Method for accurately measuring azimuth of axis of spatial universal uniform rotating magnetic field

Abstract

The application belongs to the technical field of automation engineering, and discloses a kind of accurate measurement methods of spatial universal uniform rotation magnetic field axis azimuth.First, using 3 Hall sensors and 1 3-axis acceleration sensor, the three-dimensional magnetic vector coordinates of rotating magnetic field at any two time instants are measured, and the rotation transformation relationship of rotating magnetic vector coordinates in probe coordinate system and fixed coordinate system is established.Second, with the help of space vector operation law, the normal vector of the rotating magnetic vector at the above two time instants is solved.Third, according to the orthogonal transformation principle of space vector, the spatial universal rotating magnetic field axis azimuth described by pitch angle and roll angle is obtained.Finally, according to the corresponding relationship between the normal vector of the rotating magnetic vector at any two time instants and the spatial rotating magnetic field axis azimuth, the rotating magnetic field axis azimuth represented by three-dimensional magnetic vector coordinates can be obtained.The measurement method of the application has the advantages of high measurement accuracy, good real-time performance, strong environmental adaptability, low working environment requirement, etc.

Description

Technical Field

[0001] This invention belongs to the field of automation engineering technology and relates to a method for accurately measuring the orientation of the axis of a spatial omnidirectional uniform rotating magnetic field. Specifically, it relates to the method and steps for accurately measuring the orientation of the axis of a three-dimensional rotating magnetic field using a three-dimensional magnetic field vector determined by three Hall sensors. Background Technology

[0002] Capsule endoscopy is an effective alternative to traditional gastroscopy and colonoscopy for gastrointestinal examinations, designed to perform minimally invasive procedures. This method requires no sedation and causes no discomfort or pain to the patient, making it an effective tool for monitoring small bowel diseases. Currently, magnetically driven capsule robots represent the latest research advancements in this field. Based on their working principles, magnetically driven capsules can be broadly categorized into two types: gradient magnetic field driven and uniform rotating magnetic field driven.

[0003] Gradient magnetic field driven capsules are propelled forward by the gradient magnetic pull between an external electromagnetic field and an embedded permanent magnet, and their orientation is changed by controlling the orientation of the external magnetic field. Based on this working principle, researchers have proposed various capsule structures and even launched commercial products. For example, the paper "Feasibility of stomach exploration with a guided capsule endoscope" describes a multi-coil driven magnetic navigation capsule endoscope system jointly developed by Siemens Healthineers and Olympus Medical; Wuhan Ankon Technologies Co., Ltd. also proposed a capsule endoscope system in patent US 2015 / 0018615 A1 that uses an external spherical permanent magnet to achieve active capsule movement. However, because the orientation of the external magnetic field and the precise position and direction of the capsule in the gastrointestinal tract are difficult to monitor in real time, it is impossible to precisely control the magnitude of the magnetic force and magnetic moment acting on the capsule. Furthermore, this type of capsule suffers from magnetic force-magnetic moment coupling; that is, when controlling the capsule position by magnetic force or the capsule orientation by magnetic moment, the two operations inevitably interfere with each other. Therefore, gradient magnetic field driven capsules often exhibit problems such as poor stability, difficulty in manipulation and control, and easy impact on the gastrointestinal tract in clinical applications.

[0004] Pure magnetic moment driven capsules achieve active motion and posture control through the magnetic moment between an external uniform rotating magnetic field and an embedded permanent magnet within the capsule. The external driving source for pure magnetic moment driven capsules is typically a uniform rotating magnetic field generated by a triaxial Helmholtz coil. Through the coupled magnetic torque between the external rotating magnetic field and the radially magnetized permanent magnet embedded within the capsule, the capsule's helical motion can be converted into linear motion or achieve rolling motion, as described in patent 200710159159.8. The capsule's posture can be adjusted by controlling the axial orientation of the rotating magnetic field (the normal direction of the magnetic vector rotation plane), as described in patent 201510262778.4. This type of capsule not only effectively avoids the generation of gradient magnetic field forces but also solves the magnetic moment coupling problem present in gradient magnetic field driven capsules, thus representing the latest research trend in magnetically driven capsules. The core issue in pure magnetic moment driven capsule posture control is the precise control of the orientation of the rotating magnetic field axis. The accuracy of the magnetic field axis orientation directly affects the control accuracy of the capsule posture, and the accurate detection of the magnetic field axis orientation is a basic prerequisite for achieving precise capsule posture control.

