CA1054241A - Nutating electromagnetic field transmitter - Google Patents

Abstract

OBJECT TRACKING AND ORIENTATION DETERMINATION
MEANS, SYSTEM AND PROCESS
ABSTRACT
A field (e.g., a magnetic field) which nutates about a pointing vector is used to both track or locate an object in addition to determining the relative orientation of this object. Apparatus for generating such a field includes mutually orthogonal coils and circuitry for supplying an unmodulated carrier, hereafter called DC signal, to one coil and an AC modulated carrier signal, hereafter called AC
signal, to at least one (usually two) other coil, such that the maximum intensity vector of a magnetic field produced by the currents in the coils nutates about a means axis called the pointing vector direction of the field. The generated field is sensed in at least two orthogonal directions at the object to be tracked and whose orientation is to be de-termined. The sensed signals provide an indication of the direction and orientation of the object relative to the coordinates of the generating means.

Description

-1054~41 I~ ()UNIl Ol; ~'111, INVI.NI`ION
I. f;iel~ of the Invention lhis invention relates to an objeet loeating or tracking system or process in which a vector field which is eaused to nutate about an axis ealled the pointing vector, is used to locate or traek a remote objeet. It also relates to an apparatus for generating sueh a nutating field, more particul3rly a nutatin~ magnetic fiel~ hicl nutates about an axis called the pointing vector. More partieularly, the invention relates to sueh a system or proeess whiell is eapable of determining both the relative translation and the relative angular orientation of the co-ordinate frame oE a remote object, relative to the reference eoordinate fr.~me of the apparatus wllicll generates an~ points tho nutating ~ield.
II. I)eseription of tlle l'rior ~rt ~lle use oE orthogonal eoils for ~eneratin~ an~
sensillg maglletic ields is well kno~n. Sueh apparatus has reeeivod l~ide attention in the area of mapping magnetie fields to provide a better unclerstandill~ of their characteristies for example. I~ a magnetic field around generating coils can be very aeeurately mapped througll use of sensin~ eoils, it llas also bee~n pereeived that it migllt be possible to deterlnille the location of the sensing coils relativo to the z5 generating coils based on what is sensed. Ilowever, a problem associate~ Witll doillg this is that tl~ere is more than one loeation and/or orientation withill a usual magnetie dipole field that will provide the same characteristie sensing signals in a sensing coil. In order to use a magnetic field for this ~urpose, additional informatien must therefore be provided.

-2-l{~Sg~

1 ~ne aI)proach to I)rovi(le the a~ditional inLormation rcquire~ Lor this l)urI~ose is to havc thc ~encratiIlg an~I
sensiIlg coils move with res~ect to each ot1Icr, such as is taught in lJ.S. Patent 3,644,825, entit1ed ~IAGNETIC DETECTION
SYST~I FOR ~'I'I,C'I'I~G ~IOVl~l~NT Ol' ~N OBJ~CT UTILIZING SIGN~LS
~RIV~D II~O~l TWO ORl'IIOGONAL PICKUP COILS, issued February 22, 1972 to raul I). I)avis, Jr. and 'I'IIomas r. ~IcCu110uglI. Tlle motioll Or thc coi:Ls ucncratcs cl~angcs in tlle magnctic ~iel(l, and tllC r c.su:ltillg signals tllcn may bC uscd to ~letcrmine ~iroction Or thc movenIcnt or tIIc rclative position of tlle generating an~ sensing coils. Whi1e such an approach rcmoves some amI)iguity about the ~os.ition on the basis of the field sensccI, its accuracy is ~epen~ent on tlle relativc moti.olI, an~ it ca~ ot bc usc~l at all wi.tllout thc rclati,ve motion.
Ano~lIer al)I)roaclI tlIa~ lIas l~cen s~ gostc~I to I-rovi~Ic tllo ad~itioIlal. requircd inorIllatiolI i~ to mtlke tllc ma~lIc~ic field rotate as taugllt in Kalmus, "~ Ncw ~IUitlillg an~ Trackin~
Systcm", II~I,'I`riallsactions on Acrospacc and Navigation~l 2U l,lectronics, ~larcII 1962, I)ages 7-10. 'I'o ~etermine the ~istance between a generatin~ an~ a sensing coil accurately, that approaclI requires that tlle rclative orientation of the coils bc ma:ilItalllc~ constant. It thcrc~orc cannot be used to ~eterlIline ~oth the relative translation an~l relative orientatioll oE the gencrating aIl~ sensing coils.
Wh:ilc the art o.~ locating an~ tracking remote objccts is a well ~Ievelol)ed onc, tl~erc sti.ll remains a ncc~
for a way to deter~ le the relative angular orientation of a , remote object in a~dition to locating or tra~king the object. Furthcr~ there is a nee~ for a means, system or I~rocess w1Iich oIcr.Ites on t!~e sigllals ~Ictecte~ hy one sensor, those signals resulting from the nutating field generated by one generating means, which is capable of deter-mining continuously the location of or tracking the remote object and sensor, in addition to simultaneously determining continuously the relative angular orientation of the remote object and sensor.
As here described one can determine relative trans-lation and orientation of remote objects through use of a field in a continuous manner, so that translation and orientation may be tracked and therefore determined continuously.
There is further described a system and process for locating an object precisely relative to a reference coordinate frame of the vector field generating means.
Further, a system i5 described in which a pointing vector defined by a modulated field i6 used to track an object very precisely.
A generator capable of producing electronically a field which nutates about a specified pointing vector is des-cribed, which field can be used in the above system and process.
Also described therefore is an efficient signal processing technique which results in the measure of the relative translation of a remote object (two angles) in addition to the simultaneous measure of the relative angular orientation of the remote object (three angles). That is, the teaching herein can provide a means for measuring five independent angular measure-ments utilizing only one field generating means and only one sensing means at the remote moving object.
The above and related objects may be attained through use of the system process and field generating apparatus described herein. This disclosure is based on the realization that the only positions in anutating dipole field where the `` 1054Z41 field strength is magnitude in~7ariant lie along the axis of nutation, herein called the pointing vector. This phenomenon allows very precise location or tracking of a remote object that is free to undergo not only changes in position but also changes in angular orientation.
In accordance with the invention there is provided, apparatus for generating a nutating electromagnetic field which comprises:
a) orthogonal radiators adapted to pass a current; and b) means for supplying the appropriate mixture of signals from three sources, supplying a DC signal, a first AC
signal and a second AC signal in phase quadrature with the first AC signal, respectively, to the three radiators such that the electromagnetic field produced by the currents in the three radiators i8 caused to nutate about an arbitrarily directed pointing vector of thefield.
In accordance with a second aspect of the invention there i~ provided, apparatus for generating a nutating electro-magnetic field which comprises:
a) at least two orthogonal radiators adapted to pass a current; and b) means for supplying the appropriate mixture of signals from sources supplying a DC signal, and a first AC signal, to the radiators such that the electromagnetic field generated by the currents in the coils is caused to nutate about an arbitrarily specified pointing vector of the field. Preferably the signals which excite the two orthogonal radiators cause the field to nutate in a nodding motion in a plane defined by the axis of the two radiators. Where there are three radiators and ~054Z41 in which the signal source also supplies a second AC signal in phase quadrature to the first AC signal the appropriate mixture of each of the three source signals fed to the three radiators causes the magnetic field to nutate in a conical manner about an arbitrarily but specifically directed pointing vector of the field with the apex of the cone at the intersection of the generating coils.
If the system is used to locate the object only, say for small perturbations in pointing angle, means is provided for generating a signal based on the sensed field for indicating the location of the object. If the system is used to track the object, a signal generating means is connected between the sensing means and the field generating means which provides a signal to the field generating means, based on the sensed field, for moving the pointing vector of the nutating field, toward the sensingmean~.
Preferably, orthogonal coils are us~d both in the generation of the nutating field -- in which case it is an electromagnetic field -- and in the sensing of the resulting field.

