SASING JUDE L (PH)
GUSTILO RAMON B (US)
SASING JUDE L (PH)
WO2021161158A1 | 2021-08-19 |
US20170090003A1 | 2017-03-30 | |||
US20110082366A1 | 2011-04-07 | |||
US20190285766A1 | 2019-09-19 | |||
US10884505B1 | 2021-01-05 | |||
US20070167703A1 | 2007-07-19 | |||
US20070135804A1 | 2007-06-14 |
Claims What is claimed is: 1. A magnetic tracking system for determining position and orientation of an object in three-dimensional space, comprising: an electromagnet assembly comprising first and second electromagnets that are coaxial, non-coincident, and spaced from each other by a fixed distance; at least one magnetometer positioned at a movable location relative to the electromagnet assembly and configured to measure three orthogonal components of a magnetic field vector; and a microcontroller unit operably connected to the at least one magnetometer, wherein the microcontroller unit is configured to: control measurement of magnetic fields by the at least one magnetometer; and compute a relative position and orientation of the electromagnet assembly and the at least one magnetometer in five degrees of freedom using at least two equations with two unknowns and coordinate transformation equations relating the coordinate frames of the electromagnet assembly and the at least one magnetometer. 2. The system of claim 1, wherein the microcontroller unit is configured to relate the coordinate frames of the electromagnet assembly and the magnetometer through a plane defined by first and second magnetic field vectors emanating from the first and second electromagnets, respectively. 3. The system of claim 1, wherein the electromagnet assembly further comprises a third electromagnet comprising an axis that is perpendicular to a common axis along which the first and second electromagnets are spaced from each other. 4. The system of claim 3, wherein the microcontroller unit is configured to compute the relative position and orientation of the electromagnet assembly and the magnetometer in six degrees of freedom using at least two equations with two unknowns and coordinate transformation equations relating the coordinate frames of the electromagnet assembly and the magnetometer. 5. The system of claim 1, wherein the microcontroller unit is configured to compute the relative position and orientation of the electromagnet assembly and the at least one magnetometer in five degrees of freedom using exactly two equations with two unknowns and coordinate transformation equations relating the coordinate frames of the electromagnet assembly and the at least one magnetometer. 6. The system of claim 1, wherein the at least one magnetometer comprises at least one three-axis magnetometer. 7. The system of claim 1, wherein the microcontroller unit is further operably connected to the electromagnet assembly. 8. The system of claim 1, wherein the microcontroller unit is further configured to control activation of the first and second electromagnets. 9. The system of claim 1, further comprising a secondary microcontroller unit configured to control activation of the first and second electromagnets. 10. A method of determining position and orientation of an object in three- dimensional space, comprising the steps of: activating first and second electromagnets of an electromagnet assembly, wherein the first and second electromagnets are coaxial, non-coincident, and spaced from each other by a fixed distance; positioning at least one magnetometer at a movable location relative to the electromagnet assembly; measuring three orthogonal components of a magnetic field vector with the at least one magnetometer; and computing the relative position and orientation of the electromagnet assembly and the at least one magnetometer in five degrees of freedom using at least two equations with two unknowns and coordinate transformation equations relating the coordinate frames of the electromagnet assembly and the at least one magnetometer; wherein the step of computing is performed by a microcontroller unit operably connected the at least one magnetometer, and wherein the microcontroller unit controls the measurement of magnetic field vectors by the at least one magnetometer. 11. The method of claim 10, wherein the step of computing is performed by a microcontroller unit that is further operably connected to the electromagnet assembly. 12. The method of claim 10, wherein the step of computing is performed by a microcontroller that further controls the activation of the first and second electromagnets. 13. The method of claim 10, wherein the step of activating the first and second electromagnets comprises sequentially activating the first and second electromagnets. 14. The method of claim 10, wherein the step of activating the first and second electromagnets comprises isolating and distinguishing a first and second magnetic field from the first and second electromagnets, respectively. 15. The method of claim 10, wherein the computing step further comprises using equations for magnetic field strength and magnetic field direction to determine the relative position between the magnetometer and the two electromagnets with exactly two equations and two unknowns. 16. The method of claim 15, wherein the computing step provides a partial, 2D solution in a plane containing a common axis of the first and second electromagnets and the magnetometer. 