DE102023119167B3 - Method for magnetic location of a kinematic chain - Google Patents

Abstract

The invention relates to a method for magnetically locating 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 furthermore 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. Furthermore, the invention relates to a use of the method for magnetically locating a kinematic chain for temporally tracking the movement of an object connected to the chain.

Description

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.

The kinematic chain is a well-known concept in technical mechanics, particularly gear technology, for the abstract description of a group of rigid chain links that are movably connected to one another at joint points. A distinction is usually made between closed and open kinematic chains, with the former playing a special role in gears because they allow the redirection of movements (e.g. linear -> rotating). Open chains, on the other hand, are often used as models for human or animal skeletons and can therefore also form the starting point for the construction of artificial biological body parts, e.g. robot grippers.

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 finger movements of its wearer and process them electronically. The processing result can then be used as a control command for machines, whereby the complete, time-keeping imitation of the user's movement by an artificial hand can be a possible application. Other possibilities lie in issuing machine commands while restricting the user's mobility, for example in the case of fighter pilots.

A kinematic chain is suitable for tracking the movement of an object connected to the chain, in particular a human finger, if the relative coordinates of all chain links and joints in relation to the origin of a coordinate system connected to the entire chain can be determined quickly. In many cases, a pure translation of the entire chain does not have to be recorded, but only the change in the relative positions of the chain links to one another. However, especially for the example of the data glove for recording the movements of human fingers, it is useful to locate a plurality of kinematic chains - one for each finger - simultaneously and relative to the same origin.

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

The works of Fahn and Sun, “Development of a Fingertip Glove Equipped with Magnetic Tracking Sensors”, Sensors 2010, 10, 1119-1140; doi:10.3390/s100201119 and from 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 refer to specific developments of data gloves that can detect finger movements or hand gestures by measuring magnetic fields. One advantage of magnetic tracking is seen in medical applications, as living patients neither shield nor interfere with the magnetic fields, and thus the data glove can always be located even during a medical procedure. However, the effort required to collect and process measurement data is quite considerable and is still prohibitive for routine use - as a doctor's instrument or as a therapy aid for stroke patients.

Also worth mentioning are the patent documents CN 1 12 146 657 B , CN 1 12 254 732 B and EP 0 576 187 B1 , all of which are dedicated to a magnetic location task and which have the common feature that they use a rotating magnetic dipole field that is detected and evaluated by magnetic field sensors.

The invention has the object of proposing a method with which the location of the links of a kinematic chain is carried out magnetically in a temporally step-by-step manner, while at the same time significantly reducing the measuring and computing effort.

1. a. Setzen von i=1 und Vorbestimmen der Länge eines Zeitfensters;
2. b. Messen des erzeugten Magnetfeldes mit dem wenigstens einen Magnetfeldsensor auf dem i-ten Kettenglied als Funktion der Zeit;
3. c. Ermitteln einer Auswahl von Zeitpunkten der Nulldurchgänge des gemessenen Sensorsignals innerhalb des Zeitfensters mit vorbestimmter Länge;
4. d. Bestimmen von Nulldurchgangs-Ausrichtungen des rotierenden magnetischen Dipolfeldes für die Auswahl von ermittelten Zeitpunkten der Nulldurchgänge;
5. e. Berechnen der zu extremalem Sensorsignal führenden Ausrichtung e_m des Dipolfeldes als Lotrichtung zu wenigstens zwei linear unabhängigen N ulldurchgangs-Ausrichtungen;
6. f. Berechnen des Ortes r = re_r des Magnetfeldsensors auf dem i-ten Kettenglied relativ zum Dipolzentrum und der Sensordetektionsrichtung e_s durch Iterieren von Annahmen über diese Größen, die sich aus einem Optimalitätskriterium für extremale Sensorsignale und aus der vorbekannten Position und Sensordetektionsrichtung relativ zum i-ten Gelenk bis zur selbstkonsistenten Konvergenz ergeben;
7. g. Berechnen der Position des i+1-ten Gelenks relativ zum Dipolzentrum;
8. h. Wiederholen der Schritte b. bis g. unter Ersetzen von i durch i+1 bis i den Wert N-1 annimmt;
9. i. Ausführen der Schritte b. bis f. für i=N;
10. j. Zusammenfassen aller berechneten Positionen relativ zum Dipolzentrum als Ortsdarstellung der kinematischen Kette während des Zeitfensters mit vorbestimmter Länge;
11. k. Wiederholen der Schritte a. bis j. für weitere Zeitfenster.