131~11,1: l)l,S(:RTI'I`l()N 01: '1'111, I)RAWlN(;S
lig. l lescri~es the geometry of a simple coordi-nate transformation calle~ a rotation;
r ig. 2 is the block liagram representation of a single rotation o~erator as in ~ig. 1 called a Resolver;
Fi~. 3 shows the circuit giving 360 degree pointing free~om to the two-dimensional nutating magnetic ield in the plane;
~ 4a shows the poillting angle.s Ieinel for three-dimensional pointing;
Pig. 4b illustrates the circuit corresponding to the pointing angles of Fig. 4a;
I;ig. 5 is a schematic representation of a prior art magnetic f3eld uenerating and sensing system;
lig. 6 is a representation o~ signals sensed in the system of Yig. 5;
lig. 7 is a schematic represelltation o~ u systom which will allow practice of the invention for determining location and orientation of an object which moves in two-2U dimensions;
Fig. 8 is a representation of signals sensed in the system of lig. 7;
l`ig. 9 is a re~preselltation of a simplifie~ two-~imensional system using a two-coil generator and a two-coil sensor;
lig. 10 is a schematic representation of a system in accordallce Wit]l the invention which will track the location and the angular orientation of an object free to move in two-dimensions; and Fig. 11 is a schematic representation of a system in accordance with the invention which will track the t' ~1,,,_, . . .
~054Z41 1 location or direction and thc relative angular oricntation of an object free to move in three-dimensions, subject to certain restraints.
DETAILED D~SCRIPTION OF SPECIFIC EMBODIMENTS OF THE INV~NTICN
.
Apparatus for generating a directable, nutating, magnetic field along a pointing vector includes at least two orthogonally posi-tioned coils tllrough which excitation currents can be passed. This excitation current will usually be operating at some specified carrier fre~ucncy which is modulated by a direct current (DC) signal and/or an alternating current (AC) signal. ~lereinafter, these modulation envelopes will be referred to only as DC signal or AC signal. Thc AC
signal is at the nutation frequcncy. Circuitry for supplying a DC current through one of the coils and an AC current through at lcast one additional orthogonally positione~ coil pro~uces a nutating magnetic field whose pointing vector is in the direction of the axis of the DC coil, or more properly stated, in the direction of the axis of the DC field. The amplitude of the nutation depends on the relative amplitude of AC and DC signals, in most cases taken to be equal in amplitude. If the object can move in only two dimensions, the nutation need only be a simple nodding in the plane of the motion. This can be produced by a DC signal in one of the coils and an AC signal in the second coil, with both coils in the plaIle of the motion. If the object is frec to move in three dimeIlsions, the nutation desirably describes a conical motion about the pointing vector of the field, the concial apex at the intersection of the coi~s. Such a nutating field can be generated by the combination of a DC
signal in one of the coils, an AC signal in a second coil, r- 1054Z41 1 an~ anothcr AC signal llaving a I)hase in (luadrature with the phase o~ the first AC signal, passcd through the ~hird coil, all three coils bein~ mutually spacially orthogonal.
In both the 2-D an~ 3-D nutating ficlds described above, the pointing vector is fixed to the direction of the axis of the DC ~iel~. To make this nutating field direct-able a signal processing means known as a coordinate transformation circuit must operate on the re~erence AC and ~C excitatioll signals in order to point the nutatin~ field in the desired direction. A bricf discussion of the coordi-nate transEormation known as a rotation is presented as background in order to properly teach the principles under-lying ~he techniques employed in this invention.
A vcctor transEormcd by pure rotation ~rom onc coordinatc Irame into anothcr coordirlate fralne is also said to be rcsolved Erom tlle onc into tlle ncw coordinate Erallle.
Resolve and resolution in this contcxt are synonyms Eor transEorln an~ trans~ormation. Tlle operator which transforms the comporlents of a given vector in one coordinate frame into its components in another coordinate frame where the two coordinate Erames are related by a sim~le angular rotation we will deCille as a rcsolvcr. Ihe cquations governing this transEormation are:
X 2 = xlcosA + y~sinA
Y 2 y~cosA - xlsinA
Z 2 Z ~
where in this casc the z, axis is the axis of rotation. Ihe c~uations are readily verified ~rom the geometry illustrated in Fig. 1. Note that when the two components operated on by the resolver are ordered positively (zxyzxy... ) then the first component of tlle positively ordered pair always has r 1054241 1 the positive sine term when the anglc of rotation is posi-tiv~ the ~ngle of rot~tion is ncgative then tl-c sign of the sine terms reverses. A convenient notation for a resolver is the block shown in lig. 2 wllerc the rotation in this case is shown as negative about the y-axis. The y component is therefore not affected by the transformation and this fact is indicated in this notation by passing that componellt directly throug}l the ~ox as ShOWII whcreas, the resolver block representing lig. 1 would show thc z~ axis passing directly through the box. This notation should be regarded as a signal flow or block diagram for vector components, particularly useful in describing the computa-tional strategy employed.
One ~rocess includes the generation lS of directable, nutating field, nutatin~ about all axis calle~ the pointing vcc~or. In thc 2-D case, a single resolver operates on the AC and DC
orthogonal components of the reference nutation excitation vector in ordcr to produce the propcr mixture of AC and DC
2U on each of the two generator coils such that the pointing vector, along with the cntire nutating magnctic field structure, is directed so as to make an angle A with the reEerence X-axis, as shown in ~ig. 3. The cxcitation for the two generator coils necessary to direct the pointing vector in the required direction defined by the angle A is given by the equations:
Excitation for X-coil = (DC)cosA - (AC) sinA
Excitation for Y-coil = (AC)cosA + (DC) sinA
The computational circuitry necessary for precisely directing or pointing the nutating magnetic field for the 3-D case operates, in principle much the same as in the 2-D

