Monitoring a resolver The present invention relates to methods and apparatus for monitoring a resolver, in particular for monitoring a resolver associated with a joint in an articulated robot arm. An articulated robot arm comprises a plurality of links, which are coupled to each other, to a base or to an end effector by rotatable joints. A link of such a robot arm usually houses a motor and a gear for driving the rotation of a neighboring joint, and power and signal wires for the motor of this link and for motors of more distal links and, possibly, of the end effector. In opera- tion, movement of the robot tends to wear on the isolation of the wires. In many cases, the isolation will not break down abruptly, but its resistance will decrease gradually, thereby distorting measurement signals that are fed back to a controller. Such distortion can cause the controller to derive from the measurement signals a position of the robot that differs from the real position. Such a deviation not only affects the precision with which the robot can carry out a given task but also harbingers total breakdown of the isola- tion which, when it occurs, can cause the robot to carry out unpredictable movements that can endanger people in its vicinity. Conventionally, a resolver comprises so-called rotor and stator windings, which are rotatable with respect to each other and are inductively coupled so that when an alternating current is flowing in the rotor winding, an alter- nating voltage will be induced in the stator windings. The stator windings 31. Januar 2022 being arranged at right angles to each other, the induction in one of the sta- tor windings is proportional to sin being an orientation angle ^ of the ro- tor, whereas in the other it is proportional to cos ^. These windings will therefore also be referred to as sine winding and cosine winding, respec- tively. When the resolver is operating normally, total coupling between the rotor and stator windings does not depend on the relative orientation of the wind- ings, i.e. the Pythagorean sum of the voltage amplitudes Us, Uc induced in sine and cosine windings of the stator is independent of the ori- entation of the rotor. When there is a defect in the insulation of wires asso- ciated to one of the stator windings, part or all off the voltage induced in it may be short circuited, so that a defect in insulation can be detected based on a variation of said sum. However, since the signal that must be evalu- ated in order to detect the defect is a sum of contributions from two wind- ings, which will in most cases not become defective at the same time, the defect becomes the hard to detect the smaller the contribution from the de- fective winding is. Evidently, when the rotor winding is orthogonal to the defective winding, no voltage is induced in the latter anyway, and the defect cannot be detected. When the rotor rotates out of the orthogonal orientation, the amplitude of the alternating voltage induced in the intact stator winding will decrease in proportion to the cosine of the misalignment angle, whereas in the defective winding it fails to increase. If the threshold for detection of a failure is set at e.g.95% of the nominal value of the above sum, the rotor will have to rotate by ^=12.9° until the failure is detected if the voltage induced in the defective winding is shunted completely. In practice, due to manufacturing toler- ances, temperature effects and the like, a more generous threshold may be necessary. If the failure threshold is set at 80%, position detection by the resolver can be wrong by up to ^=±36.9° before a malfunction of the re- solver is detected. If the induced voltage isn’t shunted completely, i.e. if the insulation has a nonzero residual resistance, the angle by which the resolver can rotate be- fore the malfunction is detected can still be larger. Therefore, when insula- tion gradually wears down, the defect can at first go completely unnoticed, merely causing a loss of accuracy in the movement of the robot, and, hence, a decrease in product quality. There is thus a need, in particular in collaborative robot applications, for a resolver and for a resolver monitoring method by which such a deterioration can be detected in an early stage. This need is satisfied, according to an aspect of the present invention, by a method for monitoring a resolver, the resolver comprising a pair of stator windings and rotor winding which is rotatable with respect to said stator windings and inductively coupled to these, the method comprising the steps of a) exciting the rotor winding with an alternating current having a an os- cillation frequency and a first phase, b) obtaining voltages induced in the stator windings by the alternating a current flowing in the rotor, c) deciding that the resolver is defective if a shift between phases of a first one of said induced voltages and of the alternating current differs from a nominal phase shift by more than a predetermined phase threshold. Monitoring the phases of voltages induced in the stator coils has a substan- tial advantage over monitoring total coupling in that a signal from a poten- tially defective winding can be evaluated directly, instead of first combining it with a signal from the other, presumably intact winding, and then evaluat- ing the result, so that higher sensitivity is to be expected. When the resolver is intact, and current through the stator windings is negligible, the voltages induced in both stator windings should have the same phase shift with re- spect to the excitation current. When a defect in insulation enables a cur- rent to flow in one of the stator