Method for magnetically locating a kinematic chain

Abstract

The invention relates to a method for magnetically locating a kinematic chain, wherein the chain is made of N rigid chain links known in advance and N joints, where N > 1 as a natural number, a magnetic dipole field which rotates in three dimensions is generated, and the position of the first joint relative to the dipole center is fixed and known in advance. Furthermore, for each i = 1,..., N, at least one magnetic field sensor with a sensor detection device which is known in advance is arranged on the i-th chain link at a position which is known in advance relative to the i-th joint, and for i = 1,..., N-1, the position of the i+1-th joint relative to the i-th joint is known in advance. The invention additionally relates to the use of the method in order to magnetically locate a kinematic chain for an up-to-date tracking of the movement of an object connected to the chain.

Description

[0001] METHOD FOR MAGNETIC LOCATION OF A KINEMATIC CHAIN

[0002] The invention relates to a method for locating a kinematic chain by means of measurements of a time-varying magnetic field by magnetic field sensors arranged on the chain links.

[0003] The kinematic chain is a well-known concept in technical mechanics, particularly in transmission technology, for the abstract description of a group of rigid chain links movably connected at joints. A distinction is usually made between closed and open kinematic chains, with the former playing a special role in transmissions because they allow, among other things, the redirection of movements (e.g., linear -> rotary). Open chains, on the other hand, are often used as models for human or animal skeletons and can therefore also serve as a starting point for the construction of artificial biological body parts, such as robot grippers.

[0004] Another important application of kinematic chains can be seen in the provision of a human-machine interface, for example, a so-called "data glove." Such a glove is designed to continuously record the wearer's finger movements and process them electronically. The processing result can then be used as a control command for machines, with the complete, time-synchronized imitation of the user's movements by an artificial hand representing a possible application. Other possibilities include issuing machine commands while restricting user mobility, for example, in fighter pilots.

[0005] A kinematic chain is suitable for tracking the movement of an object connected to the chain, especially a human finger, if the relative coordinates of all chain links and joints with respect to the origin of a coordinate system connected to the entire chain can be quickly determined. In many cases, a pure translation of the entire chain does not need to be recorded, but only the change in the relative positions of the chain links to each other. However, especially for the example of the data glove for recording the movements of human fingers, it is expedient to locate several kinematic chains – one for each finger – simultaneously and relative to the same origin.

[0006] Further applications of kinematic chains include motion capture, in which the natural movements of a biological actor are recorded and used to computationally model the movement of virtual avatars. Classic motion capture relies on camera recording of the actor, who is often equipped with special clothing and visual markers on limbs and joints. However, if a persistent line of sight of the camera(s) to the actor's movements cannot be guaranteed, the kinematic chain to be recorded must be able to detect and report its changing motion state using implemented sensors. One possible method of choice for this is magnetic field sensors.

[0007] The work of Fahn and Sun, "Development of a Fingertip Glove Equipped with Magnetic Tracking Sensors," Sensors 2010, 10, 1119-1140; doi:10.3390 / s100201119, and of Santoni et al., "MagIK: A Hand-Tracking Magnetic Positioning System Based on a Kinematic Model of the Hand," IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 70, 2021, point to specific developments of data gloves that can detect finger movements or hand gestures by measuring magnetic fields. Magnetic tracking is seen as particularly advantageous in medical applications, as living patients neither shield nor interfere with the magnetic fields, thus ensuring that the data glove can always be located even during a medical procedure. However, the effort required for data collection and processing is quite considerable and is still prohibitive for routine use - as a medical instrument or as a therapeutic aid for stroke patients.

[0008] Also worth mentioning are the patents CN 112146657 B, CN 112254732 B and EP 0 576 187 B1, which are all dedicated to a magnetic locating task and which have in common that they use a rotating magnetic dipole field which is detected and evaluated by magnetic field sensors.

[0009] The invention aims to propose a method by which the links of a kinematic chain are located magnetically in a time-keeping manner, while at the same time significantly reducing the measuring and computing effort.