1054;~41 1 case. The reference nutation excitation vector IIOW consists oE three coml)onellts: a I)C alld two AC signals qu~dr~ture related. Ihe pointing vector and its entire nuta-ting magnetic field structure are pointed in any desired direc-tion defined in terms of angles A and B, in this case.
Figure 4 illustrates the pointing geometry and the computa-tional coordinate transformation circuitry necessary for achieving the desired pointing direction by o~eratlng on tho given three reEerence excitation signals. A more detailed 10 explanation of coordinate transformations, calculations and applications is contained in Kuipers, J., Solutions and Simulation of ~ertain Kinematics and Dynamics Problems Using Rosolvers, rroceedings of the FiEth Congress of the Inter-_.
national ~ssociation for ~nalog Computation, Lausanne, Switzerland, August 28 - September 2, 1967, page 125 to page 13~.
~ process for tracking an object in-cludes the generation of a field which nutates about a pointing vector. The generated field is sensed in at least two axes at the object to be located or tracked. From the processed relationship between the field components sensed in each of the orthogonal axes, the position of the object relative to the pointing vector oE the field is determined to locate the object. To track the object, the pointing vector of the nutating field is moved until the field sensed on the two axes, aEter appropriate coordinate transformation processing, indicates that the object lies along the pointing vector. This has taken place when the processed signal resulting from the sensed nutating field is magnitude invariant over the nutation cycle. If a pointing error exists, tllen the amplltude of the modulation sensed in the fl~. ...
~054Z41 1 pointi1lg ~ircction is proportional to thc angular ~isplace-mellt o~ thc objcct Erom the pointillg vcctor. ~lorc speci-fically, the relative phase of the detected and processed signals coml~ared to the reference fiel~ ~encrating signals is proportional to t]~e direction o the objcct relative to the pointing vector. The modulation amplitude of the sensed and processc~ signal, in tlle pointing vector direction is proportioncll to the angular displaccment from the pointin~
vector.
Tlle abovc discussion explains that the pointing vector can continuously track the object. This results in two angular measures defining the location of the object.
Determination o~ the anugular orientation Or thc objcct is howcver an indepcndcllt matter. Ihc oricntation of the object is speci~icd in gencral by thrce lulcr tsec Kuipers' reEerence-l paper) allglcs mcasurcd rclative to tho rofercnce coordinate rame at the generator. Two o~ the orror measures o angular orientation are proportional to whatever non-zero projections of tlle sensed and processed l)C field component exist in the coordinate dircctions oE the plane perpendi-cular to the pointing direction. The third angular error measure is proportional to the relative pllase of the sensed and processed nutatioll signals in this orthogonal plane, compared to the nutation reerence excitation at the generator means.
Ihis system, apparatus for gencrating a nutating ~icld about a pointing vector, and process allows a remote object to be located and tracked very precisely, both as to position and angular orientation. While the invention should find application in a wide variety of situations wllere remote object location or tracking coordinates, in ~- iOS4Z41 itiOll to tllc orintatiol- ~ 1cs o~ thc ohjcct, is rc-quired, it is particularly adapted in its present preferred ~orm for use in tracking the position and angular orienta-tiOII of an observer's head, more specifically his line-of-S sight, for visually-coupled control system ~plications. In this limited application, the pilot's line-of-sight is continuously and precisely defined relative to the coordi-nates of the aircraft. Many other applications such as automatic l~n~illg or dockillg, remotely piloted vel-icles, automatically negotiated aiT-to-air refuelling, formation control, etc. are all applications operating over much larger domains. In general, any situation involving two or more independent bodies or coordinate frames, wherein it is desired not only that the relative distance or location oE
the frames be measured, tracked and controlled precisely but also that it is dosired simultaneously antl wi~h the salno device to precisely measure, track and control the relative angular orientation of the two frames, ls a potential application o~ the invented subjeet matter.
Referring now particularly to ~ig. 5, the elements of a prior art magnetic field generating and sensing system wllicll canllot be used to locate, track or determine the orientation oE an object, are shown. Included is a magnetic field generator 10 having a coil 12 wound of copper or other conducting wire on a magnetic, preferably isotropic, core 14. A source 16 of current i at some convenient carrier fre(luency, is connected to the coil 12 by leads 18 and 20.
Sensor 22 has a coil 24 wound preferably also on a magnetically isotropic core 25, as in the case of the generating coil 12.
Sense circuits 26 are connected to the coil 24 by leads 28 and 30.