[0005] In summary, external magnetic field orientation detection is crucial for magnetically driven capsule robots. Firstly, these robots rely on an external driving magnetic field to control the capsule's position and orientation within the gastrointestinal tract. Changes in the external magnetic field orientation affect the capsule's trajectory and position, potentially causing it to fail to reach its target location or deviate from its intended path, impacting diagnostic and treatment accuracy. Secondly, changes in the external magnetic field orientation can cause magnetic field interference, preventing the capsule from maintaining stable movement and position, thus affecting its pose stability and treatment outcomes. Thirdly, external magnetic field orientation detection allows for real-time monitoring of changes in the magnetic field orientation, enabling timely calibration and adjustment of the capsule to maintain accurate pose and improve the effectiveness and safety of medical treatment. Therefore, detecting the external magnetic field orientation of magnetically driven capsule robots, especially the axial orientation of a uniformly rotating magnetic field, is essential. It ensures the robot's motion and position control accuracy, thereby improving diagnostic and treatment effectiveness and safety. Although researchers have reached a consensus on the magnetic drive method for capsule robots and fully recognize the importance of magnetic field orientation detection, there are currently no effective instruments available on the market for detecting magnetic field orientation, particularly the axial orientation of a uniformly rotating magnetic field.

[0006] To address the aforementioned problems, this invention, based on the existing national invention patent "A Human-Machine Interactive Control Method for a Spatial Omnidirectional Rotating Magnetic Field" (Patent No.: ZL201610009285.4), utilizes three-dimensional magnetic vector information obtained from Hall sensors and accelerometers, and proposes a precise measurement method for the orientation of the axis of a spatial uniform rotating magnetic field based on the orthogonal transformation principle of spatial vectors. Specifically, using the three-dimensional magnetic vector coordinates measured by the Hall sensor at any two moments as a basis, the rotational transformation relationship of the rotating magnetic vector in the probe coordinate system and the fixed coordinate system is established. Then, combining the representation method of the orientation of the rotating magnetic field axis in the fixed coordinate system, and the correspondence between the normal vector of the magnetic vector and the orientation of the rotating magnetic field axis at any two moments, a functional expression for the orientation of the spatial rotating magnetic field axis is given.

[0007] Currently, no one has proposed a precise measurement method for the orientation of the axis of a uniformly rotating magnetic field in space. The outstanding feature of this positioning method is that it can use the three-dimensional magnetic vector coordinate information obtained by Hall sensors and accelerometers to achieve precise measurement of the orientation of the axis of a three-dimensional dynamic uniformly rotating magnetic field. This method has high measurement accuracy and strong real-time measurement capabilities, and is expected to provide strong technical support for improving the posture control accuracy of magnetically driven capsule robots. Summary of the Invention

[0008] The technical solution to be solved by this invention is to provide a method for accurately measuring the axial orientation of a spatially omnidirectional rotating magnetic field using three Hall sensors and one 3-axis accelerometer. First, the three Hall sensors and one 3-axis accelerometer are used to measure the three-dimensional magnetic vector coordinates of the rotating magnetic vector in the probe coordinate system at any two times t1 and t2, and the rotational transformation relationship of the rotating magnetic vector in the probe coordinate system and the fixed coordinate system is established. Second, the normal vector of the magnetic vector at the two times is solved using the arithmetic rules of spatial vectors. Third, according to the orthogonal transformation principle of spatial vectors, the axial orientation of the spatially omnidirectional rotating magnetic field, described by the pitch angle and yaw angle, is obtained. Finally, based on the correspondence between the normal vector of the rotating magnetic vector at times t1 and t2 and the axial orientation of the rotating magnetic field, the axial orientation of the rotating magnetic field, described by the three-dimensional magnetic vector coordinates, can be obtained.

