallel to each other and have the same direction. Without loss of generality, the coordinates of S3 in coordinate systems S1 and S2 are recorded as (x1, y1, z1) and (x2, y2, z2) respectively. Coordinate system S3 is established at this position as the origin. The coordinate axes X3, Y3, and Z3 of coordinate system S3 coincide with the three axes of sensor S3. The horizontal projection angles γ1 and γ2 are respectively the X and Y axes of sensor S3 in coordinate system S* (* = 1 and 2, representing the relevant parameters corresponding to the two magnetic sources, the same below). * Y * Projection of the plane and X * The angle between the positive semi-axis of the axis; the elevation angles δ1 and δ2 are respectively the angles between the line between the origin of the coordinate system S* and the center point of S3 and the line at the X * Y * The angle between the projections of the planes. is the attitude angle of sensor S3, which can be regarded as rotating S3 around the X3 axis of coordinate system S3 by an angle ψ, then rotating it around the Y3 axis by an angle θ, and finally rotating it around the Z3 axis The angle is parallel to the three axes of the global coordinate system S1; R1 and R2 are the rotation matrices of the sensor S3 in the S* coordinate system. * The product with the coordinate axis of the coordinate system S3 is parallel to the direction of the coordinate axis of the coordinate system S*.

[0007] The fast electromagnetic tracking method based on a planar rotating magnetic field provided by the present invention comprises the following specific steps:

[0008] Step 1: Use sine and cosine constant currents of the same frequency and amplitude to simultaneously excite two coils constituting a magnetic field source; then excite two coils constituting another magnetic field source in the same manner; and respectively record the magnetic induction intensity collected by the three-axis magnetic sensor each time;

[0009] Step 2: Calculate the position coordinates of the magnetic sensor according to the magnetic induction intensities collected twice;

[0010] Step 3: Calculate the magnetic induction intensity of the sensor location in the three coordinate axis directions of the coordinate system S1 and S2 according to the magnetic dipole model formula;

[0011] Step 4: Calculate the rotation matrix of the magnetic sensor according to the magnetic induction intensity detected by the three axes of the magnetic sensor and the magnetic induction intensity in the directions of the three coordinate axes of the coordinate system S1 and S2, and further calculate its posture angle.

[0012] Further:

[0013] In step 1, the dual-axis coil constituting the magnetic field source is excited with an AC constant current in the following manner:

[0014] For magnetic field source S * X * Axis, Y * The axis coil simultaneously applies cosine excitation current Icos(ω0t) and sine excitation current Isin(ω0t) with amplitude I and angular frequency ω0, and records the signal collected by the magnetic sensor S3, that is, the magnetic induction intensity in the three coordinate axis directions of the coordinate system S3.

[0015] In step 2, the position coordinates of the magnetic sensor are calculated according to the magnetic induction intensities collected twice. The specific process is as follows:

[0016] The magnetic induction intensity modulus at the position of S3 is decomposed along the axis directions of the two coordinate systems S1 and S2, and recorded as Incentive * When the coil is connected, according to the magnetic dipole model, the sensor S3 collects The module can be equivalent to formula (1):

[0017]

[0018] In the formula, is the projection value of the modulus of the magnetic induction intensity detected by S3 in the three coordinate axis directions of the coordinate systems S1 and S2; μ0 is the magnetic permeability of vacuum / air; N is the number of turns of the magnetic field source coil; S is the area of ​​the magnetic field source coil; r * is S3 and magnetic field source S * The Euclidean distance of the magnetic induction intensity is obtained by phase analysis of the magnetic induction intensity relative to the excitation current. * , which is related to the horizontal coordinate x of S3 * and the ordinate y * Related. * / x * =tan(γ * ), then the horizontal projection angle γ * It can be calculated using formula (2):

[0019]

[0020] Analyzing formula (1), we can see that the modulus of magnetic induction intensity changes sinusoidally. There is a maximum value and minimum value

[0021] Sky elevation angle δ * It can be calculated by formula (3):

[0022]

[0023] Using the horizontal projection angles γ1, γ2 and the elevation angles δ1, δ2, the position coordinates of the sensor S3 in the coordinate systems S1 and S2 can be obtained by formula (4):