` 1054Z41 1 In us~ in ~ccor~allce with prior ~rt tcchniqucs, thc passagc o.f currcnt i through coil 12 crcates a m~nctic field 32. Coil 24 of sensor 22 is moved to different points around the generating coil 12, and currents induced in the coil 24 provide a measure of the strength of the magnetic field 32 at the different points. With reference to the referellcc coordillate axes 34, 36, and 38, in addition to simple translation o~ coil 24 in the directions X, Y and/or Z, the coil 24, wllosc coord:illate axcs are ~.~, 35 and 37, may assume different relative angular orientations by rotations about these axes x, y and/or z.
~ig. 6 shows the output signal and coil 24 measured by sense ci.rcuit 26 for a given field 32 generated by current 1 ~low.ing througll the co.il 12, as coil 24, is rotated for 360 dcgrecs about either thc y axis 35 or the z axis 37. In fact, coil 24 could bc translated to uncoun~ab.ly many poillts around coil 12 where thc above rotations oE coil 24 would again give the same output signal shown in Tig. 6.
Ihis demonstrates simply why the prior art appar~tus cannot be used to uniquely define the relative position of nor the relative angular orientation of the sensing coils 24 with respect to coil 12.
I-i.gs. 7 and 8 show coil 12 which nutates the field 32 in a simple nodding motion, induced by nutating means 44 connected to coil 12 by line 46, through a predetermined angle 48, c.g., 45 clegrees, and the resultin~ output curvcs as sensed by circuits 26. The translation and rotation motions to be considered are restricted to the X-Y plane.
The curves of l~ig. 8 illustrate the basis underlying stra-tegy. In Fig. 7 note that two orthogonal angular orientations are shown for the sensor 1 coil 24. In cach of tllcse two oricntations thcrc is, in general, an AC an~ a DC coml~onellt induce~l in coil 24. When coil 24 is aligned with the y-axis which is assume~ to be orthogonal to the pointing axis 50, the induced signal consists of a zero ~C component at the fundamental nutation ~requency and a zero DC component. When coil 24 is aligned with the x-axis, which is coincident with the pointing axis 50, the illdUCCd signal consists of the entire nc colnponent and agaill zero ~C at the fundamcntal nutation fre(~uency.
The two pertinent signals for determination of relative orientation an~ translation, are the DC signal induced in coil 24 when in the y-position and the AC signal when in the x-position. Both are zero as illustrated in the ~irst two curves o~ . 8 whcn there is no orient.ltion or t.anslatiolt lS error.
If a translation error exi~ts tllen tlle scnsor coil 24, in the x-position, will sense some ~C signal 47 at the fundamental nutatioll frequency. The magnitude of this signal will be proportional to the magnitude of the translation error; its phase, either 0 degrees or 180 degrees, will indicate the direction of the error.
If an orientation error exists, then thc sensor coil 24 in thc y-position will sense some DC signal 45. The magnitude and polarity of this DC signal will indicate the magnitude and direction of the orientation error, respectively.
Tlle apparatus of ~ig. 7 will allow practice of the process to determine the location and orientation of coil 24 by alternately positioning the coil 24 along the x and y axes, assuming freedom.to move or orientate the coil 24 alternately to coincide with the x and y axes. I r movcmcnt occurs in each of the X, Y and Z