[0009] The technical solution of the present invention:

[0010] A method for accurately measuring the orientation of the axis of a spatial omnidirectional uniform rotating magnetic field, comprising the following steps:

[0011] As attached Figure 1a and Figure 1bAs shown, a probe coordinate system Ox′y′z′ and a fixed coordinate system OXYZ are introduced. The origin of the probe coordinate system Ox′y′z′ is located at the lower left corner of the probe, and the Ox′, Oy′, and Oz′ axes are parallel to the three sides of the cuboid probe, respectively. The origin of the fixed coordinate system OXYZ is located at the center of the three-axis Helmholtz coil, and the coordinate axes OX, OY, and OZ are perpendicular to the outer, middle, and inner principal planes of the three-axis Helmholtz coil, respectively, as shown in the attached diagram. Figure 1b As shown. (Attached) Figure 1a In the rectangular probe, three Hall sensors are orthogonally arranged, with their principal planes perpendicular to the Ox′, Oy′, and Oz′ axes of the probe's coordinate system Ox′y′z′, respectively. Since the probe can rotate freely, different measurement values ​​can be obtained at the same measurement point depending on the probe's orientation. Therefore, a 3-axis accelerometer is introduced to determine the probe's orientation. The principal plane of the 3-axis accelerometer is perpendicular to the Oz′ axis of the probe's coordinate system Ox′y′z′.

[0012] like Figure 2a As shown, the orientation of the measuring probe relative to the fixed coordinate system OXYZ can be described using Cardan angles: Assuming the fixed coordinate system OXYZ initially coincides with the probe coordinate system Ox′y′z′, first, rotate the fixed coordinate system OXYZ counterclockwise by α around the OY axis to obtain coordinate system Ox1Yz1. Then, rotate Ox1Yz1 counterclockwise by β around the Ox1 axis to obtain coordinate system Ox1y′z'. Finally, rotate Ox1y′z' counterclockwise by γ along the Oz' axis to obtain the probe coordinate system Ox′y′z′. Therefore, the orientation of the measuring probe can be represented by Cardan angles α, β, and γ. Since rotation of the Oz′ axis about itself does not change its orientation in the fixed coordinate system OXYZ, the orientation of the Oz′ axis is only related to the Cardan angles α and β, and is independent of the γ angle. Therefore, the orientation of the measuring probe can be represented solely by the Cardan angles α and β. That is, the probe coordinate system Ox′y′z′ can be obtained by first rotating the fixed coordinate system OXYZ counterclockwise about the OY axis by α, and then rotating it counterclockwise about the Ox′ axis by β, as shown in the attached figure. Figure 2b As shown. Therefore, the rotation transformation matrix from the probe coordinate system Ox′y′z′ to the fixed coordinate system OXYZ can be expressed as:

[0013]

[0014] The attitude angles α and β of the probe relative to the fixed coordinate system OXYZ in equation (1) can be measured by a 3-axis accelerometer. Figure 2aAs shown, when the probe coordinate system Ox′y′z′ coincides with the fixed coordinate system OXYZ, the gravitational acceleration coordinates measured by the 3-axis accelerometer are (0,0,z), where z is the gravitational acceleration g. Assuming that the probe coordinate system Ox′y′z′ rotates (α, β) relative to the fixed coordinate system OXYZ, the gravitational acceleration coordinates measured by the 3-axis accelerometer are (x', y', z'), then the following relationship exists.

[0015]

[0016] From equation (2), we can obtain

[0017]

[0018] According to equation (3), the attitude angles α and β of the measuring probe relative to the fixed coordinate system OXYZ can be obtained. Combining with equation (2), the three-dimensional magnetic vector coordinates (B) in the probe coordinate system Ox′y′z′ can be obtained. x ',By',B z The corresponding coordinates in the fixed coordinate system OXYZ are ').