[0024]

[0025] In step 3, the calculation of the magnetic induction intensity of the magnetic sensor location in the directions of the coordinate axes of the coordinate systems S1 and S2 specifically includes:

[0026] The S3 coordinates (x * ,y * ,z * ) is substituted into the magnetic dipole model formula to obtain the excitation magnetic field source S * The decomposition value of the magnetic induction intensity detected by S3 in the direction of each coordinate axis of the coordinate system S*

[0027]

[0028] In step 4, the calculation of the rotation matrix and attitude angle of the magnetic sensor specifically includes:

[0029] R1 and R2 are the rotation matrices of sensor S3 in the S1 and S2 coordinates respectively. They can be regarded as Rotate around the Z axis in sequence Angle, rotate θ angle around the Y axis, rotate ψ around the X axis to get According to the rotation matrix principle, its expression is:

[0030]

[0031] Convert the rotation matrix R2 in S2 coordinates to S1:

[0032]

[0033] Since the constant current of the excitation magnetic field source is a sinusoidal current, the magnetic induction intensity signal collected by sensor S3 is is also sinusoidal. and Expressed in matrix form:

[0034]

[0035] Where a * , b * is the amplitude of the sine and cosine signals decomposed from the magnetic induction intensity signal.

[0036] According to the definition of rotation matrix, the rotation matrix R * The magnetic induction intensity collected by S3 The product of is the magnetic induction intensity in each coordinate axis direction of the coordinate system S* Right now Rotation matrix R * The calculation formula is:

[0037]

[0038] in:

[0039]

[0040] [c *X ,c *Y ,c *Z ]=[a *X ,a *Y ,a *Z ]×[b *X ,b *Y ,b *Z ],

[0041] Formula (10) is the result calculated by formula (9), a 3×3 matrix R * Since the specific calculation formula needs to be expanded item by item according to the calculation of matrix multiplication and inverse matrix, and the expression for inverting the third-order matrix is ​​relatively complicated, m, n, and p are used to replace each item of the matrix calculated by formula (9):

[0042]

[0043] Combined with the expansion of the rotation matrix, it can be solved by formula (11) That is, the attitude angle of S3:

[0044]

[0045] The position coordinates and attitude angle of the positioning target S3 can be obtained through the above steps. Most of the current electromagnetic tracking methods require multiple excitations of the magnetic field source or multiple magnetic field sources, and rely on solving complex nonlinear equations to obtain the attitude information of the target through iterative calculations. The complexity of its calculation, the power consumption and response time of the system are relatively high. The present invention only requires two excitations, which reduces the demand for the number of magnetic field sources and control circuits and simplifies the hardware design; the position coordinates and attitude angles of the target can be obtained by linear operations, which reduces the requirements for processor performance and avoids the iterative convergence problems that may occur in the nonlinear solution process of traditional methods. That is, the present invention improves the response speed of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Schematic diagram of the process of rapid electromagnetic tracking method based on rotating magnetic field.

[0047] Figure 2 Schematic diagram of the coordinate system and projection angle involved in the electromagnetic positioning system.

[0048] Figure 3 Schematic diagram of a planar rotating magnetic field generated by exciting a dual-axis coil with orthogonal currents. DETAILED DESCRIPTION

[0049] The following will describe the technical solutions in the embodiments of the present invention in detail in conjunction with the accompanying drawings in the embodiments of the present invention. The described embodiments are only part of the embodiments of the present invention.

[0050] like Figure 1 As shown, the correction algorithm flow of the electromagnetic positioning system for AC excitation of the present invention is as follows:

[0051] Step 1: Use sine and cosine constant currents of the same frequency and amplitude to simultaneously excite two coils constituting a magnetic field source; then excite two coils constituting another magnetic field source in the same manner; and respectively record the magnetic induction intensity collected by the three-axis magnetic sensor each time;

[0052] Step 2: Calculate the position coordinates of the magnetic sensor according to the magnetic induction intensities collected twice;

[0053] Step 3: Calculate the magnetic induction intensity of the sensor location in the three coordinate axis directions of the coordinate system S1 and S2 according to the magnetic dipole model formula;

[0054] Step 4: Calculate the sensor rotation matrix based on the magnetic induction intensity detected by the three axes of the magnetic sensor and the magnetic induction intensity in the three coordinate axis directions of the coordinate system S1 and S2, and further calculate its posture angle.