[0010] The problem is solved by a method for the magnetic location of a kinematic chain, wherein the chain is formed from N rigid and previously known chain links and from N joints with N > 1 as a natural number, wherein a magnetic dipole field rotating in three dimensions is generated and wherein the position of the first joint relative to the dipole center is fixed and previously known, wherein for each i = 1, ... , N on the i-th chain link at least one magnetic field sensor with a previously known sensor detection direction is arranged at a previously known position relative to the i-th joint and wherein for i = 1, ... , N-1 the position of the i+1-th joint relative to the i-th joint is previously known, characterized by the steps: a. setting i = 1 and predetermining the length of a time window; b. measuring the generated magnetic field with the at least one magnetic field sensor on the i-th chain link as a function of time; c.Determining a selection of zero-crossing times of the measured sensor signal within the time window of predetermined length; d. Determining zero-crossing orientations of the rotating magnetic dipole field for the selection of determined zero-crossing times; e. Calculating the orientation leading to the extremal sensor signal. m of the dipole field as a perpendicular direction to at least two linearly independent zero-crossing orientations; f. Calculate the location r = re r of the magnetic field sensor on the i-th chain link relative to the dipole center and the sensor detection direction e sby iterating assumptions about these quantities, which result from an optimality criterion for extremal sensor signals and from the previously known position and sensor detection direction relative to the i-th joint, until self-consistent convergence is achieved; g. calculating the position of the i+1-th joint relative to the dipole center; h. repeating steps b. to g. replacing i by i+1 until i takes on the value N-1; i. performing steps b. to f. for i=N; j. summarizing all calculated positions relative to the dipole center as a spatial representation of the kinematic chain during the time window of predetermined length; k. repeating steps a. to j. for further time windows.

[0011] The subclaims are directed to advantageous embodiments of the method and to uses.

[0012] Simple magnetic field sensors either measure only one component of the magnetic field vector (e.g., a flat coil) or they display a significant measurement signal for only one field component (e.g., magnetoelectric bending beam sensors). More complex magnetic field sensors for complete field measurements can be assembled from simple sensors, but for the purposes of the invention, simple sensors with a known sensor detection direction are sufficient and even advantageous.

[0013] For the kinematic chain to be located here, a schematic structure as shown in Fig. 1 is provided:

[0014] The beginning of the chain—and simultaneously the origin of the coordinate system in which all chain links and joints are located—is a magnetic field generator that generates a magnetic dipole field rotating in three dimensions. The beginning of the chain, or origin, is also referred to below as the dipole center. A first joint G1 has a fixed, known position r. G1 relative to the dipole center. The first joint G1 is followed by the first - movable - chain link, whose continuously changing position is to be recorded in time. The chain link itself is rigid and carries its own coordinate system, in which the first joint G1, for example, is located at the origin and at least one magnetic field sensor S1 and the second joint G2 are located at pre-known positions r'. sl , r' G2 are arranged. Furthermore, the sensor detection direction e slfreely selectable and therefore preferably arranged pointing from the first to the second joint. The further structure of the kinematic chain from the second joint G2 onwards is designed analogously to the first chain link, with all coordinates of the magnetic field sensors and joints being shown in the respective chain link coordinates, exemplified by r" S2 and e S2 , are known in advance. The Nth chain link extends from the Nth joint and carries only one magnetic field sensor. For simplicity, all chain links are modeled as linear rods.

[0015] The task of locating the chain is to be understood as determining the locations of the joints or magnetic field sensors relative to the dipole center during a time window of predetermined length. The time window must be long enough to capture a large number of magnetic field measurements and perform the processing according to the invention, yet short enough so that the position of the chain cannot change significantly during this time and the location is valid for the time window. Data processing must be carried out accordingly quickly.

[0016] To achieve this, the invention combines a criterion derived from magnetostatics with the constraints of the motion of the kinematic chain and utilizes this in a very rapidly converging iteration process. For better understanding, the criterion used is not only named but also formally justified below. To avoid misunderstandings, it should be clarified that the position vector r = re r always refers to the dipole center.

