CA2124180A1 - Acoustic digitizing system - Google Patents

Abstract

ABSTRACT

An acoustic position sensing apparatus is described which determines the position of an indicator in relation to a datum surface or volume. The apparatus comprises an acoustic point source transmission device mounted on the indicator for transmitting a sequence of periodic acoustic oscillations, and a plurality of acoustic point receivers positioned about the datum surface for receiving the acoustic oscillations. Comparators are connected to each acoustic receiver for converting the received acoustic oscillations to square waves having logical up and down levels. A register or other time determining circuit is coupled to each comparator and receives at least a leading portion of a square wave and provides an output if it determines that the portion exhibits one of the aforesaid logical levels for a predetermined time duration. A processor is responsive-to the outputs from the registers to find the position of the indicator.

The acoustic point source transmission device is configured both as a linear stylus and as a planar "puck", both having at least a pair of acoustic transmitters. The apparatus employs, for two dimensional position detection, at least three acoustic receivers arranged in a non-linear fashion. A three dimensional position detector system is described which employs four receivers, three of which are oriented in one plane and a fourth in another plane.

Description

~ 21241~0 I. GILCHRIST

ACQUSTIC DIGITIZING_SYSTEM
The present application is a Division of Canadian APplication Serial No. 2!024,527 filed Septemher 4!
1990.

FIELD OF THE INVENTION
This invention relates to an apparatus for locatin~ a point in either two dimensional or three dimensional space and, more particularly to an acoustic position sensing apparatus.

BACKGROUND OF THE INVENTION
Acoustic position locating systems are well known in the prior art. Some systems employ a pointer having a spark gap incorporated into its structure. The spark gap generates an acoustic si~nal which is propagated to orthogonally oriented, linear microphones. The arrival of the spark acoustic signal at a microphone is detected by an amplitude discrimination circuit and then passed to a timing circuit which compares the time of arrival of the signal with the time of the signal's ~eneration, to thereby achiev~ a range determination. Spark-acoustic position determining systems are disclosed in U.S.
Patents 3,838,212 to Whetstone et al.; 4,012,588 to Davis et al.: 3,821,469 to Whetstone et al.; 4,357,672 to Howells et al.; and 3,731,273 to Hunt.

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212A~80 Spark-based acoustic ranging systems exhibit a number of disadvantages. The generated spark creates both possible shock and fire hazard, makes an audible noise which is, at times disconcerting, and creates electromagnetic interferenCe. Further, since the spark generates a shock acoustic wave, its detection is dependent upon the accurate ~ensing of the leading edge of the wavefront. Due to changes in amplitude as the spark source is moved relative to the microphones, and further, due to the wavefront's non-linear rise time, accurate sensing is difficult to implement reliably.
In fac~, systems which employ sparX gap ranging exhibit a limited distance resolution specifically due to the detection problems which arise from the use of a shock : . :. .
acoustic wave.

A further class of acoustic wave position determining systems employ emitted, periodic, acoustic signals for ranging purposes. For instance, in U.S. Patent ~,504,~34 to Turnage, Jr., microphone receivers of the bar type are oriented alon~ X and Y axes, and measure the propagation time of an acoustic signal from a measuring point to the respective receivers. The measured times are converted to minimum dis~an~es between the measuring point and the respective receivers, thereby enabling the coordinates of the measuri~g point to be determined. Bar-type microphones, (used by the Turnage, Jr.) are both expensive and are difficult to apply to limited-size position determining sy~tems (e.g. desk top size).
Furthermore, th¢ accuracy o* ~ystem~ which employ bar-type microphone~ depends on the uni~ormity of the emitted acoust~c wave~ront, and if there is any 2~2~1~0 a~erration in the wavefront, :Lnaccurate range measurements result.

Another patent which employs bar-t~e microphones is 4,246,439 of Romein. Romein employs a pair of acoustic transmitters mounted on a stylus, ~hich transducers enable the precise position of the stylus tip to be determined.

Others have attempted to overcome the above-stated problems by employing d~screte point microphone receivers. In U.S. Patent 3,924,450 of Uchiya~ et al., a three dimensional acoustic range determining system is broadly described and includes three microphones placed about a ~ur~ace to be digitized. A
stylus having two acoustic sources is used to point to various points on the 3-D surface. Signals ~rom the stylus are received by the microphones and analyzed to determine the digital position o~ the sur~ace point.
Little detail is given o~ the measurement method employed by Uchiyama et al.