1 directions, tl-at is, in all tllrec dimensions, thcn morc than a simplc plallar nutation in the X-Y planc is required to characterize that movement, as will be considered in more detail below. In the X-Y plane, however, rather than a successive positioning oE the coil 24, it is far simpler to utilizc two orthogonal coils, as in the apparatus of ~ig. 9.
Therefore, coil 24 of Fig. 7 has been replaced by ortho-gonally positioned coils 52 and 54, each connected to sense circuits 26 by leads 56 and 58, and 60 and ~2, respcctively.
While nutation of the field 32 in Fig. 7 through the angle 48 can be accomplislled by any convenient method, such as by means 44 giving a mechanical nutating motion of the coil 12 in Fig. 7, it is best accomplished electrically, utilizing a pair of coils 64 and 66, also orthogonal. Current sources 68 and 70 are connccted to each of tl)ese coils by leads 72 and 74 and 76 an~ 78, respectively. As sllown, currcnt source 68 supplies a DC signal i to coil 6~, and currcnt source 70 supplies an AC signal, say ~sin wt, to coil 66.
These signa]s can be either simple DC and AC or may be both superimposed on a suitable carrier frequency such as 10 kilohertz, in which case the terms AC and ~C pertain to the modulation envelope definillg each curve. In either case, the resulting tnagnetic Eield in the apparatus of Fig. 9 will nutate about a pointing axis 80 which is always coincident with the axis of the coil 64 as the AC signal in coil 66 produces an alternating magnetic field which adds vectorially to the magllctic field generated by the ~C signal in coil 64.
In l~ractice, an object having orthogonal sensing coils 52 and 54 mounted on it is free to mo~e anywhere in the plane defined by the axes of the coils. If the system is to track the ob.ject, generating coils 64 and 66 should ~054Z41 1 have the capability to gcnerate a magnctic field which nutatcs about a pointing vector 80, with a pcak-to-leak angular nutation amplitude 49, in W}liCh the pointing vector 80 does not coincide with the axis of coil 64. Such a magnetic field can be created by supplying the appropriate mixtures of the AC and DC signals to coil 64 and to coil 66.
As was described earlier, the amplitude 44 of nutation angle depends upon thc relative amplitude o~ thc re~erence DC and AC sources, 68 all~ 70, respcctively. Ihe angle that the pointing vector 80 makes with the the reference x-axis of the coil 64 is governed by the mixing process ~erformed by the resolver circuit or process suggested in the discussion relate~ to ~ig. 3, inserted in the leads 72, 74, 76 and 78 bctween sourcos 68 and 70, and coils 64 and 66, rcspec-tively. The resolver operates on the fixed rcfeTence DC and AC si~nals Erom sourccs 68 and 70, such tllat thc ~rocesscd signals receive~ rom the resolver for cxciting the ~enera-tor coils 64 and 66 now have the capability of dirccting the pointing vector 80 of the nutating field, at any desired angle A, tllrougll a full 360 degrees, in accordance with the equations Bxcitation of coil 64 = (DC)cosA - tAC)sinA
~xcitation of coil 66 = (AC)cosA ~ (DC)sinA
In order to provide sufficient information for tracking in a plane the position and the angular orientation o~ an object havillg sensing coils 52 and 54 mounted on it, the sense circuits 26 should have the capability to detect, after coordinate rotation processing of the signals induced in the sensing coils 52 and 54, the hC error. component in the pointing vector directioll and the DC error component in the directioll orthogonal to the pointing vector. The r.
~054Z~
I relative ~ s~ d ~m~ ld~ o~ tl)e .Ibove melltiotle(l ~(` erto is l~rol~ortional to the ~irection an~ magnitude Or the l~ointillg error. Ihe pol.lrity all(llllagnitude Or tl~e ahove mentiolled l)C error co~ ollent is l)roportio]lal to the direction arld magnitu~e Or the error in the compute~ orientatioll angle o-~ the remote object. These two error signals, WlliC]l are proportional to the angular error in the ~ointing angle and to the angular error in the relative orient~tion allgle o~
the object, resl)ectiveLy, are used to make corrections in the previous measure of these two angles. Ihe change in tlle pointing angle will s}lift the pointing veetor until the sensor coils 52 alld 54 lie along it, at which time the AC
error signal, measured in tlle direction of the pointing vector 8(), will be zero. Ihe indicated cl)ange re(luired in the orientatioll angle will im~rove or correct the eomputed orientatioll angle whicll represents tl~e relative eoordinate relationsl~ betwecll tl~e coordillate ~rame oC tl~e gellerator coils 64 and 66, and the eoordinate rame of the sensor eoils 52 an~ 54. If tllis relations}lip is prol~erly repre-sented in the signal proeessor, by tlle orientation angle resolver ~, then the DC error signal cleteeted in tlle direc-tion orthogonal to the l)ointillg vector 80, will be zero.
In summary, and witll added reference to ~:ig. 10, apparatus for eontinuously tracking the relative location or direction and the relative allglllar orientation between two indepelldent bodies in a ~ ne, is descril)e(l. Tlle re~erence coordinates oÇ the plane are de~ined hy the Y~-axis 84 and the Y-axis 86 which are coincidellt with the field generating coils 64 and 66, respectively. Both the translation and the orientation angles will be measured with respect to this reference 1054Z~l 1 coordinate ~rame. The sensor coils 52 and 54 are fixed to the rcmotely moving object, and thcir mutually orthogonal axes 90 and 92 de~ine the coordinate frame of the object to be tracked both as to location an~ orientation. In order to generate a nutating magnetic field pointe~ in a prescribed direction relative to the fixed coordinate frame of the generator coils 64 and 66, a particular mixture of VC and AC
excitation signals is rcquircd in each of the gcnerating coils. lhe resolver 102 processes the reference ~C and AC
excitation signals received on leads 104 ànd 106 from sources 68 and 70, respectively, in accordance with the presumed input pointing angle A 82, to give the appropri-atcly mixcd rosolvcr output cxcitation signals whicll are connccted ~y lcads 108 and 110 to the generator coils 64 and 66, respectively, such that tho pointing vector 80 and its attcndant nutating field structure makcs ~ho an~lc A with respect to the reference X-axis. lhe gencrated nutating icld points nominally at the sensor coils 52 and 54. The peak-to-pcak amplitude o~ the nutation 88 is fixed, usually 45 to 90 degrees, and depends upon the relative magnitude of the two fixed reEerence DC and AC excitation signals from sourccs 68 and 70. It is clear that the signals induced in tlle sensor coils 52 and 54 depend not only on the pointing angle A but also on the Telative orientation angle ~ 94. It is for this reason that tlle induced signals in coils 52 and 54 are connected by leads 112 and 114 to resolver 96 and to be processed by resolver 96 which removes or unmixes that part of the AC and DC mixing of the two signals that is attributable to the non-zero orientation angle ~ 94. The two output si.gnal components from resolver 96 arc connected by lca~s 116 and 118 to resolver 98 W}liCh further unmixes ~,o5424~
thc 1)(: an~l A(: si.g~ l s mixin~ that was ncccssary to achicvc the desired pointing angle A 82. If the presumed pointing anule A alld thc prcsumcd oricntatioll anglc ~ are corrcct, then t}-e out~ut components from resolver 98 will be totally unmixed. That is, there will be no AC modulation error on the nominal DC output signal 120 which indicates that there is no pointing error, and also there will be no DC component on the nominally AC signal 122 which indicates that the computed orielltatioll anglc is corcct. In the cvcnt that thc angles ~ and/or A are incorrect, as will be the case, since very small errors are expected, when operating under dy-namically changing circumstances, then sense circuits 26 will ~etect the AC and DC errors on lines 120 and 122, rcspcctively, relate them to crrors in the angles G and A, r~spcctivcly, and on leads 124 an~ 126 introduce the cor-responding incrcmctltal changes acculllulate~ by Anglc ~lea-suring Circuit 100, in thc respective angles. These im-proved angle measures of ~ and A are connected to the appropriate resolvers employed in this embodiment on leads 132, 134 and 136 in a stable feedback arrangement. That is, the corrections made in the outputs 128 and 130 tend to reduce the errors measured on components 124 and 126. These principles can l~c extended to ap~licatiolls in threc dimcn-sions by em~loying the system shown in ~igure 11.
As in the system of ~igure 10, the system of Fi~urc 11 illcludes magnetic field generating coils 64 and 66 and magllctic field sensing coils 52 and 54. ~ third magnetic field generating coil 158, which is mutually orthogonal to coils 64 and 66, and a third magnetic field.sensing coil 248, which is mutually orthogonal to coils 52 and 54, is provi(led in orcler to measure informat;on in the third ~054Z4~
l dimensioll. Ior easc of un~crstan~ing, thc thrce coils in eacll casc havc becn Sl10WII as spacillly separatcd In actuality, the maglletic axes Or both the ~cnerator coils and the sensor coils intersect in a mutually orthogonal rela-tionship as shown ~y the cartcsian coordinate framcs 84, 86, 160, and 90, 92, 170, respectively. It should also be noted tllat an additiollal AC reference excitation signal has been providccl such that ACl and ~C2 arc (luaclraturc rclatcd or 90 dcgrecs l~hasc related. T}lcy may be col~sidcrccl as sinusoids of equal amplitudc but 90 degrces out o~ phasc, althougll tlle two reference ACl and ~C2 signals need not necessarily be sinusoidal in the practical embodiment of the system.
Refer~nce is again made to ~ig. 4 whicll was related to the earlier discllssioll oE coordinate trans~ormation circuitry and wllicll shows the three dimension~l pointing ~eomctry. ~s in thc ~a~o oE thc two dimcnsional cml)odimellt SllOW1l in l~
10, tlle ability to l)oint the poillting vcctor 180 in any direction in W]liC]l tl-e assembly of sensing coils 52, 54 and 248 are free to move enables the sensing coils to be tracked.
Tlle reference excitation ])C, ACl and AC2 signals from sources 68, 70 and 140, respectively, define a conically nutating 164 mclgnetic field about a pointing axis 180 wllich is coincident with the axis of the DC component of the field. It should be emphasized again that the pointing of the vector 180 is accomplished electrically by the circuit to be described while the generating coils 64, 66 and 158 maintaill a fixed orientation pllysically. DC source 68 and AC2 source 140 are connected by leads 142 and 144, respec-tively, to resolver 220, whose output lead L48 and output lead 146 from ~Cl source 70 are connected to resolver 222.
Ihe output leads 154 and 156 provide the excitation signals r ~OS4Z41 1 from resolvcr 222 to generator coils 64 and 66, resl)ec-tively. Generator coil 158 is excited through connection 152 fro]n the output of resolver 220. The two angles A and B
of resolver 222 and 220, respectively, are thus operating on the refcrellce nutating field vector input whose components are the reference excitations from sources 68, 70 and 140, so as to point the pointing vector 180 and its attendant nutating field structure in accordallce witll the geometry shown in ~ig. 4. rhe pointing vector 180 is presumed to be pointing nominally at the sensor whicll is fixed to the remote o~ject to be tracked by the system. This sensor con-sists of the three mutually orthogonal sensor coils 52, 54 and 248, which are fixed to the remote object and in the preferrecl elllbo~iment are aligned to the prillcipal axes of the remote object, so that in the proeess of determining the orielltation Or the sensor triad the orientation of the remote object is therefore determined. ~s in the diseussion of the two ~imensional ease, illustrated in ~ig. 10, the signals in~uce~ in the sensor coils 52, 54 an~ 248 ~epend on the orientation of their sensor coordinate frame, definod by the mutually orthogonal coordinate axes 90, 92 and 170, relative to the pointing axis 180 and its two orthogonal nutation components of the nutating field. In other words, tl-e particular mixing of the three reference excitation signals DC, ACl, and AC2 from sources 68, 70 and 140, indueed in eaell of the three sensor coils 52, 54 and 248, depell~ls not only upon the two pointing angles A and B which govern the composite pointing coordinate transformation circuit 252 but also upon the three Euler angles defining the relative angular orientation of the remote object and which govern the composite orientation coordinate trans-~054Z41 1 Lormation circuit 250. '~`he principal function of thc two coordinate transformation circuits 250 and 252 in the overall computatiollal stratcgy of thc system is th~t the transformation circuit 250 unmixes that part of the re-ference signal mix induced in the sensor coils attributable to the relative orientation of the remote object, and coordinate trans~ormation circuit 252 unmixes the remainin~
part of tllc rcfere]lce signal mix that was dlle to the pointing angles. I~ tlle thrce oricntatioll all~les defining coordinate transformation circuit 250 and the two pointing angles definin~ the coordinate transformation circuit 252 properly represent the physical relationship between the sensor and generator coordinate frames, then the si~nals sense~ by the scnse circuits 26 will correspond to the unmixed re~erence signals DC, ~Cl and AC2, respectively, ~rom sources 68, 70 an~ 140.
Ihe sensor coils 54 and 248 are connected to resolver 224 by leads 168 and 172, respectively. The output of sensor coil 52 and one output from resolver 224 connect to resolver 226 by leads 166 and 174, respectively. One output from resolver 224 and one output from resolver 226 connect to rcsolver 228 by leads 176 and 178, respectively.
Tlle two outputs ~rom resolvcr 228 are connected to resolver 230 by leads 186 and 188, respectively. One output from resolver 226 and one output ~rom resolver 230 connect to resolver 232 on leads 184 and 190, respectively. One output fronl resolver 230 and the two outputs from rcsolver 232 provide the processcd signal inputs to sense circuits 26 by connections 192, 194 and 196, respectively.. Sense circuits 26 operates on the three in~ut signals provided by leads 194, 192 an~ 196, to sense deviations from their nominally l correct valucs which shoul~l corrcspon~ to thc reEcrcnce excitation signal components 68, 70 and 140, respectively.
lhe signal sense~ on le~d 194 should be nominally l)C. If lead 194 contains an AC crror signal at the nutation fre-quency then a l)ointing error exists, that is, the ~ointing vector 180 is not pointing l~recisely at the sensor coils 52, 54 and 248. T]lat portion of the AC error signal, cletcctc~
on lcad 1~4 that is oE the samc al~solute p]lase as the excitation sig~ 6, is ~ro~ortiollal to an crror in the pointing angle ~. This pointing anglc error in ~ is con-nected to thc anglc measuring circuits 100 by lea~ 200.
'rhat portion of thc AC error signal detecte~ on lea~ 194 that is of the same absolute phasc as the cxcitation signal 1~4, is l~lol~o~tionaL to an crror in the poillting iangle ~.
'I'his detectcd crror in pointing an~lc 13 is connccted to tlle anglc nlc.lsuring ~ircu;it~ lO0 l~y Load 2()2. 'I'ho si~n.ll that apl~cars on lea~ 192 shouLd bc nominally ~(: .It the nutation ~re~ucllcy and no I)C signal. Whatevcr ~C sigllal appcars on lcacl 192 is proportional to an orientation angle error in the angle ~, called the relativc bearing anglc. This detected error in the rclative bearing angle ~, is connected to the angle mcasurillg c;ircuits by leacl 208. 'I'hc signal that appcars on lcad 196 should also bc nominally ~C at the nutatioll frequency and should contain no DC. Whatever l)C
signal is present on signal lead 196 is proportional to an crror in thc rclative orientation anglc ~, calle~ the relative clcvation anglc. Tllis crror in thc rclative elevatioll angle ~, is connected to the angle measuring circuits 100 by lead 206. As mentioned above, the nominal signals alpearing on leads 192 and 196 are not only char-acterize(l as beillg ~C at tl-e nutation frequency but also `` lOS~Z41 (iu.l(lrut;urc lCJ<ltC(I lS <lrc tllc~ir no~ rcrcrcll~C Si~
counterparts ~Cl and ACZ. ~loreover, whatever phase dif-ference exists betl~een the signal on lead 192 an~ signal source 70, or alternatively, wllatever pllase ~ifference exists between the signal on lead 196 and signal source 140, is proportional to an error in the relative orientation an~le ~, calle~ the relative roll angle. lhis error in the relative roll angle ~, is conllecte~l to the allgle measurillg circuit 100 by lcad 204. Ihe function of the an~le measuring circuits 100 is to ~rovide correct or correcte~ measures of the two pointing angles A an~ B on lea~s 210 and 212, respectively, base~ upon the angular errors sense~ by sense circuits 26. ~notller functioll oE the angle measuring circuits 100 i5 to provi~e correct or corrected measures oE
~he tllrèe relative orientatioll anglQs ~, ~ an~ ~, on lea~ls 214, 216, an~ 218, res~ectively. 'I`hese continuously im-proved angle measures, appearing on leads 210, 212, 214, 216, 218, are connected by leads 234 and 240, 236 and 238, 246, 244, 242, to resolvers 222 and 230, 220 and 232, 224, 226, 228, all respectively, in a stable feedback arrange-ment. That is, the corrections made in tlle respective angles by tlle angle measuring circuits 100 tend to reduce to zero the error signals ~etecte~ by sense circuits 26 a~pearing on leads 194, 192 and 196.
It shoulcl be pointed out that the sequence of angles an~ tlleir corresponding axes of rotation, for both the pointing coordinate trans-formatioll circuit 252 and the relative orientation coordinate transformation circuit 250, are not unique. Tllat is, other angle definitions and rotation sequences can be used for either of the two trans-fOrmatiOIIs S-lbj ect to their having the require~ pointing and ~054241 1 relativc oricntation ~r~e~om.
It should be pointed out that the system here described can use state-of-the-art tech-niques using digital, analog or hybrid circuitry.
It sllould also be pointed out that whcrcas the des-cribed system mi~ht be also regarded as a unique five degree-of-frccdom transducing system between two remotely separated independent coordinate frames, employing only one generating sourcc in onc of tllc coordillate ramcs alld only one sensor in the other coordinate frame, the system can easily be extended to provide a measure of the full six de~rees-of-freedom by usinS two generating means. 'Ihe second generating mcans would or could be located at another point in thc coordinate framc of the first generating means, operating cooperativcly with the first ~encrating means on a time shared basis, thereby allowing thc thir~ translation coordi-nate, that o~ relative range, to be detcrmined by trian~u-larization, using the same computational techni~lues employed in the invention.
It should also be emphasized that the teachinq herein applies to a wide range of applications operable in domains fronl a few cubic feet or less to applications operable in domains of several cubic miles.
In the discussion above it is to be understood that the sense circuits 26 are internally supplied with the components of the reference excitation signals from sources 68, 70 and 140 in order to logically perform the discrimi-nating sensing function required of their sensing circuits 26.
The resolvers which form components of-the circuitry described herein may be fabricated, by way of example, in 105~Z41 1 accordal-ce witll the teaching~ of llnited states I'atent No.