[0017] The field of a magnetic dipole moment m = me m arranged at the origin is of the general form with bold letters for vectors and with the dot as the common symbol for the scalar product. A magnetic field sensor at location r = re r designed to measure a magnetic field component along a sensor detection direction e s detects the projection of the magnetic field in this direction.

[0018] B sensor (m, r, e s ) = B dip (m, r) ■ e s (2)

[0019] The question of interest here is whether the directions of the involved vectors can be directly inferred from the measurable sensor signal, especially its zeros and extrema. The distance-dependent scalar prefactor will be ignored in the following.

[0020] For the special case that e r and e s are linearly dependent, one can easily see from the square brackets that B Sensor becomes extremal if and only if e m and e r are linearly dependent. However, if e r and e s linearly independent, then they span a plane – hereinafter referred to as the measuring plane. Components of the dipole vector m that are perpendicular to the measuring plane contribute nothing to the measurable magnetic field at the sensor. Therefore, the directional dependence of the field is represented by a vector e m, which lies in the measurement plane, is fully described. The problem can be treated two-dimensionally in the measurement plane.

[0021] Fig. 2 a) sketches the magnetic dipole at the origin and the location of the sensor at a point on the x-axis, ie e r is chosen arbitrarily here. From Eq. (3) and the angles in Fig. 2 a)

[0022] B S ensor ~ 3 COS <p COS a — COS(< > — «) (4) or alternatively by applying the addition theorem cos(a ± b) = cos a cos b + sin a sin b

[0023] The angles a and (p are interchangeable, and if one of these angles is set to a fixed value, then the measurable magnetic field results as a cosine function of the other angle with 2K periodicity and exactly two zeros at a distance K. This means that for any fixed choice of one of the vectors e m or e s an axis exists in the measuring plane which corresponds to B Sensor= 0 when the other, rotating vector crosses this axis. Such a zero axis exists in every measurement plane, regardless of its orientation in 3D space. At the same time, the axis perpendicular to the measurement plane is also always a second, linearly independent zero axis, as discussed previously. Consequently, a zero plane always exists in 3D space.

[0024] To discuss the extrema of the measurable magnetic field, the direction of e m arbitrarily chosen perpendicular to the x-axis. The position vector of the magnetic field sensor r is now variable and encloses the angle ß with the x-axis. The angles a and (p) are shown in Fig. 1 b) and were taken from Fig. 2 a). With the substitutions ß = - a and xp = ß + <p lässt sich Gl. (5) umschreiben zu

[0025] ^sensor ~ cosQS - p smß + sin(2 - i ) (7)

[0026] In order to determine the sensor detection direction for the magnetic field sensor when guiding the sensor around the fixed dipole e m around in the measuring plane an extremal measuring signal is detected, a differentiation is made according to the angle ß:

[0027] The derivative disappears noticeably and B Sensor becomes extremal if and only if 2ß - and n is an odd integer. In the explicit form Both angles should be restricted to the interval [0, 2n], so that only n = ±1 is possible. The second derivative of Eq. (8) is negative for n = 1 and positive for n = -1, ie, one solution describes the maxima and the other the minima of the sensor signal.

[0028] For a graphical illustration of the result for n = 1, see Fig. 3. The direction of m is shown in the center of the figure, and the sensor detection directions e s, which lead to maximum measurement signals on the sensor at locations r around the origin of the measurement plane. This discovered relative arrangement of the vectors to each other is referred to below as the "optimality criterion for extremal sensor signals."

[0029] It may be noticeable that this arrangement of the e s in Fig. 3 around the fixed vector m in the center corresponds to that arrangement of permanent magnet dipoles in a Halbach ring, which generate a homogeneous magnetic field in the direction of m in the interior of the ring.