windings, it can be expected to affect the phase of the voltage due to the inductivity of the winding itself. Deciding whether said first induced voltage is critically phase-shifted can comprise the steps of d) deriving a reference signal from the alternating current, wherein the reference signal has the oscillation frequency and is phase shifted with re- spect to the alternating current by said nominal phase shift, e) detecting a phase difference between the reference signal and said first induced voltage, and f) deciding that the resolver is defective if said phase difference ex- ceeds the phase threshold. The operating temperature of the resolver may have an effect on the phase shift between the exciting current and the first induced voltage in a perfectly intact resolver. Since operating temperatures of the two stator windings will not differ much, such an effect may be compensated by choosing the sec- ond one of said induced voltages or a signal derived therefrom as the refer- ence signal. According to an alternative, deciding whether said first induced voltage is critically phase-shifted can comprise the steps of d) deriving a reference signal which has the oscillation frequency and is phase shifted with respect to the alternating current by said nominal phase shift plus or minus ^/2, e) detecting a phase difference between the reference signal and said first induced voltage, f) deciding that the resolver is defective if said phase difference differs from ± ^/2 by more than the phase threshold. According to this alternative, when the phase difference between the refer- ence signal and said first induced voltage is ± ^/2, an integral over time of a product of the first induced voltage and the reference signal will be zero. Therefore, by calculating the integral, a phase shift different from ± ^/2 can be detected with high sensitivity. Since the second induced voltage will be zero while the rotor windings is or- thogonal to the associated stator winding, it can be desirable to generate the reference signal independently from said induced voltages, e.g. by an oscillator which is tuned to the oscillation frequency and is phase coupled to the reference signal, or by monostable circuitry triggered by the refer- ence signal. The nominal phase shift can be made adaptable; in particular it may be contemplated to measure an existing phase shift between the exciting cur- rent and the induced voltages at a predetermined instant at which the re- solver is assumed to be intact, e.g. when it is used for the first time after having been built into a device, such as an articulated robot arm, and to set the phase shift measured at that instant as the nominal phase shift. The decision of step c) could be based on whether a time integral of the in- duced voltage times an appropriately defined normal signal exceeds a pre- determined threshold. When the induced voltage has the nominal phase shift, and the normal signal is phase shifted by 90° with respect to the refer- ence signal, such an integral, taken over an integer number of periods of the exciting current, would be zero, and a significant deviation from zero might be regarded as indicative of a defect. In practice, such an integral can be approximated, more or less precisely, by numerical means, based on samples of the first induced voltage, said samples at least comprising first samples obtained at a first predetermined sampling phase of the alternating current. The first predetermined sampling phase should be selected so that when the phase shift between the alternating current and said first induced volt- age is the nominal phase shift, sampling times of said first samples are shifted with respect to a peak of the first induced voltage, and are prefera- bly synchronized with zero crossings of the first induced voltage. Thus the samples will be zero while the resolver is intact, and whenever the first samples differ from zero by more than an allowed voltage threshold, the re- solver can be assumed to be defective. A second sampling phase for obtaining second samples is preferably se- lected so that when the phase shift between the alternating current and said first induced voltage is the nominal phase shift, the first sampling phase is at a maximum of the first induced voltage. While the resolver is in- tact, second samples from both stator windings can be used for determin- ing the orientation of the rotor. A third sampling phase for obtaining third samples is preferably opposite in phase to the second sampling phase. Thus, second and third samples will usually have opposite signs but identical amounts, and will cancel out in a numerical integration. If they do not cancel out, they indicate a DC bias in the samples, which can be taken account of when evaluating the first sam- ples. A straightforward way of taking into account a possible DC bias is by judg- ing the phase threshold to be exceeded if said first samples differ from the average of said third and second samples by more than an allowed voltage threshold. According to a second aspect, the invention provides a resolver controller comprising a power supply for providing an alternating current having an oscillation frequency and a first phase to a rotor winding of a resolver, and a processor adapted to obtain voltages induced in the stator windings by the alternating cur- rent flowing in the rotor; and to decide that the resolver is defective if a shift between phases of a first one of said induced voltages and of the alternating current differs from a nominal phase shift by more than a predetermined phase threshold. The same controller may comprise calculating