[0019]

[0020] Assume that the rotating magnetic vectors measured by the measuring probe at times t1 and t2 are respectively (B x1 ',B y1 ',B z1 ') and (B x2 ',B y2 ',B z2 '), and the corresponding magnetic vectors in the fixed coordinate system OXYZ are B1 and B2 respectively (e.g. Figure 2b As shown), the normal vector n corresponding to B1 and B2 can be obtained as follows:

[0021]

[0022] In the formula, B0 is the magnetic flux density amplitude of the rotating magnetic field, and satisfies

[0023] According to the description in patent ZL201610009285.4, a uniformly rotating magnetic field in space can be represented in a rotating magnetic field coordinate system Ox1y1z1 (the magnetic vector B rotates in the Ox1z1 plane, the normal direction of which is along the Oy1 axis), such as... Figure 3a As shown. Figure 3a The normal direction of the rotating magnetic vector plane is defined as the orientation n of the axis of the rotating magnetic field. B ,from Figure 3a It can be seen that the orientation of the axis of the rotating magnetic field is n BIn a fixed coordinate system OXYZ, the yaw angle ψ and pitch angle θ can be used to represent the pitch angle, i.e., n B = (ψ, θ). Figure 3a Orientation n of the magnetic field axis B It can be obtained through the following orthogonal transformation process: Assuming the initial time n B To obtain a rotating magnetic field with azimuth along Oy1 along the OY axis of a fixed coordinate system OXYZ, the fixed coordinate system OXYZ can be rotated clockwise by ψ (lateral yaw angle) around the OZ axis, and then rotated counterclockwise by φ (pitch angle) around Ox1. Therefore, the orthogonal transformation matrix from the fixed coordinate system OXYZ to the rotating magnetic field coordinate system Ox1y1z1 can be expressed as:

[0024]

[0025] According to equation (4), the orientation of the rotating magnetic field axis in coordinate system Ox1y1z1 can be expressed in fixed coordinate system OXYZ as follows:

[0026] n B =A2 -1 (0 1 0) T =(sinψcosφ cosψcosφ sinφ) T (7)

[0027] Combination Figure 3a and Figure 2b It can be seen that, Figure 2b The normal vector n of the magnetic vectors B1 and B2 should be... Figure 3a The axes of the rotating magnetic field coincide, i.e., n = n B By combining equations (5) and (7), we can obtain

[0028]

[0029] From equation (8), the orientation of the spatial rotating magnetic field axis, expressed in terms of the lateral tilt angle ψ and the pitch angle φ, can be obtained as follows:

[0030] n B =(ψ,φ) (9)

[0031] in,

[0032]

[0033] In summary, as long as the three-dimensional magnetic vector coordinates of the rotating magnetic vector B at any two moments in the fixed coordinate system OXYZ are obtained by measuring the probe, the orientation of the axis of the uniformly rotating magnetic field in space can be obtained according to equation (9).

[0034] The beneficial effects of this invention are as follows: This measurement method utilizes the three-dimensional magnetic vector coordinates measured in real time by a Hall sensor, and establishes a precise mathematical relationship between the three-dimensional magnetic vector coordinates and the orientation of the rotating magnetic field axis in a fixed coordinate system through the arithmetic rules of spatial vectors and the principle of orthogonal transformation. This enables real-time and accurate measurement of the orientation of the axis of a spatially dynamic, uniformly rotating magnetic field. This method fills the gap in the technology for measuring the orientation of the axis of a spatially uniformly rotating magnetic field, solves a key problem affecting the precise pose control of a magnetically driven capsule robot, and improves the accuracy and real-time performance of the rotational magnetic field axis orientation measurement. A significant feature of this measurement method is that it can obtain the orientation of the axis of a three-dimensional dynamically uniformly rotating magnetic field in real time solely based on the three-dimensional magnetic vector coordinate information obtained from the Hall sensor. This measurement method has advantages such as high measurement accuracy, good real-time performance, strong environmental adaptability, and low requirements for the working environment. Attached Figure Description

[0035] Figure 1a This is a schematic diagram of the probe structure and chip location.

[0036] Figure 1b This is a schematic diagram of the probe operating in a triaxial Helmholtz coil.

[0037] Figure 2a It is the complete representation of the probe's attitude in the fixed coordinate system OXYZ.