[0055] (1) Excitation magnetic field source, sensor acquisition signal

[0056] Figure 2 It is a schematic diagram of the coordinates of the whole system, where S1 and S2 are two-axis magnetic field sources, and the distance between their center points is d=40cm. S3 is the three-axis magnetic sensor to be positioned. Coordinate systems S1 and S2 are established with the center points of the two magnetic sources as the coordinate origins. The coordinate axes X1 and Y1 of coordinate system S1 coincide with the axes of the two orthogonal coils that constitute the magnetic field source S1. The coordinate axes X2 and Y2 of coordinate system S2 coincide with the axes of the two orthogonal coils that constitute S2. Among them, X1 and X2 are parallel to each other but in opposite directions; Y1 and Y2, Z1 and Z2 are parallel to each other and in the same direction.

[0057] At the same time, the X1 and Y1 axis coils of S1 are excited with 1kHz, 1A cosine and sine currents, such as Figure 3 . Record the magnetic induction intensity collected by the magnetic sensor, recorded as Similarly, repeat the above steps to stimulate S2, and the magnetic induction intensity collected by the sensor is recorded as

[0058] (2) Calculate the coordinates of the magnetic sensor

[0059] When S1 is stimulated, the magnetic induction intensity signal collected by the sensor α1 is obtained through phase analysis. Then the horizontal projection angle γ1 of the magnetic field is obtained, that is:

[0060]

[0061] Similarly, through Phase analysis is used to solve the second horizontal projection angle γ2.

[0062] When S1 is stimulated, the magnetic induction intensity collected by the magnetic sensor is The maximum value of The minimum value is recorded as The elevation angle δ1 of the target position is obtained by formula (2):

[0063]

[0064] Similarly, analysis The modulus value can be used to obtain the elevation angle δ2. Using these four angles, the position coordinates of the magnetic sensor S3 can be obtained through formula (3):

[0065]

[0066] (3) Calculate the magnetic induction intensity of the coordinate point (x, y, z) in the directions of the three coordinate axes of the coordinate system S1 and S2.

[0067] Substitute the S3 coordinates (x, y, z) obtained in step 3 into the magnetic dipole model formula to obtain the magnetic induction intensity generated in the three coordinate axis directions of the coordinate system S1 and S2 when S1 and S2 are excited respectively

[0068]

[0069] In the formula, x ′ =dx, r1, r2 are the Euclidean distances between the coordinate point (x, y, z) and the magnetic field sources S1 and S2 respectively.

[0070] (4) Calculate the target attitude angle

[0071] Taking the stimulus S1 as an example, the The magnetic induction intensity collected by the sensor Expressed as a 3×2 matrix:

[0072]

[0073] In the formula, a and b are the amplitudes of the sine and cosine signals decomposed from the collected magnetic induction intensity signal. The matrix is ​​cross-multiplied and expanded, and the rotation matrix R1 is obtained by formula (6):

[0074]

[0075] in,

[0076] [c X ,c Y ,c Z ]=[a X ,a Y ,a Z ]×[b X ,b Y ,b Z ].

[0077] Similarly, we can and The rotation matrix R2 is calculated. Since the specific calculation formula needs to be expanded item by item according to the matrix multiplication and the calculation of the inverse matrix, and the expression for the inverse of the third-order matrix is ​​relatively complicated, m, n, and p are used to replace each item of the matrix calculated by formula (6):

[0078]

[0079] Combined with the expansion of the rotation matrix, we can solve it by formula (8): That is, the attitude angle of S3:

[0080]

[0081] At this point, the target S3 sensor is tracked and its position coordinates (x, y, z) and attitude angle are obtained.