means for deducing an an- gular position of the resolver from voltages sampled from said stator wind- ings. According to a further aspect, the invention provides a resolver assembly comprising the resolver controller as defined above and an associated re- solver. Such an assembly can further comprise an articulated robot arm having a joint to which the resolver is associated. According to a still further aspect, the invention can be embodied in a com- puter-readable storage medium having stored thereon a plurality of instruc- tions which, when executed by a processor, cause the processor obtain voltages induced in the stator windings by the alternating a current flowing in the rotor; and to decide that the resolver is defective if a shift between phases of a first one of said induced voltages and of the alternating current differs from a nominal phase shift by more than a predetermined phase threshold. Further features and advantages of the invention will become apparent from the subsequent description of embodiments, referring to the appended drawings. Fig.1 is a schematic view of a robot and its controller; Fig.2 is a schematic diagram of a resolver; Fig.3 is a block diagram of the robot and its controller according to an embodiment of the invention; and Fig.4 is a block diagram of the controller according to another em- bodiment. Fig.1 is a schematic view of a robot system comprising an articulated robot arm 1. The robot arm 1 has a stationary base 2 fixed to a support, and a plurality of links 3 rotatably connected to each other and to the base 2 by joints 4. The most distal link carries an end effector 5. The links 3 are shown with part of their casing removed, so that motors 6 and gears 7 for driving rotation of the joints 4 can be seen inside the casing. A resolver for measuring a rotation position could be mounted at the axis of rotation of each joint 4; in the embodiment of Fig.1 a resolver 8 is mounted at a shaft 9 extending from the motor 6 to the reducing gear 7. A wire harness 10 extends along the articulated arm 1 between a controller 11 on one end and the motors 6 and resolvers 8 on the other, supplying the motors 6 with energy from a power supply circuit 12, and feeding back out- put from the resolvers 8 to a processor 13. The wire harness 10 must adapt to every movement of the robot arm 1, which may wear down the isolation of individual wires in it. Fig.2 is a schematic diagram of one of said resolvers 8. The resolver 8 has stator windings 14s, 14c, also referred to here as sine winding 14s and co- sine winding 14c, whose axes extend at right angles to one another in a plane, and a rotor winding 15 which is rotatable with respect to the stator windings around an axis of rotation perpendicular to said plane. eds an exciting current Ir to rotor winding 15 by wires of harness 10. The exciting current Ir has an oscillation frequency which is much higher than a rated maximum rotating frequency of the motor 6, e.g. between 1 and 10 kHz, so that in a cycle of the exciting current, rota- tion of the shaft 9 is negligible. The exciting current Ir induces alternating voltages Us, Uc in sine winding 14s and cosine winding 14c, respectively. When the resolver is operating correctly, the two voltages differ in ampli- tude depending on the instantaneous orientation of the rotor, i.e. in the con- figuration shown, with the rotor winding 15 nearly parallel to cosine winding 14c and nearly orthogonal to sine winding 14s, the amplitude of Uc is near maximum, represented by a dotted curve, whereas Us is close to zero, and phases of Us, Uc are shifted with respect to Ir by substantially the same amount ^ ^ ₀ , referred to as the nominal phase shift. While a small load on Uc due to an insulation defect in the wires 10c ex- tending between the cosine winding 14c and the controller 11 may not have a significant influence on the amplitude of Uc, it may cause the actual phase shift ^ ^ to differ noticeably, by from the nominal phase shift ^ ^0, as shown in the diagram U c(def.) of Fig.2. Of course, an insulation defect in wires 10s leading to the sine winding 14s would have the same effect on Us. According to a first embodiment of the invention, the processor 13 continu- ously samples Us and Uc, derives a 90° phase shifted signal from one, e.g. U _s , preferably by forming its time derivative , ^^ _^^ , and approximates the inte- gra being an integer number of periods of the ex- citing current Ir. When the wires of both stator windings 14s, 14c are intact and have the same phase shift ^ ^ relative to I _r , the integral ^^ will be zero. Any phase shift between U _s and U _c will show by ^^ becoming different from zero, so that based on an appropriately selected threshold the re- solver 8 can be judged to be defective In order to prevent a DC bias on one of Us and Uc or some other outside in- terference from causing the integral E to diverge, a high-pass filter can be provided. Such a filter can be located between each of the wires 10s, 10c and input ports of the processor 13, or it may be implemented by software within the processor 13, operating either on each of the input signals Us and Uc, or on a product of both, such as ^^ _^^ ^^ _^^ . The high-pass filter is trans- parent at the frequency of the exciting current Ir, but should block the rated maximum rotating frequency of the motor 6. The above embodiment has a problem in that whenever the rotor winding 15 is perpendicular to one of the stator windings 14s, 14c, no voltage is in- duced in that winding, and the phase shift ^ ^ cannot be measured. This problem can be overcome by associating an electric oscillator to each