[0030] As a conclusion of the previous considerations, it can be stated that the knowledge of the vector m is sufficient to determine the bearing of the location of the magnetic field sensor e r and its orientation e sto be determined exactly when the sensor signal reaches an extremum - e.g., a maximum. Advantageously, this is always the case exactly between two zero crossings at a constant rotation frequency of the dipole moment. During the zero crossings, however, the dipole moment points along the aforementioned zero axis in the measuring plane, and by rotating the measuring plane around one of its axes, any number of zero axes in the aforementioned zero plane can be crossed. If two linearly independent zero axes are selected and their directions in space are determined, the vector e m, which leads to extremal sensor values, are perpendicular to these and can be calculated as their cross product. According to the invention, in order to locate the i-th chain link, the zeros of the sensor signal of the at least one magnetic field sensor on the i-th chain link are therefore first detected, which lie within the time window of predetermined length, wherein actually only a selection of times of the zeros is taken into account. For each chain link, a finite sequence of zeros is selected, wherein the sequences are arranged one after the other in the sequence of the indexing of the chain links. The first step is to determine the respective position of the vector m at the times of the zeros.

[0031] In a preferred embodiment of the method, the rotating magnetic dipole field is electrically generated by three generating coils aligned perpendicular to each other. Each of the three coils can be independently supplied with alternating current of constant amplitude and frequency, so that a dipole field rotating in 3D space is readily established. Preferably, two of the frequencies are set to be equal and greater than 1 kHz, so that the dipole rotates in a first plane at a frequency greater than 1 kHz. As already mentioned, this generates at least 1000 zeros in the sensor signals per second. Advantageously, it is then possible to determine the zero-crossing orientations of the magnetic dipole field based on measurements of the currents through the generating coils at the selected times of the zero crossings of the sensor signal.

[0032] It is an advantageous embodiment of the invention that the rotating magnetic dipole field rotates in at least a second plane at a frequency that is at least two orders of magnitude lower than the frequency in the first plane. This can be easily achieved by energizing the third coil with an alternating current of correspondingly reduced frequency. The first plane with the rapid (> 1 kHz) rotation of the dipole then rotates about one of its axes - or in the second plane - at the frequency of the third coil. As a result of the rotation of the first plane in the second plane, the orientation of the magnetic dipole assumes any orientation in 3D space over time. However, the rotation is deliberately slowed down so that a short sequence of zeros of a sensor signal can be detected for which the first plane is approximately at rest.For a stationary first plane, the zero-crossing orientations of the dipole field all lie along the same zero axis in the measurement plane, so that the coil current readings are averaged at the times of the zero crossings, e.g., by summing to suppress noise effects.

[0033] It is also advisable to process the sensor signals of the magnetic field sensors with a bandpass filter that is tuned to the effective rotation frequency of the dipole field in order to capture the signals with as little noise as possible.

[0034] If the first plane is now rotated in the second plane, the now rotated zero axis can be determined in the same way using another short sequence of zeros. As already mentioned, the zero axes all lie in a common zero plane, the position of which in turn depends on the direction e. mwhich leads to extremal sensor signals on the at least one magnetic field sensor of the i-th chain link. From two linearly independent zero axes, e m can now be calculated by forming a vector product.

[0035] Is e m determined by measurements, then the location r = re r and the sensor detection direction e s can be calculated very quickly using a simple iteration. This is explained using the example of the first link in the chain:

[0036] If one initially assumes any sensor detection direction as given, e.g., through random initialization, then the structure of the kinematic chain with a known location of the first joint and a previously known location of the magnetic field sensor relative to the first joint immediately yields the location of the magnetic field sensor relative to the dipole center through simple vector addition, which, in all probability, is initially incorrect. The optimality criterion for extremal sensor signals discussed above, which must apply to the true location and true sensor orientation, assigns a new sensor detection direction to the initially determined location. This results in a new calculation of the position vector through vector addition, which is again compared with the optimality criterion, and so on.After a few iteration steps, the new numerical data deviate from those of the previous iteration step by less than a predetermined acceptance threshold, and convergence is achieved.

[0037] It should be emphasized that the optimality criterion is based on fundamental magnetostatics and therefore guarantees the existence and uniqueness of a convergence solution.