The object is achieved by a method for magnetically locating 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 furthermore 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:

1. a. Setting i=1 and predetermining the length of a time window;
2. 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;
3. c. Determining a selection of times of the zero crossings of the measured sensor signal within the time window of predetermined length;
4. d. determining zero-crossing orientations of the rotating magnetic dipole field for the selection of determined zero-crossing times;
5. e. Calculating the orientation e _m of the dipole field leading to the extremal sensor signal as a perpendicular direction to at least two linearly independent zero-crossing orientations;
6. f. Calculating 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 _s by iterating assumptions about these quantities resulting 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;
7. g. Calculate the position of the i+1-th joint relative to the dipole center;
8. h. repeating steps b. to g. replacing i by i+1 until i reaches the value N-1;
9. i. Perform steps b. to f. for i=N;
10. j. Summarising all calculated positions relative to the dipole centre as a spatial representation of the kinematic chain during the time window of predetermined length;
11. k. Repeat steps a. to j. for additional time slots.

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

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

• Den Anfang der Kette - und zugleich den Ursprung des Koordinatensystems, in dem alle Kettenglieder und Gelenke zu orten sind - bildet ein Magnetfelderzeuger, der ein in drei Dimensionen rotierendes magnetisches Dipolfeld generiert. Der Kettenanfang bzw. Ursprung wird im Folgenden auch als das Dipolzentrum bezeichnet. Ein erstes Gelenk G1 besitzt eine feste, vorbekannte Position r_G1 relativ zum Dipolzentrum. Dem ersten Gelenk G1 schließt sich das erste - bewegliche - Kettenglied an, dessen fortlaufend veränderliche Lage zeitlich Schritt haltend erfasst werden soll. Das Kettenglied selbst ist starr und trägt ein eigenes Koordinatensystem, in dem das erste Gelenk G1 beispielsweise im Ursprung und wenigstens ein Magnetfeldsensor S1 sowie das zweite Gelenk G2 an vorbekannten Positionen r'_S1, r'_G2 angeordnet sind. Überdies ist die Sensordetektionsrichtung e_S1 frei wählbar und daher vorzugsweise vom ersten auf das zweite Gelenk weisend eingerichtet. Der weitere Aufbau der kinematischen Kette ab dem zweiten Gelenk G2 ist jeweils in Analogie zum ersten Kettenglied ausgestaltet, wobei alle Koordinaten der Magnetfeldsensoren und Gelenke in den jeweiligen Kettenglied-Koordinaten, gezeigt sind exemplarisch r''_S2 und e_S2, vorbekannt sind. Das N-te Kettenglied geht vom N-ten Gelenk aus und trägt nur noch einen Magnetfeldsensor. Alle Kettenglieder sind zur Vereinfachung als lineare Stäbe modelliert.

For the kinematic chain to be located here, a schematic structure as in 1 intended:

• The beginning of the chain - and at the same time the origin of the coordinate system in which all chain links and joints are to be located - is formed by a magnetic field generator which generates a magnetic dipole field rotating in three dimensions. The beginning or origin of the chain 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, the continuously changing position of which is to be recorded in step with time. The chain link itself is rigid and has its own coordinate system in which the first joint G1 is arranged, for example, at the origin and at least one magnetic field sensor S1 and the second joint G2 are arranged at known positions r' _S1 , r' _G2 . In addition, the sensor detection direction e _S1 is freely selectable and is therefore preferably set up to point from the first to the second joint. The further structure of the kinematic chain from the second joint G2 is designed in analogy to the first chain link, whereby all coordinates of the magnetic field sensors and joints in the respective chain link coordinates, shown as examples r'' _S2 and e _S2 , are known in advance. The Nth chain link starts from the Nth joint and only carries one magnetic field sensor. For simplicity, all chain links are modeled as linear rods.