Another acoustic point digitizer employing a wireless stylus or puck is de~cribed by Herrington et! a~. 'in U.S. Patent 4,654,648. In that system, a stylus emits acoustic ~ignals ~nd a linear array o~ microphones receive3 the signals and determines the position o~ the stylus by hyperbolic triangulation. ~err.ington et al.
uses point source ~coustic transmitters which enable uni~orm transmission patterns to be achieved. ~he measurement techn$que employed by Herrington et al.
that the output ~rom the sensing microphones be - selectively 8witched to ~eed ~nto a detectox circuit, which circuit in addition to including a zero crossing 21~180 detector, also samples and holds the value o~ peak amplitudes of each cycle. This data is used to determine range lnformation and ~rom that, to obtain positional triangulation o~ the acoustic transmitter.
While the Herrington et al. system overcomes many prior art problems, its use of a linear array of microphones;
the switching o~ the microphones; and the sampling of the input signals to determine instantaneous amplitudes all present problems which lead to an unnecessarily complex and expensive system.

Accordingly, it is an object of this invention to provide an acoustic position determining system which provides improved position accuracy and detection.
It is another object o~ this invention to provide an acoustic position digitizing system which is not dependant upon the amplitude of a received acoustic signal;
It is still another object of this invention to provide an acoustic position determining system which enables arbitrary positioning of acoustic r~ceiving units.

It is another obj ect of thls invention to provide an acoustic position determining 6ystem which is easily calibrated.

It is a further ob~ect of this invention to provide an acoustic positi~n digitizing system which employs an open-loop signal processing element ~or determLning the time o~ arrival o~ an acoustic signal.

212~1~0 SUMMARY OF THE INVENTION

An acoustic position sensing apparatus is described which determines the position o~ an indicator in relation to a datum surface or volume. The apparatus comprises an acoustic point source transmission device mounted on the indicator for transmitting a sequence of periodic acoustic oscillations, and a plurality of acoustic point receivers positioned about the datum surface for receiving the acoustic oscillations~
Comparators are connected to each acoustic receiver for con~erting the received acoustic oscillations to square waves having logical up and down levels. A register or other time determining circuit ls coupled to each comparator and receives at least a leading portion of a square wave and provides an output if it determines that the portion exhibits one of the aforesaid logical levels ~or a predetermined time duration. A processor is responsive to the outputs grom the registers to find the position of the indicator.
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The acoustic point source transmission device i5 configured both as a linear stylus and a~ a planar "puck", both having at least a ,pair of lacous~ic transmitters. The apparatus employs, for two dimens~onal position detectlon, at least three acoustic receivers arranged in a non-linear fashion. A three dimensional position detector system is described which employs four receivers, three of which are oriented in one plane a~d a.fourth ln another plane.

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BRIEF_DESCRIPTION OF THE DRAWINGS

Fig. 1 is a schematic diagram of the invention as it is employed to determinQ thQ position o~ a point in a two dimensional space.

Fig. 2 is a schematic diagram of the invention employed to determine the pGsition of a point in a three dimensional space. -~

Fig. 3 is a diagram indicating how the acoustic receivers, shown schematically in Fig. 2, may be positioned to properly receive the emitted acoustic signals from a stylus or puck.

Fig. 4 iS a section view of an acoustic point source -~
transmitter.
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Fig. 5 is a front view o~ the transmitter of ~ig. 4.

Fi~. ~ is an acoustic diagram helpful in understanding the operation of the acoustic transmitter of Fig. 4.
", Fig. 7 i~ an explod~d view of an acoustic receiver ~ -employed by the invention.

Fig. 8 is a plan view o~ a puck with a pair of acoustic transmi~ters mounted thereon.
, Fig. 9 is a block diagram of the position detection circuitry used by the invention.

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212~0 Fig. 10 is a schematic block dia~ram o~ a pre~erred signal detector for sensing the "front porch" of a recPived acoustic signal.

Fig. 11 is a schematic block diagram of another signal correlation detection circuit which is more resistant to noise than the circuit of Fig. 10.

Fig. 12 defines the points used in the two dimensional position determination mathematics.

Fig. 13 shows an a~rangement ~or calibration o~ the invention.

Fig. 14 defines the points used in the three dimensional position determination mathematics.