of the stator windings 14s, 14c, which is phase coupled to the induced voltage Us, Uc of its associated stator, and from which a signal proportional to can be derived even when the rotor orientation causes U _s or Uc to be zero. When the phase shift ^ ^ ^ does not vary much due to temperature or other environmental conditions of the resolver, an oscillator or a delay circuit 16 may be directly connected to the wire exciting current Ir from power supply circuit 12. Processor 13 is connected to both the power supply circuit 12 and each stator winding 14s, 14c, so as to measure, in an initialization pro- cedure, a phase shift between Ir and Us or Uc, which, when the resolver 8 is new and free from defects, will be ^ ^ ^. Processor 13 programs a phase shift of the oscillator or a delay of the delay circuit 16 based on the meas- ured phase shift ^ ^ ^. E.g. the delay circuit 16 may be a programmable counter designed to count between zero and and an initialization value after having been triggered by e.g. a zero crossing of I _r , and to toggle an output signal D between 1 and -1 each time it finishes counting. By setting an ap- propriate initialization value, the processor 13 synchronizes toggling of the delay circuit output D with a maximum of induced voltages Us or Uc of intact resolver 8, or, in more general terms, sets a 90° phase shift between D and Us or Uc. By periodically sampling D, Us and Uc, processor 13 evaluates and detects a defect of the re- solver whenever ^| ^^ _^^ ^| or ^| ^^ _^^ ^| equals or exceeds ^^ _{^^ ^^ ^^} . According to a second, particularly simple embodiment, processor 13 takes a first sample U ₁ of U _s and U _c once per period of I _r , namely at the nominal phase shift ^ ^0 relative to Ir. Alternatively, similar to what has been outlined above, U _c may be sampled at a zero phase shift relative to U _s based di- rectly on U _s or on an oscillator synchronized to U _s , and vice versa. In either case, while the induced voltage Uc holds the nominal phase shift ^ ^0 rela- tive to I _r , samples U ₁ will be zero, whereas in case of a phase shift ^ ^ _def of e.g.10° the sample U1(def) (see diagram Uc(def) of Fig.2) will amount to sin 10°=0.1736 times the peak voltage of Uc. A DC component might be induced in Uc for other reasons than a defective insulation, for example auxiliary circuitry connected to the feed wires of winding 14s or 14c. It may therefore be necessary to distinguish between such a DC component and a deviation from the nominal phase shift. For doing this, additional samples are needed. According to a third embodi- ment, therefore, second and third samples U ₂ , U ₃ are collected in each pe- riod of I _r , namely at phases ^ ^ ₀ - ^ and ^ ^ ₀ + ^ ^ ^When there is no DC compo- nent, these samples U2, U3 should be proportional to sin(- ^) and sin( ^), re- spectively, so that the average of both should vanish. When circuitry con- nected to the windings 14s, 14c is known to produce a certain DC bias, the average (U2+U3)/2 can be compared to U1, and the resolver is judged to be defective if either (U2+U3)/2 is outside an expected range or if |U1- (U2+U3)/2| exceeds a predetermined threshold. While the resolver 8 is intact, and U _s and U _c have the nominal phase shift A(|)o relative to l _r , the amplitudes of U _s and U _c can be measured, and hence the orientation of the rotor can be determined, by sampling U _s and U _c at their respective peaks or troughs, at phases and t is conven- ient, theref ore, to choose and to collect the second and third samples at phases A respectively. Thus, the same circuitry or soft- ware for processor 13 can be used both for determining the amplitudes of Us and U _c and for detecting a possible defect.

Fig. 4 illustrates an alternative structure of controller 11 . The controller has two branches for processing voltages U _s and U _c induced in sine and cosine winding 14s, 14c of the resolver. Since both branches have identical struc- ture, it is sufficient to describe structure and operation of one of them here. A phase detector 17s is connected to power supply circuit 12, on the one hand, and to winding 14s on the other, in order to detect and output a phase difference A<|>s between the excitation current l _r and induced voltage U _s .

The phase detector 17s has its output connected to a storage cell 18s. The storage cell 18s is controlled to store a phase difference Ac|>s output to it when the resolver is operated for the first time or when it has been reset af- ter maintenance or repair. A comparator 19s has one input connected to storage cell 18s and another connected to phase detector 17s, so as to re- ceive the phase shift stored in storage cell 18s as a nominal phase shift A(|)o, and the phase shift Ac|>s from phase detector 17s as an instantaneous phase shift. Comparator 19s compares the difference |Ac|>o— Ac|>s| mod u be- tween the two phase shifts with a predetermined threshold, and outputs a signal DEF indicative of a defect of the resolver when the difference ex- ceeds the threshold. It should be noted that the phase difference here should be confined to a range from 0 to u by the mod u operation and not to

0 to 2 7t, as might be expected, since an abrupt phase change by u will be e rotation of the rotor sign.

2 base 3 link 4 joint 5 end effector 6 motor 7 gear 8 resolver 9 shaft 10 wire harness 10c wire 10s wire 11 controller 12 power supply circuit 13 processor 14c stator winding (cosine winding) 14s stator winding (sine winding) 15 rotor winding 16 delay circuit 17s phase detector 17c phase detector 18s storage cell 18c storage cell 19s comparator 19c comparator 20 comparator