The task of locating the chain is to be understood as determining the locations of the joints or the magnetic field sensors in relation to the dipole center during a time window of predetermined length. The time window must be long enough to record a large number of magnetic field measurements and to be able to carry out the processing according to the invention, and at the same time short enough so that the position of the chain cannot change significantly during this time and the location is valid for the time window. The data processing must be carried out accordingly quickly.

In order to achieve this, the invention combines a criterion derived from magnetostatics with the constraints of the movement of the kinematic chain and uses it in a very fast converging iteration process. For better understanding, the criterion used is not only named below, but also formally justified, whereby it should be made clear to avoid misunderstandings that the position vector r = re _r always refers to the dipole center.

mit fett gedruckten Buchstaben für Vektoren und mit dem Punkt als gängiger Kennzeichnung des Skalarproduktes. Ein Magnetfeldsensor am Ort r = r e_r ausgebildet zur Messung einer Magnetfeldkomponente entlang einer Sensordetektionsrichtung e_s detektiert die Projektion des Magnetfeldes auf diese Richtung. $$B_{Sensor}\left(m,r,e_s\right)=B_{dip}\left(m,r\right)\cdot e_s$$

$$B_{Sensor}\left(m,r,e_s\right)=\frac{m^2}{2\pi r^3}\left[3\left(e_r\cdot e_s\right)\left(e_m\cdot e_r\right)-e_m\cdot e_s\right]$$

The field of a magnetic dipole moment m = me _m located at the origin is of the general form $$B_{dip}\left(m,r\right)=\frac{1}{4\pi r^2}\frac{3r\left(m\cdot r\right)-m{r}^2}{r^3}$$

with bold letters for vectors and with the dot as the common designation of the scalar product. A magnetic field sensor at the 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. $$B_{SensOr}\left(m,r,e_s\right)=B_{dip}\left(m,r\right)\cdot e_s$$

$$B_{SensOr}\left(m,r,e_s\right)=\frac{m^2}{2\pi r^3}\left[3\left(e_r\cdot e_s\right)\left(e_m\cdot e_r\right)-e_m\cdot e_s\right]$$

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

For the special case that e _r and e _s are linearly dependent, it is easy to see from the square brackets that B _sensor becomes extremal if and only if e _m and e _r are also linearly dependent. If, however, e _r and e _s are linearly independent, then they span a plane - referred to as the measuring plane. Components of the dipole vector m that are perpendicular to the measuring plane do not contribute anything to the measurable magnetic field at the sensor. In this respect, the directional dependence of the field is completely described by a vector e _m that lies in the measuring plane. The problem can be treated two-dimensionally in the measuring plane.

oder alternativ durch Anwenden des Additionstheorems cos(a ± b) = cos α cos ά ∓ sin a sin b $$B_{Sensor}~\text{cos}\phi \text{cos}\alpha +\text{cos}\left(\phi +\alpha \right)$$

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 equation (3) with the angles from 2 a) $$B_{SensOr}~3\text{cos}\phi \text{cos}\alpha -\text{cos}\left(\phi -\alpha \right)$$

or alternatively by applying the addition theorem cos(a ± b) = cos α cos ά ∓ sin a sin b $$B_{SensOr}~\text{cos}\phi \text{cos}\alpha +\text{cos}\left(\phi +\alpha \right)$$

The angles α and φ are interchangeable, and if one of these angles is set to a fixed value, then the measurable magnetic field is a cosine function of the other angle with 2π periodicity and exactly two zeros at a distance of π. This means that for any fixed choice of one of the vectors e _m or e _s , an axis exists in the measurement plane that leads 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 previously discussed. Consequently, there is always a zero plane in 3D space.