17. A method of determining position and orientation of an object in three- dimensional space, comprising the steps of: activating first, second and third electromagnets of an electromagnet assembly, wherein the first and second electromagnets are coaxial, non-coincident, and spaced from each other by a fixed distance, and the third electromagnet is oriented with its axis orthogonal to the common axis of the first and second electromagnets; positioning at least one magnetometer at a movable location relative to the electromagnet assembly; measuring three orthogonal components of a magnetic field vector with the at least one magnetometer; and computing the relative position and orientation of the electromagnet assembly and the at least one magnetometer in six degrees of freedom using at least two equations with two unknowns and coordinate transformation equations relating the coordinate frames of the electromagnet assembly and the at least one magnetometer; wherein the step of computing is performed by a microcontroller unit operably connected the at least one magnetometer, and wherein the microcontroller unit controls the measurement of magnetic field vectors by the at least one magnetometer. 18. A method of determining position and orientation of an object in five degrees of freedom for an electromagnet assembly relative to a magnetometer spaced from the electromagnet assembly, wherein the electromagnet assembly comprises first and second electromagnets spaced from each other along a common axis, wherein a center of the magnetometer is spaced at a first distance from the first electromagnet and spaced at a second distance from the second electromagnet, and wherein the magnetometer is configured to measure magnetic field strength in three orthogonal directions, the method comprising the steps of: computing a magnitude of a first magnetic field vector at the center of the magnetometer; determining a direction of the first magnetic field vector at the center of the magnetometer, wherein the direction of the first magnetic field vector is represented as where θ1 is a first colatitude angle between the common axis extending from the first electromagnet and a first line extending from the first electromagnet to the center of the magnetometer; computing a magnitude of a second magnetic field vector at the center of the magnetometer; determining a direction of the second magnetic field vector at the center of the magnetometer, wherein the direction of the second magnetic field vector is represented as where θ2 is a second colatitude angle between the common axis extending from the second electromagnet and a second line extending from the second electromagnet to the center of the magnetometer; computing the angle between the first magnetic field vector and the second magnetic field vector, the angle being represented as where B1 is the magnitude of the first magnetic field vector and B2 is the magnitude of the second magnetic field vector; solving the following first and second equations as a system of two non-linear equations with unknowns θ1 and θ2 determining a 3D position and orientation of the electromagnet assembly by identifying a plane containing the common axis from the directions of the magnetic field lines emanating from the first and second electromagnets. 19. The method of claim 18, wherein the step of computing the magnitude of the first magnetic field vector at the center of the magnetometer comprises a first field strength magnitude represented by where µo is a permeability of free space, M is a magnitude of the dipole moment, and r1 is a distance between the center of the magnetometer and the first electromagnet. 20. The method of claim 18, wherein the step of computing the magnitude of the second magnetic field vector at the center of the magnetometer comprises a second field strength magnitude represented by where µo is a permeability of free space, M is a magnitude of the dipole moment, and r2 is a distance between the center of the magnetometer and the second electromagnet. |
[0017] Figure 1 is a perspective view of one embodiment of an electromagnet assembly spaced from a magnetometer, in accordance with the systems and methods described herein; [0018] Figure 2 is schematic view of an exemplary magnetic dipole and its magnetic field lines; [0019] Figure 3 is a schematic view of an electromagnet assembly and a magnetometer; [0020] Figure 4 is another schematic view of an electromagnet assembly and a magnetometer; [0021] Figure 5 is a perspective view of another embodiment of an electromagnet assembly spaced from a magnetometer, in accordance with the systems and methods described herein. Detailed Description [0022] Referring now to the Figures, wherein the components are labeled with like numerals throughout the several Figures, and initially to Figure 1, a perspective view of one embodiment of the present invention is shown. An electromagnet assembly (EMA) 4 is composed of two electromagnets, electromagnet (EM) 1 and electromagnet (EM) 2, oriented to be coaxial along axis 6 and spaced apart by a known fixed distance 7. Magnetometer (MM) 5 is a 3-axis magnetometer that can measure magnetic field strength in three orthogonal directions. MM 5 can therefore measure both the magnitude and direction of the magnetic field vector. MM 5 is preferably a magnetoresistive type of magnetometer, although it can also be of a different type such as a Hall Effect or a search-coil type magnetometer, for example. EM 1 and EM 2 can be activated using standard AC or DC techniques so that their respective magnetic fields can be isolated and measured separately by MM 5. The objective is to determine the position and orientation of EMA 4 and the MM 