[0082] In order to verify the effectiveness of the present invention, Figure 2 64 test points are arranged in the space shown. The test points are evenly distributed in a grid manner, and the three-dimensional coordinate range is 5cm-35cm. The attitude angle of the sensor is fixed to (30°, -45°, 60°). Under the conditions of this specific embodiment, the sensor is placed at each test point. The system only takes 2ms to track the position and attitude of the sensor. Table 1 shows the coordinate error Δr and attitude error of the tracking method of the present invention. Statistical results.

[0083] Table 1, tracking effect of the present invention

[0084]

[0085] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions and variations of these embodiments are made without departing from the principles and spirit of the present invention, and still fall within the scope of protection of the present invention.

Claims

1. A fast electromagnetic tracking method based on a planar rotating magnetic field, characterized in that: The magnetic tracking system involved includes two magnetic field sources and a three-axis magnetic sensor for tracking the target; each magnetic field source is composed of two mutually orthogonal coils, and the three-axis magnetic sensor is used to sense the magnetic induction intensity in three mutually orthogonal directions; the planar rotating magnetic field is generated by twice exciting the magnetic field source, and the three-axis magnetic sensor collects signals and obtains its position and attitude information through linear operations; For ease of explanation, three coordinate systems S1, S2 and S3 are defined; S1 is a global coordinate system, whose coordinate axes X1 and Y1 coincide with the axes of the two orthogonal coils constituting the magnetic field source S1, and the coordinate axis Z1 is the cross product of X1 and Y1; the center point of the two orthogonal coils constituting the magnetic field source S1, i.e., the origin of the coordinate system S1, is (0,0,0); the coordinate system S2 is a coordinate system corresponding to the magnetic field source S2, whose coordinate axes X2 and Y2 coincide with the axes of the two orthogonal coils constituting the magnetic field source S2, and the direction of the coordinate axis Z2 is opposite to the cross product of X2 and Y2; the center point of the two orthogonal coils constituting the magnetic field source S2 is located at Origin; the origin of coordinate system S2 is located at (d, 0, 0) of the global coordinate system, that is, the distance between the center points of the two magnetic field sources is d; in addition, X1 and X2 coincide but are in opposite directions; Y1 and Y2, Z1 and Z2 are parallel to each other and in the same direction; let the coordinates of magnetic sensor S3 in coordinate systems S1 and S2 be recorded as (x1, y1, z1) and (x2, y2, z2) respectively; establish coordinate system S3 at this position as the origin; the coordinate axes X3, Y3, and Z3 of coordinate system S3 coincide with the three axes of magnetic sensor S3; let the horizontal projection angles γ1 and γ2 be the X and Y axes of magnetic sensor S3 in coordinate system S* (*=1, 2, the same below) respectively. * Y * Projection of the plane and X * The angle between the positive semi-axis of the axis; let the elevation angles δ1 and δ2 be the line between the origin of the coordinate system S* and the center point of S3 and the line at the X * Y * The angle between the projections of the planes; is the attitude angle of the magnetic sensor S3, which can be regarded as rotating the magnetic sensor S3 around the X3 axis of the coordinate system S3 by an angle ψ, then around the Y3 axis by an angle θ, and finally around the Z3 axis. After the angle is adjusted, it is parallel to the three axes of the global coordinate system S1; let R1 and R2 be the rotation matrices of the magnetic sensor S3 in the S* coordinate system respectively; the rotation matrix R * The product with the coordinate axis of the coordinate system S3 is parallel to the direction of the coordinate axis of the coordinate system S*; Therefore, the specific steps of the electromagnetic tracking method are: Step 1: Use sine and cosine constant currents of the same frequency and amplitude to simultaneously excite two coils constituting a magnetic field source; then excite two coils constituting another magnetic field source in the same manner; and respectively record the magnetic induction intensity collected by the three-axis magnetic sensor each time; Step 2: Calculate the position coordinates of the magnetic sensor according to the magnetic induction intensities collected twice; Step 3: Calculate the magnetic induction intensity of the magnetic sensor in the three coordinate axis directions of the coordinate system S1 and S2 according to the magnetic dipole model formula; Step 4: Calculate the rotation matrix of the magnetic sensor according to the magnetic induction intensity detected by the three axes of the magnetic sensor and the magnetic induction intensity in the directions of the three coordinate axes of the coordinate system S1 and S2, and further calculate its posture angle.