[0038] Figure 2b It is a simplified representation of the probe's attitude in the fixed coordinate system OXYZ.

[0039] Figure 2c This is a schematic diagram illustrating the definition of the normal vector of a magnetic vector.

[0040] Figure 3a This is a schematic diagram illustrating the orthogonal transformation principle of the orientation of a omnidirectional rotating magnetic field in space.

[0041] Figure 3b This is a schematic diagram of the orientation of the axis of a uniformly rotating magnetic field in space measured by a Hall sensor. Detailed Implementation

[0042] The following section takes the measurement of the orientation of the axis of the uniformly rotating magnetic field generated by a triaxial orthogonal Helmholtz coil as an example, and describes the specific implementation in detail with reference to the technical solution and accompanying drawings.

[0043] The uniformly rotating magnetic field generated in the central region of a triaxial orthogonally nested Helmholtz coil is as follows: Figure 3b As shown in the figure, B is the basic unit of a spatial rotating magnetic field—the rotating magnetic vector. The normal direction of the plane of rotation formed by the rotating magnetic vector is the orientation n of the axis of the rotating magnetic field. B .

[0044] Example:

[0045] like Figure 3b As shown, the measuring probe is inserted into the working area of ​​the triaxial square Helmholtz coil. According to formula (4), the three-dimensional magnetic field vector coordinates of the uniform rotating magnetic field at times t1 and t2 can be determined as B1=(0.0058,-0.0082,0). T And B2 = (-0.0041, -0.0029, 0.0087) T Using the rules of spatial vector operations, the normal vector n of magnetic vector B1 and magnetic vector B2 can be expressed as n = B1 × B2 = (0.7071, 0.5000, 0.5000). T .

[0046] like Figure 3a As shown, to quantitatively describe the spatial rotating magnetic vector generated by a triaxial square orthogonal Helmholtz coil, a rotating magnetic field coordinate system Ox1y1z1 is introduced. The rotating magnetic vector B rotates counterclockwise within the Ox1z1 plane, forming a magnetic vector rotation plane, with the Oy1 axis along the normal direction of this plane. It is easy to see from the figure that the direction of the Oy1 axis is the orientation n of the rotating magnetic field axis. B In the rotating magnetic field coordinate system Ox1y1z1, the orientation of the magnetic field axis is n. B = (0,1,0) T Assuming that the initial rotating magnetic field coordinate system Ox1y1z1 coincides with the fixed coordinate system OXYZ, the rotating magnetic field coordinate system ox1y1z1 can be obtained by first rotating the coordinate system OXYZ clockwise by ψ (side angle) about the OZ axis, and then rotating it counterclockwise by φ (pitch angle) about the x-axis of the intermediate coordinate system. Therefore, the rotation transformation matrix from the fixed coordinate system OXYZ to the rotating magnetic field coordinate system Ox1y1z1 can be expressed as A=(d,e,f), where d=(cosψ,sinψcosφ,-sinψsinφ). T ,e=(-sinψ,cosψcosφ,-cosψsinφ) T f = (0, sinφ, cosφ) T Therefore, the orientation n of the rotating magnetic field axis B In a fixed coordinate system OXYZ, it can be represented as n B =A -1 n B '=A -1 (0,1,0) T =(sinψcosφ,cosψcosφ,sinφ) T .

[0047] because Figure 2b The normal vector n of the rotating magnetic vectors B1 and B2, as determined by the measuring probe, is the axial orientation n of the rotating magnetic field. B That is, n B=n, therefore we have (sinψcosφ,cosψcosφ,sinφ). T =(0.7071,0.5000,0.5000) T From the above formula, we can obtain ψ = 54.7356° and φ = 30°. Therefore, the orientation of the axis of the uniformly rotating magnetic field in space should be n in the fixed coordinate system OXYZ. B =(ψ,φ)=(54.7356°,30°).