[0038] With the convergence of the data for r = re r and e s consistent with the measured e mand the chain geometry, the location of the at least one magnetic field sensor on the first chain link is completed. As a direct consequence of the chain arrangement, which assigns the second joint a previously known position relative to the first joint and the first chain link a now determined orientation, the location of the second joint relative to the dipole center is obtained. The location method according to the invention can be repeated for the second chain link and subsequently all subsequent links. For each of these repetitions, a sequence of times of the zero points of the sensor signal of at least one magnetic field sensor on each chain link is required. Each of these sequences comprises a plurality of short sequences, wherein each short sequence serves to approximately determine a zero point axis - assumed to be briefly stationary - from current measurement data of the generator coils.The majority of short sequences serve to capture a plurality of linearly independent zero axes so that a perpendicular direction to the zero plane can be calculated. This perpendicular direction defines the direction e. m fixed for the sensor data of the magnetic field sensor on the i-th chain link and thus also the input to the iteration for finding the location and orientation of this sensor.

[0039] The inventive iteration of the sensor detection direction and the position of the at least one magnetic field sensor on the i-th chain link for each i = 1, N comprises the steps: a. Setting an initial estimated value for the sensor detection direction relative to the dipole center; b. Calculating a position of the at least one magnetic field sensor on the i-th chain link relative to the dipole center that is consistent with the estimated value from the predetermined position of the i-th joint relative to the dipole center and the previously known position and sensor detection direction of the magnetic field sensor relative to the i-th joint; c. Inserting the calculated position into an optimality criterion for extremal sensor values ​​and reading off a consistent sensor detection direction; d. If the deviation of the consistent sensor detection direction from the estimated value is greater than a predetermined acceptance threshold, then inserting the consistent sensor detection direction as a new estimated value and e.Repeat steps b to d until self-consistent convergence.

[0040] With the completion of the localization of the last chain link, the localization of the kinematic chain as a whole is completed for the time window of predetermined length, which contains all sequences and short sequences of times of zero crossings of the magnetic field signals.

[0041] The length of the time window can be freely predetermined, but it cannot be chosen arbitrarily short, as a number of zero crossings of the sensor signals must be analyzed for each chain link, as it cannot be assumed that all sensor detection directions lie in the same plane. The joints discussed so far are provided with two degrees of freedom, but a third degree of freedom, namely the rotation of a chain link around its own axis, can certainly also be handled by providing more than one magnetic field sensor per chain link, for example, one on each side of the chain link. This would also increase the required length of the time window.

[0042] On the other hand, the time window cannot be chosen too long, because the chain must be considered quasi-stationary during the time window in order to consecutively locate all chain links. The actual object movement, which is to be captured by positioning the chain on the object, must therefore be slow compared to the length of the time window.

[0043] Time windows with lengths in the order of milliseconds or less are achievable with the invention. The required iteration to locate the individual chain links does not place significant computational demands on today's commercial computers, as initial analyses show.

[0044] Convergence is achieved in a maximum of 15 iteration steps with a processor time of the order of microseconds per chain link.

[0045] The user of the invention will need to select a rotation frequency of the dipole field appropriate for their application in order to dimension suitable time windows. Further considerations include the magnetic field strength to be established, taking into account the maximum possible chain length, and the technology of the magnetic field sensors. Magnetoelectric cantilever sensors are particularly interesting here, as they can be resonantly excited in their natural oscillation modes, which makes these sensors very sensitive and reduces the field strength required for significant output voltage signals. It can therefore be advantageous to tune the rotation frequency of the dipole field to the mechanical resonant frequency of the cantilever oscillation.

[0046] Finally, it should be emphasized that the invention also offers the possibility of locating multiple kinematic chains simultaneously and relative to the same dipole center of the rotating magnetic dipole field. This is easily understood because the first joint of a chain can be set to any fixed position. In this respect, different chains can also be located simultaneously, because the magnetic field measurement data and the subsequent calculation steps can be determined and executed separately for each chain in parallel processing. This provides a powerful basis for implementation in the "data glove" mentioned above.