Fig. 15 shows the placement of an additional ~caling transmitter used for mea~urement correction.
DETAILED DESCRIPTION OF THE II`~VENTIoN

Referring now to Fig. 1, a rectangular two dimensional workspace lO is is defined by its X and Y bounda~i~s.
Work space 10 may contain a drawing, a planar construct or some other planar arrangement whose points are to be digitized, ~or either dlsplay on a computer terminal or for torage in a computers memory. Three acoustic receivers 12, 14, and 16 are arrayed about the perimeter o~ work~pac~ 10, with each being connected to a two dimensional position dete¢tion circuit 18. Whil~
acoustic receivers 12, 1~, and 16 may be placed arbitrarily about work~pace lO, the one constraint i5 ' :, ~ - ;

, , ~ " ~ - , ; , ,, ;., ~ , 212~i~0 ~ -. .

- that they should not be placed along a single line.
The reason for this will become apparent hereinbelow ~-A stylus 20 is adapted to be moved by a user so that its pointed end 22 touches a point in workspace 10 to be digitized. A pair of acoustic point source transmitters 24 and 26 are mounted on stylus 20 and are oriented along a line 28 which also intersects pointed end 22. Stylus 20 is connected to 2-D position detection circuit 18 via conductor 30.

Broadly stated, the operation of the system of Fig. 1 is similar to the prior art in that acoustic point source transmitters 24 and 26 emit bursts ~f periodic acoustic oscillations which are sensed by acoustic receivers 12, 14, and 16. By determining the time of arrival of the acoustic signals, the 2-D position detector` 18 is able to determine the position in workspace 10 at which point end 22 of stylus 20 is pointed. Furthermore, by properly analy~ing these -~
signals, the orientation o stylus 20 can be determined.

As aforestated, two dimensional position detection,h~s been accomplished heretofore, in its most simple form, by employing a pair o~ acoustic receivers. This geometry has led to a nu~ber of disadvantages. First, the Y coordinate value was subject to larger error deviations than the X coordinate value because the Y
coordinate value was calculated from a combination of a slant range and the X coordinate value. ~ny errors associated with the X coordinate value thus combined with errors arising ~rom the measurement of the slant range. Furthermore, a squiare root ~unction, needed to ,, :

212~80 determine the Y coordinate, did not allow for its sign to be determined. As will be understood below, the use of three acoustic receivers completely avoids the aforestated problems.
In Fig. 2, the acoustic position digitizing system is shown, as modified for three dimensional point determination. In this case, workspace 32 is three dimensional and is bounded by X, Y, and Z coordinates.
The stylus employed is identical to that shown in Fig.
l; however in this case, four acoustic recelvers 34, 36, 38, and 40 are arrayed around workspace 32. Each receiver is arranged so that it is capable of receiving acoustic signal emanationS from either of point source transmitters 24 or 26. Acoustic receivers 34, 36, and 38 are arrayed in one plane whereas acoustic receiver 40 is positioned in a different plane. Outputs from each of the aforestated receivers are fed to three dimensional position detection circuit 42.
In Fig. 3, a pre~erred mounting arrangement for each of acoustic receivers 34, 36, 38, and 40 is shown. All of the receivers are supported by head 44 which is, in turn, mounted at an end of cantilever ~eam 44. Ea~h'of the receivers is attached to a connecting post 48 which provides ~oth mechanical support and electrical connection to the position detaction clrcuitry.
Receivers 34, 36, and 38, are arrayed in plane 50 while receiver 40 is displaced there~rom. This enables the receiver array to ~e arbltrarily located w$thout degradation o~ calculated coordinate values due to slant range distance from the array plane. This arrangement also avoids the problems which were inherent in previous three dlmensional acoustic array ~ .

212~1~0 sensing systems which employed only three receivers.
In those systems, the Z coord~na~e was susceptible to larger error devlations t~an the X and Y coordlnate values as it was calcula~ed ~rom a slant range and the X and Y coordinate values. Any errors associated with - the X and Y coordinates a~ded to errors due to the measurement of the slant range and thereby contributed to less than desirable accuracy. Sensors 34, 36, 38, and 40 provide independent X, Y, and Z coordinate measuremen~s so that errors do not accumulate for the Z
coordinate.

Referring now to Flgs. 4 and 5, the 5tructure o~ an acoustic point source transmitter is shown. Each acoustic transmitter comprises a conical resonator 60 which is mounted on a piezoelectric actuator 62. Both resonator 60 and piezoelectric actuator 62 are mounted on a pedestal 64, and the actuator i5 connected to pins 66 and 68 via conductors 70 and 72 and thence to pulse source 77. The transmitter structure is mounted in a houslng 74 which ~6 provided with a ~aceplate 7~ (see Fig. 5). An opening 78 is centrally locate~. in faceplate 76 and provides a "point ~ource'7 effect for the acoustic emanation~ produced by piezoele~t~ic actuator 62 and re~onator 60. Th~ diameter d of opening 7~ involves a trade o~ between em$tted power and wave front beam width.