3,187,169, entitled l,L~CTRONIC RESOLV~R, issued June 1, 1965 to Robert I). Irammell, Jr. and l~obert S. Johnson, and United States Patent No. 2,927,734, eIltitled CO~II'UTING SYSTE~1 ~OR
ELECTRONIC RESOLVIR, issued ~larch 8, 1960 to Arthur W.
Vance. The sensing circuits, again by way of example, may be fabricated in accordance with the teacl-ings of a circuit ~iagralll a~ e.lring at p.lgC 67 Or tl~e hook entitle~ "Ilec-tronics (ircuit I)esigners ~asehook", publisl~e~ by Ilec-tronics, ~IcGraw Ilill, No. 14-6. The angle measuring cir-cuitry may take the form of any o~ a vast number of well-known Type I Servomechanisms. There are, of course, numerous alternate constructions available Eor each o~ tllese com-ponents as will be readily appreciatecl by those skille~l in the art.
I~ slloul~l now be apl)arent that n romote objeet tracking an~ orientation ~etermination system eapa~le of attainlng the stated objeets has been l~rovided. Tl~e system and proccss described utilizes a field for the purpose of determining tracking and orienta-tion angles of a remote object very precisely relative to the coor~inate frame o~ the apparatus wl~ich generates the field. With a two--limensional nutation of the generated fiel~, the tracking and orientation angles of the remote object in the plane of nutation may be determined. With a three-~IimeIlsional nutatioIl, the direction to and the orienta-tion oE a remote object may be determined.
It will be appreciated by those skilled in the art, additioIlally, that (a) the raw output ~rom the angle measuring circuitry will be useful in certain situations in an open looped system although ordinarily, for ~, ~ and ~ to .