und ψ = β + φ lässt sich GI. (5) umschreiben zu $$B_{Sensor}~\text{cos}\left(\psi -\beta \right)\text{cos}\left(\frac{\pi }{2}-\beta \right)+\text{cos}\left(\frac{\pi }{2}+\psi -2\beta \right)$$

$$B_{Sensor}~\text{cos}\left(\beta -\psi \right)\text{sin}\beta +\text{sin}\left(2\beta -\psi \right)$$

For a discussion of the extrema of the measurable magnetic field, see 2 B) the direction of e _m is arbitrarily chosen perpendicular to the x-axis. The position vector of the magnetic field sensor r is now variable and includes the angle β with the x-axis. The angles α and φ are in 1 b) presented and from 2 a) With the substitutions $\beta =\frac{\pi }{2}-\alpha$

and ψ = β + φ, equation (5) can be rewritten as $$B_{SensOr}~\text{cos}\left(\psi -\beta \right)\text{cos}\left(\frac{\pi }{2}-\beta \right)+\text{cos}\left(\frac{\pi }{2}+\psi -2\beta \right)$$

$$B_{SensOr}~\text{cos}\left(\beta -\psi \right)\text{sin}\beta +\text{sin}\left(2\beta -\psi \right)$$

In order to determine for which sensor detection direction the magnetic field sensor detects an extremal measurement signal when guiding the sensor around the fixed dipole e _m in the measuring plane, a differentiation is made according to the angle β: $$\frac{d{B}_{SensOr}}{d\beta }~-\text{sin}\left(\beta -\psi \right)\text{sin}\beta +\text{cos}\left(\beta -\psi \right)\text{cos}\beta +2\text{cos}\left(2\beta -\psi \right)=3\text{cos}\left(2\beta -\psi \right)$$

und n eine ungerade ganze Zahl ist. In der expliziten Form $$\beta =\frac{\psi }{2}+n\frac{\pi }{4}$$

sollen beide Winkel auf das Intervall [0,2π] beschränkt bleiben, so dass nur n = ±1 in Frage kommen. Die zweite Ableitung von GI. (8) wird negativ für n = 1 und positiv für n = -1, d.h. die eine Lösung beschreibt die Maxima und die andere die Minima des Sensorsignals.The derivative disappears and B _sensor becomes extremal exactly when $2\beta -\psi =n\frac{\pi }{2}$

and n is an odd integer. In the explicit form $$\beta =\frac{\psi }{2}+\mathrm{<figure-callout\; id="4"\; label="n\; \pi "\; filenames="DE102023119167B3\_0013.png"\; state="\{\{state\}\}">n</figure-callout>}\frac{\pi }{}\frac{}{4}$$

both angles should be limited to the interval [0,2π], so that only n = ±1 comes into consideration. The second derivative of equation (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.

To illustrate the result for n = 1, see 3 The direction of m can be seen in the center of the figure, and the sensor detection directions e _S , which lead to maximum measurement signals on the sensor, are each at the 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".

It may be noticeable that this arrangement of the e _s in 3 around the fixed vector m in the center corresponds exactly 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.

As a conclusion from the previous considerations, it can be stated that 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 _s exactly when the sensor signal assumes an extremum - e.g. a maximum. Advantageously, with a constant rotation frequency of the dipole moment this is always the case exactly between two zero crossings. During the zero crossings the dipole moment points straight along the aforementioned zero axis in the measuring plane, and by rotating the measuring plane about 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, must be perpendicular to them 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 first detected, which lie within the time window with a predetermined length, whereby only a selection of times of the zeros is actually taken into account. For each chain link, a finite sequence of zeros is selected, whereby 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.

In a preferred embodiment of the method, the rotating magnetic dipole field is generated electrically by means of three generator coils aligned perpendicular to each other. Each of the three coils can be independently fed with alternating current of constant amplitude and frequency, so that a dipole field rotating in 3D space is easily established. Preferably, two of the frequencies are set to be the same and greater than 1 kHz, so that the dipole rotates in a first plane with a frequency greater than 1 kHz. As already mentioned, this creates 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 generator coils at the selected times of the zero crossings of the sensor signal.