5 relative to each other. [0023] In general and according to aspects of the systems and methods described herein, a microcontroller unit (not illustrated) is provided that is configured to control measurement of magnetic fields by the magnetometer(s) and compute a relative position and orientation of the electromagnet assembly and the magnetometer(s) in five degrees of freedom using at least two equations with two unknowns and coordinate transformation equations relating the coordinate frames of the electromagnet assembly and the magnetometer(s). The microcontroller unit may be further configured to control activation of the first and second electromagnets. The system may also include a secondary microcontroller unit configured to control activation of the first and second electromagnets. [0024] EM 1 and EM 2 are identical in some embodiments, but they can instead have different properties. In the equations that follow, EM 1 and EM 2 are assumed to be magnetic dipoles. This simplifies the equations, and is valid for distances much larger than the radii of the electromagnets. Since the magnetic fields of EM 1 and EM 2 are axisymmetric, they can be represented and analyzed on a 2D coordinate frame containing the common axis 6. [0025] Figure 2 shows a 2D representation of magnetic field lines 8 emanating from a magnetic dipole 9 at the origin of coordinate frame 10. Equations describing the magnitude and direction of the magnetic field vector of a magnetic dipole are available in the art. The magnitude of the magnetic field at a point P can be computed from equation (1) below, with reference to Figure 2. where: B = magnitude of the B-field at point P µ o = permeability of free space M = magnitude of the dipole moment θ = colatitude (or polar) angle of point P r = distance of point P from the origin The direction of the magnetic field vector at point P can be determined from equation (2) below. (2) where: α = angle between the radial direction (from dipole 9 to point P) and the magnetic field vector [0026] Figure 3 shows a 2D schematic representation of EMA 4 attached to 2D coordinate frame 11 with the z-axis collinear with axis 6 and the origin at the center of EM 1. Point P is at the center of MM 5, located at an arbitrary and/or movable location relative to coordinate frame 11. The following equations (3) through (6) are derived by applying equations (1) and (2) to the magnetic fields emanating from EM 1 and EM 2, measured at point P, where the subscripts 1 and 2 refer to EM 1 and EM 2, respectively. Combining equations 3 and 4 gives: In circumstances where EM 1 and EM 2 have identical properties with equal energizing currents, M 1 and M 2 cancel out and (7) simplifies to Alternatively, if EM 1 and EM 2 are not identical, a correction factor equal to the ratio M 1 / M 2 can be used. [0027] From Figure 3, it can be seen that Substituting (9) into (8) gives where: Vector magnitudes B 1 and B 2 can be determined from the orthogonal components of the magnetic fields measured by MM 5. [0028] Referring again to Figure 3, the following equations (12) and (13) are derived. Angle α d can be computed from the dot product of vectors and as shown in equation (14) below: The dot product of vectors and can be computed using the orthogonal components of vectors and measured by MM 5. [0029] Substituting equations (5), (6), and (13) into equation (12) gives Equations (11) and (15) can be rearranged into the following equations (16) and (17). [0030] Equations (16) and (17) can then be solved as a system of two non-linear equations with two unknowns ( θ 1 and θ 2 ). This can be performed, for example, by Newton’s Method, or by other methods known to one skilled in the art. The solution to equations (16) and (17) converge quickly and can be easily implemented in a computer program. Once θ 1 and θ 2 are solved, the other variables can be determined. The x and z coordinates of point P can be determined from θ 1 and r1 or θ 2 and r 2 . [0031] The above solution determines the location of MM 5 relative to EMA 4 in 2D. To determine 3D position and orientation, it is necessary to determine the orientation of coordinate frame 11 (x-z plane of Figure 3) relative to MM 5. This can be done using the directions of vectors . Figure 4 shows coordinate frame 12 which is attached to MM 5. The i, j and k axes are coincident with the measuring axes of MM 5. The origin 13 of coordinate frame 12 coincides with the center of MM 5 and point P from which the two vectors are measured. [0032] Since the magnetic fields of both EM 1 and EM 2 are axisymmetric along axis 6, vectors (measured at the same point) are always on the same plane and both are coplanar with axis 6. Since EM 1 and EM 2 are coaxial but spaced a distance apart, vectors will not be collinear except at points along axis 6. The directions of the two vectors can therefore be used to define the plane R containing coordinate frame 11 in Figure 4, except when point P is located along axis 6. In practice, errors increase as point P gets near axis 6. However, for many applications, tracking needs to be done only within a specific volume which can be sufficiently far from axis 6. The directions of vectors can be determined from the orthogonal components of the magnetic field measured by MM 5 for each vector. [0033] Using the solved values of the x and z coordinates of point P relative to coordinate frame 11 and the magnitudes of the orthogonal components of vectors and , measured from coordinate frame 12, transformation equations can be used to