~OS~Z41 1 l~C accur~tc, tllC gCIlcrator mll~t bc poillting ~ircctly at the sensing mcans; an~ (b) absolute location and orientation (including distance) of an object rclative to the reference source can be ~etermincd by utilizing two physically dis-placed generators such as that shown in Fig. 11 Wit]l appro-priate receivillg and output circuitry at the object.
While a system has becn dcscribcd in dctail for trackillg the movcmcllt and all~ular orienta-tiOII of a gcncralizc~ rcmotc objcct, it shoul~ bc rcadily apparent to one art-skilled that the disclosu~ may be use~
in a variety o~ object locating, tracking and orientation angle determination applications. One apl)lication currently in ~cvclopmcnt is tracking thc move1ncnt and oricntation o~
an obscrvcr's l~ead, or more specifically, his line-of-sight ~or use in a Visually-Coupled-Control Systcm. Othcr potcn-tial applications: a two-dimcnsional sy~tom might be employed with surface modes of transportation, such as in the dockin~ of sllips or maintaining proper distances betwcen passel-gcr cars in an automated public transportation systcm.
Other aircra~t navigation problems suitable for handling Witll the invcntion inclu(le airborne alignment of missle systems, automated coupling of boom-nozzle alld receptacle for in-~ligllt refuelling oE aircraft, ~ormation flyin~, instrumellt landing of vertical take-off and landing craft, and the like.
While the above description treats preferred eml)odimcllts Or thc inventioll, it should bc rca~ily .Ipp.lrcnt that a variety of modifications may be madc in the systcm and process within the scope of the al)pcnded claims.