As can be seen from Fig. 6, when piezoelectric actuator 62 is energized, it creates an acoustic wave~ront ~0.
When wavefront 80 pass~s through opening 78, assuming opening 78 is ~uf~iciently small, the transmitted wave~orm assume~ an omnidlrectional wavefront 82 due to di~fraction beam-width formation. However, if opening .

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2~241~30 7~ is made too small, the power of the transmitted acoustic signal ls greatly constrained. On the other hand, if it is made too large, wave~ront 82 is distorted with poor side lobe beam pa1:terns. From the system standpoint, it is most desirable that wavefront 82 be as close to omnidirectional as possible so the diameter d o~ opening 78 is made as small as possible.

To overcome the power reduction created by a minimum diameter opening 7a, it has been found that piezoelectric actuator 62 can he pulsed with high voltage pulses while still re~aining within the allowable power dissipation limits of the actuator.
one piezoelectric actuatar which is commercially àvailable from the Panasonic Corporation, when energized, provides a 40 kHz output frequency. Its specifications call ~or a maximum voltage rating o~ 20 volts for continuous opera~ion. It has been ~ound that by app~ying a 300 volt pulse for lOO microseconds, at a repetition rate o~ one pulse every five miliseconds, that the output tra~smitted acoustic energy can be substantially increa6ed without creating damage to actuator 62. Furthermore, the application of this extremely high energizing potential creates a b~t~er 2S omnidirectional beam pattern and improved amplltude signal levels. It has been ~ound that if the applied voltage pulse level to actuator 62 i8 reduced, the beam pattern degrades and the amplitude o~ the trans~itted ` acoustic signal drops. Thu~, it i~ preferred that the level o~ the app~lied voltage pulse and ~ts duty cycle be such that it not exceed th~ maximum power ratlng of the actuator, but that the voltaye be such that it substantially exceeds ~he appli~d voltage ratLng of the device. It ~hould be under~tood that the above-noted 212~180 values are merely exemplary and that the values employed with actuators ha~ing differirlg specifications will vary in accordance with the above teachings.
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Referring now to Fig. 7, an exploded view of an acoustic receiver is shown. The acoustic receiver comprises an electret membrane 90 mounted on an electrode ring 92. A rear electrode plate 94 is mounted ~ehind the front electrode ring and the entire structure is contained within housing 96. While not shown, a ~ield effect transistor i5 connected to one o~
the electrode plates to amplify the signal created by the movement of membran~ 90 in response to a received acoustic signal. A face plate 98 having an opening 100 is positioned over the receiving structure. As with the acoustic transmitters, opening loo provides a "point source" reception capability. The operation of the receiver is conventional and wlll not be ~urther descri~ed.
Referring now to Fig. 8, an alternative position encoder is shown in lieu of stylus 20 (see Fig. 1).
Position encoder 101 (hereinafter called a "puck") comprises a housing 102 which has an aperture 1~4 in which a pair of crosshair~ 106 and 108 are posltioned.
Crosshairs 106 and 108 may be embedded in a transparent glass or poly6tyrene that enables a user to see the underlying workspace and to precisely position crosshair point 110. A pair o~ acoustic transmitters 112 and 118 are~centered along a line coincident with crosshair 106 and are equidistant from crosshair point 110. A depresslbl~ select$on bar 120 enables a user to provide an output pul~ on line 30 when crosshair point 110 is positioned over a surface point to be digitized.

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2124~0 As is well known, the puck 101 ls placed ~lat on a workspace (e.g. workspace 10 ln Fig. 1) and is moved thereabout to position the crosshair point 110 over a surface point to be digitized, at whic:h time, the user depresses ~ar 120 and causes the transmitters 112 and 118 to emit pulses of acoustic energy to receivers positioned about the workspace.