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 easily be achieved by supplying the third coil with an alternating current of correspondingly reduced frequency. The first plane with the fast (> 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 takes on 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 resting first plane, the zero-crossing orientations of the dipole field all lie along the same zero axis in the measurement plane, so that the readings of the coil currents at the times of the zero crossings are averaged, e.g. by summing to suppress noise effects.

It is also advisable to process the sensor signals from 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.

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 _m , which leads to extremal sensor signals on the at least one magnetic field sensor of the i-th chain link. e _m can now be calculated from two linearly independent zero axes by forming a vector product.

• Nimmt man zunächst irgendeine Sensordetektionsrichtung als gegeben an, z.B. durch eine zufällige Initialisierung, dann ergibst sich aus dem Aufbau der kinematischen Kette mit bekanntem Ort des ersten Gelenks und vorbekanntem Ort des Magnetfeldsensors relativ zum ersten Gelenk durch eine einfache Vektoraddition sofort der Ort des Magnetfeldsensors relativ zum Dipolzentrum, welcher nach aller Wahrscheinlichkeit zunächst falsch sein dürfte. Das oben diskutierte Optimalitätskriterium für extremale Sensorsignale, welches für den wahren Ort und die wahre Sensorausrichtung gelten muss, weist dem zunächst gefundenen Ort eine neue Sensordetektionsrichtung zu. Mit dieser ergibt sich eine neue Berechnung des Ortsvektors durch Vektoraddition, die erneut mit dem Optimalitätskriterium verglichen wird, und so fort. Nach einigen - meist wenigen - Iterationsschritten weichen die neuen numerischen Daten von denen des vorangegangenen Iterationsschrittes um weniger als einen vorbestimmten Akzeptanzschwellenwert ab, und man erreicht die Konvergenz.

If e _m is determined by measurements, then the location r = re _r and the sensor detection direction e _s can be calculated very quickly by a simple iteration. This is explained using the example of the first chain link:

• If one initially assumes any sensor detection direction as given, e.g. through random initialization, then the structure of the kinematic chain with known location of the first joint and 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 by a 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 the true sensor orientation, assigns a new sensor detection direction to the initially found location. This results in a new calculation of the location vector by vector addition, which is again compared with the optimality criterion, and so on. After a few - usually 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.

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

When the data for r = re _r and e _s converge in a way that is consistent with the measured e _m and the chain geometry, the location of the at least one magnetic field sensor on the first chain link is complete. 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 specific 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 then all subsequent ones. 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, each short sequence serving to approximately determine an assumed briefly stationary zero axis from current measurement data from the generator coils. The majority of short sequences serve to record a plurality of linearly independent zero axes so that a perpendicular direction to the zero plane can be calculated. This plumb direction determines the direction e _m for the sensor data of the magnetic field sensor on the i-th chain link and thus also the input into the iteration for finding the location and orientation of this sensor.

1. a. Setzen eines initialen Schätzwertes für die Sensordetektionsrichtung relativ zum Dipolzentrum;
2. b. Berechnen einer mit dem Schätzwert konsistenten Position des wenigstens einen Magnetfeldsensor auf dem i-ten Kettenglied relativ zum Dipolzentrum aus der vorbestimmten Position des i-ten Gelenks relativ zum Dipolzentrum und der vorbekannten Position und Sensordetektionsrichtung des Magnetfeldsensors relativ zum i-ten Gelenk;
3. c. Einsetzen der berechneten Position in ein Optimalitätskriterium für extremale Sensorwerte und Ablesen einer konsistenten Sensordetektionsrichtung;
4. d. Falls die Abweichung der konsistenten Sensordetektionsrichtung vom Schätzwert größer ist als ein vorbestimmter Akzeptanzschwellenwert, dann Einsetzen der konsistenten Sensordetektionsrichtung als neuen Schätzwert und
5. e. Wiederholen der Schritte b. bis d. bis zur selbstkonsistenten Konvergenz.