Claims (4)

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:

1. Apparatus for generating a nutating electromagnetic field which comprises:
a) orthogonal radiators adapted to pass a current;
and b) means for supplying the appropriate mixture of signals from three sources, supplying a DC signal, a first AC
signal and a second AC signal in phase quadrature with the first AC signal, respectively, to the three radiators such that the electromagnetic field produced by the currents in the three radiators is caused to nutate about an arbitrarily directed pointing vector of the field.

2. Apparatus for generating a nutating electromagnetic field which comprises:
a) at least two orthogonal radiators adapted to pass a current; and b) means for supplying the appropriate mixture of signals from sources supplying a DC signal, and a first AC
signal, to the radiators such that the electromagnetic field generated by the currents in the coils is caused to nutate about an arbitrarily specified pointing vector of the field.

3. The apparatus of claim 2 in which the excitation signals cause the field to nutate in a nodding motion in a plane defined by the axes of the two radiators excited.

4. The apparatus of claim 2 in which there are three radiators and in which the signal source also supplies a second AC signal in phase quadrature to the first AC signal; and means for supplying the appropriate mixture of each of the three source signals to the three radiators whereby the magnetic field is caused to nutate in a conical manner about an arbitrarily but specifically directed pointing vector of the field, the apex of the cone being at the intersection of the generating coils.