relate the position and orientation of coordinate frames 11 and 12 relative to each other. Different combinations of rotation and translation equations may be used depending on the preferred order of rotation and translation to be done. [0034] After the translation and rotation equations are applied, the i, j, and k coordinates of the origin of coordinate frame 11 relative to coordinate frame 12 can be determined. The orientation (roll and pitch) of axis 6 can also be determined. This provides a 5 DOF solution for the position and orientation of EMA 4 relative to MM 5. Since the magnetic field of EMA 4 is axisymmetric, it is not possible to determine the yaw of EMA 4 around axis 6. The magnitudes and directions of vectors are axisymmetric about axis 6 and will not change regardless of the azimuthal angle of MM 5 around axis 6. Thus, only 5 DOF can be determined. [0035] In another embodiment of the present invention, a third electromagnet is added to EMA 4 to provide data needed to determine position and orientation in 6 DOF. Figure 5 shows EMA 14 which is similar to EMA 4 but additionally includes a third electromagnet. EMA 14 has two coaxial electromagnets EM 15 and EM 16, spaced apart by a known distance along axis 17. A third electromagnet EM 3 is positioned along axis 17 at a known distance from EM 15, such as halfway between EM 15 and EM 16, for example. The axis 18 of EM 3 is oriented orthogonal to axis 17. Coordinate frame 19 is defined as having its origin O at the center of EM 3 with the z- axis collinear with axis 17, and the x-axis collinear with axis 18. Also shown in Figure 5 is MM 5 with coordinate frame 12 whose origin is coincident with point P with an azimuth angle φ relative to axis x. Coordinate frame 19 ′ is a 2D coordinate frame with its origin O ′ at the center of EM 15 and the z ′ -axis collinear with axis 17. The orientation of axis x ′ is such that it is coplanar with both point P and axis z ′ . [0036] EM 15 and EM 16 are identical in some embodiments but they can instead have different properties. EM 15, EM 16, and EM 3 can be activated by AC or DC techniques to isolate and measure their respective magnetic fields. The purpose of EM 3 is to provide information to determine the azimuthal angle φ of point P relative to coordinate frame 19. In this embodiment, coordinate frame 19, together with EMA 14, is fixed and coordinate frame 12, together with MM 5, is moving and tracked relative to coordinate frame 19. One advantage of this configuration for determining 6 DOF position and orientation is that MM5 can be very small, in the order of 1 mm, for example, so that it can be attached to the object to be tracked without being obtrusive. Another advantage of this configuration is that multiple magnetometers can be tracked simultaneously using the same magnetic fields from EM 15, EM16, and EM 3, and the same equations used for tracking MM5 applied to each magnetometer. Alternatively, MM5 and coordinate frame 12 can be fixed and coordinate frame 19, together with EMA 14, is moving and tracked relative to coordinate frame 12. [0037] Referring again to Figure 5, Vector is the magnetic field vector emanating from EM 3, at point P. Vector is the vector from origin O to point P. From Figure 5, equations (18) and (19) can be derived. (18) a = V 0 cos θ 3 (19) a = P x ′ cos φ where: V0 = magnitude of vector θ 3 = colatitude angle of point P relative to axis 18 P ′ = x′ coordinate of point P r ′ x elative to coordinate frame 19 φ = azimuthal angle of point P relative to the x-axis of coordinate frame 19 Combining equations (18) and (19) provides the following equation (20): Applying equation (2) to provides the following equation (21): where: α 3 = angle between vectors With some trigonometric manipulation, equation (21) can be transformed into equation (22). Substituting equation (22) into equation (20) provides the following equations (23) and (24): [ 0038] The value of cos ∝ 3 can be computed from the dot product of 0 and and the magnitudes of . The dot product of vectors can be computed from the orthogonal components of . The components of vector can be derived from the measurements of MM 5 while the components of can be derived from the x ′ and z ′ coordinates of point P relative to coordinate frame 19 ′ . The components can be transformed to a common coordinate frame by applying appropriate transformation equations to and/or before evaluating the dot product. The magnitudes of and , on the other hand, can be computed from their corresponding components relative to any coordinate frame. The azimuthal angle φ can now be computed from equation (24). Once the azimuthal angle is determined, the position and orientation of coordinate frame 12 relative to coordinate frame 19 can be determined in 6 DOF (x, y, and z coordinates, and pitch, roll, and yaw). [0039] In another embodiment for a 6 DOF system, two 5 DOF electromagnet assemblies are combined such that their respective common axes are perpendicular to each other. This configuration can be used to determine azimuthal orientation to provide a 6 DOF solution for position and orientation. [0040] The foregoing detailed description and examples have been given for clarity of understanding only. No unnecessary limitations are to be understood therefrom. It will be apparent to those skilled in the art that many changes can be made in the embodiments described without departing from the scope of the invention. Thus, the scope of the present invention should not be limited to the structures described herein.