Claims

1. A method for accurately measuring the orientation of the axis of a spatial omnidirectional uniform rotating magnetic field, characterized in that, The steps are as follows: First, a probe coordinate system Ox′y′z′ and a fixed coordinate system OXYZ are introduced. The origin of the probe coordinate system Ox′y′z′ is located at the lower left corner of the probe, and the Ox′, Oy′, and Oz′ axes are parallel to the three sides of the cuboid probe, respectively. The origin of the fixed coordinate system OXYZ is located at the center of the three-axis Helmholtz coil, and the coordinate axes OX, OY, and OZ are perpendicular to the principal planes of the outer, middle, and inner coils of the three-axis Helmholtz coil, respectively. The three Hall sensors in the measuring probe are orthogonally arranged, and their principal planes are perpendicular to the Ox′, Oy′, and Oz′ axes, respectively. The principal plane of the three-axis accelerometer is perpendicular to the Oz′ axis. The first step is to determine the rotation transformation matrix from the probe coordinate system Ox′y′z′ to the fixed coordinate system OXYZ based on the following relationship: the probe coordinate system Ox′y′z′ is obtained by first rotating the fixed coordinate system OXYZ counterclockwise by α around the OY axis and then by β around the Ox′ axis. In the second step, when the probe coordinate system Ox′y′z′ coincides with the fixed coordinate system OXYZ, the gravitational acceleration coordinates measured by the 3-axis accelerometer are (0,0,z). After the probe coordinate system Ox′y′z′ rotates (α,β) relative to the fixed coordinate system OXYZ, the gravitational acceleration coordinates measured by the 3-axis accelerometer are (x',y',z'). The data measured by the 3-axis accelerometer in the two steps satisfy the following relationship: According to equation (2), the attitude angles α and β of the measuring probe relative to the fixed coordinate system OXYZ are obtained as follows: The third step is to use the three-dimensional magnetic vector coordinates (B) measured by the triaxial Hall sensor in the probe. x ',By',B z '), and the rotation transformation matrix A1 of the probe coordinate system Ox′y′z′ relative to the fixed coordinate system OXYZ, to obtain the three-dimensional magnetic vector coordinates (B) in the probe coordinate system. x ',By',B z The corresponding coordinates of ') in the fixed coordinate system OXYZ are Fourth step: According to the rules of spatial vector operations, the normal vector n corresponding to magnetic vectors B1 and B2 is obtained. In the formula, B0 is the magnetic flux density amplitude of the rotating magnetic field, and satisfies The fifth step is to define the normal direction of the plane of rotation of the magnetic vector generated by the triaxial Helmholtz coil as the axial orientation n of the uniformly rotating magnetic field in space. B Therefore, n B In the rotating magnetic field coordinate system Ox1y1z1, it is represented as (0,1,0); in the fixed coordinate system OXYZ, n B It is expressed using the yaw angle ψ and the pitch angle θ, i.e., n B = (ψ,θ); orientation of the magnetic field axis n B It is obtained through the following orthogonal transformation process: assuming the initial time n B To obtain a rotating magnetic field with orientation along the OY axis of the fixed coordinate system OXYZ, the fixed coordinate system OXYZ should first rotate clockwise by ψ around the OZ axis, and then rotate counterclockwise by φ around Ox1. Therefore, the orthogonal transformation matrix from the fixed coordinate system OXYZ to the rotating magnetic field coordinate system Ox1y1z1 is expressed as: Combining equation (6), the correspondence between the orientation of the magnetic field axis in the rotating magnetic field coordinate system Ox1y1z1 and the orientation of the rotating magnetic field axis in the fixed coordinate system OXYZ is obtained as n. B =A2 -1 (0 1 0) T =(sinψcosφ cosψcosφ sinφ) T (7) Step 6: The normal vectors of rotating magnetic vectors B1 and B2 satisfy the following relationship with the orientation of the axis of the uniformly rotating magnetic field in the fixed coordinate system OXYZ: the normal vector n of B1 and B2 is the orientation of the axis of the uniformly rotating magnetic field, that is, n = n B Combining equations (5) and (7), we get From equation (8), the orientation of the spatial rotating magnetic field axis, expressed in terms of the lateral swing angle ψ and the pitch angle φ, is obtained as follows: n B =(ψ,φ) (9) in,

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