2. The rapid electromagnetic tracking method according to claim 1, characterized in that: In step 1, the dual-axis coil constituting the magnetic field source is excited with an alternating constant current in the following manner: For magnetic field source S * X * Axis, Y * The axis coil simultaneously applies cosine excitation current Icos(ω0t) and sine excitation current Isin(ω0t) with amplitude I and angular frequency ω0, and records the signal collected by the magnetic sensor S3, that is, the magnetic induction intensity in the three coordinate axis directions of the coordinate system S3.

3. The rapid electromagnetic tracking method according to claim 2, characterized in that: In step 2, the position coordinates of the magnetic sensor are calculated based on the magnetic induction intensities collected twice. The specific process is as follows: The magnetic induction intensity modulus at the location of the magnetic sensor S3 is decomposed along the axis directions of the two coordinate systems S1 and S2, respectively, and recorded as Incentive * When the coil is connected, according to the magnetic dipole model, the sensor S3 collects The module equivalent of is formula (1): In the formula, is the projection value of the modulus of the magnetic induction intensity detected by S3 in the three coordinate axis directions of the coordinate systems S1 and S2; μ0 is the magnetic permeability of air; N is the number of turns of the magnetic field source coil; S is the area of ​​the magnetic field source coil; r * is S3 and magnetic field source S * The Euclidean distance of the magnetic induction intensity is obtained by phase analysis of the magnetic induction intensity relative to the excitation current. * , which is related to the horizontal coordinate x of S3 * and the ordinate y * related to; * / x * =tan(γ * ), then the horizontal projection angle γ * Calculate using formula (2): From formula (1), we can see that the modulus of magnetic induction intensity changes sinusoidally, and there is a maximum value and minimum value Therefore, the elevation angle δ * Calculated by formula (3): Using the horizontal projection angles γ1, γ2 and the elevation angles δ1, δ2, the position coordinates of the sensor S3 in the coordinate systems S1 and S2 are obtained by formula (4):

4. The rapid electromagnetic tracking method according to claim 3, characterized in that: The calculation of the magnetic induction intensity of the magnetic sensor at the location in the directions of the coordinate axes of the coordinate systems S1 and S2 in step 3 specifically includes: The S3 coordinates (x * ,y * ,z * ) is substituted into the magnetic dipole model formula to obtain the excitation magnetic field source S * The decomposition value of the magnetic induction intensity detected by S3 in the direction of each coordinate axis of the coordinate system S* 5. The rapid electromagnetic tracking method according to claim 4, characterized in that: The calculation of the rotation matrix and attitude angle of the magnetic sensor described in step 4 specifically includes: According to the rotation matrix principle, the expression of rotation matrices R1 and R2 is: Convert the rotation matrix R2 in S2 coordinates to S1: Since the constant current of the excitation magnetic field source is a sinusoidal current, the magnetic induction intensity signal collected by the magnetic sensor S3 is is also sinusoidal, and Expressed in matrix form: Where a * 、b * The amplitude of the sine and cosine signals decomposed from the magnetic induction intensity signal; According to the definition of rotation matrix, the rotation matrix R * The magnetic induction intensity collected by S3 The product of is the magnetic induction intensity in each coordinate axis direction of the coordinate system S* Right now Rotation matrix R * The calculation formula is: in: [c *X ,c *Y ,c *Z ]=[a *X ,a *Y ,a *Z ]×[b *X ,b *Y ,b *Z ]; Formula (10) is the result calculated by formula (9), a 3×3 matrix R * ; Since the specific calculation formula needs to be expanded item by item according to the calculation of matrix multiplication and inverse matrix, and the expression for inverting the third-order matrix is ​​relatively complicated, m, n, and p are used to replace each item of the matrix calculated by formula (9): Combined with the expansion of the rotation matrix, we can solve it using formula (11): That is, the attitude angle of S3: Thus, the position coordinates and attitude angle of the positioning target S3 are obtained.

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