Claims

A N S P R Ü C H E 1. A method for the magnetic location of a kinematic chain, wherein the chain is formed from N rigid and previously known chain links and from N joints with N > 1 as a natural number, wherein a magnetic dipole field rotating in three dimensions is generated and wherein the position of the first joint relative to the dipole center is fixed and previously known, wherein for each i = 1, ... , N on the i-th chain link at least one magnetic field sensor with a previously known sensor detection direction is arranged at a previously known position relative to the i-th joint and wherein for i = 1, ... , N-1 the position of the i+1-th joint relative to the i-th joint is previously known, characterized by the steps: a. setting i = 1 and predetermining the length of a time window; b. measuring the generated magnetic field with the at least one magnetic field sensor on the i-th chain link as a function of time; c.Determining a selection of zero-crossing times of the measured sensor signal within the time window of predetermined length; d. Determining zero-crossing orientations of the rotating magnetic dipole field for the selection of determined zero-crossing times; e. Calculating the orientation leading to the extremal sensor signal. m of the dipole field as a perpendicular direction to at least two linearly independent zero-crossing orientations; f. Calculate the location r = re r of the magnetic field sensor on the i-th chain link relative to the dipole center and the sensor detection direction e sby iterating assumptions about these quantities, which result from an optimality criterion for extremal sensor signals and from the previously known position and sensor detection direction relative to the i-th joint, until self-consistent convergence is achieved; g. calculating the position of the i+1-th joint relative to the dipole center; h. repeating steps b. to g. replacing i by i+1 until i takes on the value N-1; i. performing steps b. to f. for i=N; j. summarizing all calculated positions relative to the dipole center as a spatial representation of the kinematic chain during the time window of predetermined length; k. repeating steps a. to j. for further time windows.

2. Method according to claim 1, characterized in that the rotating magnetic dipole field rotates in at least a first plane at a frequency greater than 1 KHz.

3. Method according to claim 2, characterized in that the rotating magnetic dipole field rotates in at least a second plane at a frequency which is at least two orders of magnitude lower than the frequency in the first plane.

4. Method according to one of the preceding claims, characterized in that three generator coils arranged concentrically and perpendicular to one another are supplied with alternating current in order to generate the rotating dipole field.

5. The method according to claim 4, characterized in that the zero-crossing orientations of the magnetic dipole field are determined based on measurements of the currents through the generator coils at the selected times of the zero crossings of the sensor signal.

6. Method according to one of the preceding claims, characterized in that the iteration of the sensor detection direction and the position of the at least one magnetic field sensor on the i-th chain link for each i = 1, ..., N comprises the following steps: a. Setting an initial estimated value for the sensor detection direction relative to the dipole center; b. Calculating a position of the at least one magnetic field sensor on the i-th chain link relative to the dipole center that is consistent with the estimated value from the predetermined position of the i-th joint relative to the dipole center and the previously known position and sensor detection direction of the magnetic field sensor relative to the i-th joint; c. Inserting the calculated position into an optimality criterion for extremal sensor values and reading off a consistent sensor detection direction; d.If the deviation of the consistent sensor detection direction from the estimate is greater than a predetermined acceptance threshold, then insert the consistent sensor detection direction as the new estimate and e. repeat steps b. to d. until self-consistent convergence.

7. Method according to one of the preceding claims, characterized by the use of magnetoelectric bending beam sensors as magnetic field sensors, wherein the rotation frequency of the dipole field is tuned to the mechanical resonance frequency of the bending beam oscillation.

8. Method according to one of the preceding claims, characterized in that a plurality of kinematic chains are located simultaneously and relative to the same dipole center of the rotating magnetic dipole field.

9. Use of the method according to one of the preceding claims for magnetically locating a kinematic chain for temporally tracking the movement of an object connected to the chain.

10. Use according to claim 9 for temporally tracking the finger movement of a user.

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