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:

1. a. Setting an initial estimate for the sensor detection direction relative to the dipole center;
2. b. Calculating a position of the at least one magnetic field sensor on the i-th chain link relative to the dipole center 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, which is consistent with the estimated value;
3. c. Inserting the calculated position into an optimality criterion for extremal sensor values and reading a consistent sensor detection direction;
4. d. If the deviation of the consistent sensor detection direction from the estimate is greater than a predetermined acceptance threshold, then using the consistent sensor detection direction as the new estimate and
5. e. Repeat steps b. to d. until self-consistent convergence.

With the completion of the location of the last chain link, the location 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.

The length of the time window can be freely predetermined, but it cannot be chosen to be arbitrarily short, since a number of zero crossings of the sensor signals must be analyzed for each chain link, because it cannot be assumed that all sensor detection directions are in the same plane. The joints in the previous consideration 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 also be handled if more than one magnetic field sensor is provided per chain link, for example one on each side of the chain link. This would also increase the required length of the time window.

On the other hand, the time window cannot be chosen to be too long, because the chain must be considered quasi-stationary during the time window in order to be able to locate all chain links consecutively. The actual object movement, which is to be recorded by arranging the chain on the object, must therefore be slow compared to the length of the time window. Time windows with lengths of the order of milliseconds or less can be achieved with the invention.

In any case, the iteration required to locate the individual chain links does not place great computational demands on today's commercial computers, as initial analyses show. Convergence is achieved in a maximum of 15 iteration steps with a processor time of the order of microseconds per chain link.

The user of the invention will have to select a rotation frequency of the dipole field that is appropriate for his application in order to dimension suitable time windows. Further considerations concern the magnetic field strength to be set up in view of the maximum possible chain length and the technology of the magnetic field sensors. Magnetoelectric bending beam sensors are particularly interesting here because they can be resonantly excited in their natural oscillation modes, which makes these sensors very sensitive and reduces the field strength required for clear output voltage signals. It can therefore be advantageous if the rotation frequency of the dipole field is adjusted to the mechanical resonance frequency of the bending beam oscillation.

Finally, it should be emphasized that the invention also offers the possibility of locating a plurality of kinematic chains simultaneously and relative to the same dipole center of the rotating magnetic dipole field. This is easy to understand 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 further calculation steps can be determined or carried out separately for each chain in parallel processing. This forms a powerful basis for implementation in the "data glove" mentioned at the beginning.

Claims (10)

Method for magnetically locating 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 a three-dimensional rotating magnetic dipole field is generated and wherein the position of the first joint relative to the dipole center is fixed and known in advance, wherein for each i = 1, ..., N on the i-th chain link at least one magnetic field sensor with a known sensor detection direction is arranged at a 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 known in advance, 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 times of the zero crossings 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 times of the zero crossings; e. Calculating the orientation e _m of the dipole field leading to an extremal sensor signal as a perpendicular direction to at least two linearly independent zero-crossing orientations; f. Calculating 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 _s by 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; g. Calculating the position of the i+1-th joint relative to the dipole center; h. Repeating steps b. to g. replacing i with i+1 until i assumes the value N-1; i. Carrying out steps b. to f. for i=N; j. Summarizing all calculated positions relative to the dipole center as a location representation of the kinematic chain during the time window with a predetermined length; k. Repeat steps a. to j. for additional time slots. Procedure 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. Procedure 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. 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. Procedure 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. 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 estimate 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 estimate 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 inserting the consistent sensor detection direction as a new estimate and e. Repeating steps b. until d. until self-consistent convergence. 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. 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. Use of the method according to one of the preceding claims for the magnetic location of a kinematic chain for the temporally step-by-step tracking of the movement of an object connected to the chain. Use according to Claim 9 for tracking a user’s finger movements over time.

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