In Fig. 9, a block dlagram is shown of the circuitry employed to determine the range from one or more acoustic transmitters to ~he aaoustic receivers and to then process that range information to arrive at a digitization of a point in the workspace. All circuitry shown in Fig. g is under control o microprocessor 200, however the contrsl lines have been omitted to avoid unnecessarily complicat~ng the diagram. The circuitry of F~g. 9 implements the 3-D
position detector 42 shown in Flg. 2 Acoustic point source transmitters 24 and 26 are alternately pulsed to generate periodic acoustic signals which are txan~mitted towards acoustic receivers 34, 36, 38, and 40. Each acoustic receiver feeds an independent circuit which comprises !a frdnt end receiver/comparakor 202, a ~ignal detactor 204, and a counter and latch 206. whllQ these independent ~ignal chains are not shown separately on Fig. 9, lt is to be understood that ~ront-end receivers/comparators 202 contains ~our separate front-end receivers, comparators, signal detectors, etc.

Thus, a received acoustic sig~al is passed from its acou~tic reaeiver (~.g. 34) to a~ as~ociated ~ront end receiver Z02 where it ls ampll~ied and applied to a .' ` ': "" ': .,, .. ~ . ': : . ' ' .

21241~0 1~

comparator The comparator (also sometimes called a zero crossing detector) is an analog circuit which outputs a high logical level when its analog input traverses in a positive going direction past a reference voltage and it outputs a down level when its analog input ~raverses in a negative going direction past the reference voltage. In essence, therefore, the comparator is a wave shaper which converts an analog burst of period acoustic oscillations to a series of square waves whose positive and negative going transitions are coincident with the positive and negative going transitionS of the analog signal.

Signal detector 204 receives the square wave output from the comparator and both detects the leading edge of the first square wave (or a subsequent one) and determines that it is, in fact, a portion of a cycle from a received acoustic signal. Assuming that the signal is identified as an acoustic signal by detector 204, a stop pulse is generated to a counter and latch circuit 206. Previously, microprocessor 200, via multiplexer 208 and transmitter drivers 210 caused acoustic transmitter 24 to emit an acoustic signal. At the same time, a clock signal was applied from c~o~X
212 to a counter in counters and latches 206. When that counter receives a pulse "stop" signal from signal detector 204, it stops the count and enters it into a latch whose output is, in turn, fed to microprocessor 200. That count is then used by microprocessor 202 to determine the slant range o~ acoustic transmltter 24 from acoustic receiver 34. The range circuits associated with each of acoustic receivers 36, 38, and 40 act iden~ically to that above described.

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212~180 Multiplexer 208 causes transmitter drivers 210 to alternately apply energizing pulses to transmitters 24 and 26 so that the slant range to those transducers can be alternately detected and calculated. Additionally, S a correctlon transducer 212 is provided which, prior to each range measurement, sends out an acoustic signal which is sensed by acoustic receivers 34, 36, 38, and 40 and is subsequently processed to determine the slant range to the correction transmitter. The position of transmitter 212 is fixed so that microprocessor 200 is able to derive a correction factor from that range measurement. That correction factor is used to alter a subsequent measurement to take lnto account any atmospherically induced changes in the transmitted signal's transit time.

Referring now to Fig. 10, a preferred signal detector circuit is illu~trated. The circuik in Fig. 10 is designed to detect the "front porch" of the ~irst positive going hal~ cycle of a received signal from receiver/comparator c~rcuit 202. The detector circuit comprises a serial shift register 250, each o~ whose stages has an output which ~eeds into a multiple input NAND gate 252. ThP output o~ NAND gate 252 re~lec~s'an up level on line 254 at all times except when there is a "one" bit ln each stage of ~hi~t register 250, at which time its output on line 254 ~alls. A shlft clock is applied via conductor 256 to ~hift register 250 and steps input signals appearing on line 258 into the register.

I~ it i~ assumed that wave~orm 260 evidences the in~ially ~ransmittsd ~ir8t half cycl~ Sro~ s~ylu~ 20, and that a resulting received signal 262 is impressed 21241~0 on line 25~, it can be seen that the voltage levels shifted into shift register 250 will rlepresent waveform 262. Assumlng that there are su~icient stages in shift register 250 to hold only a portion of a half cycle ~f wave~orm 262, all stages thereo~ will reflect the "one" state, a determined number of shi~t clock pulses after the arrival of the high state 263 of waveform 262. When all stages of shift register 250 evidence the "one" level, NAND gate 252 drops its output. That drop in output causes a counter in counters and latches 206 to cease counting, with the count indicative, after processing, o~ the time of transmission o~ a transmitted signal between an acoustic transmitter and receiver.

If the number o~ stages in shift register 250 is sufficient to handle a full hal~ cycle of waveform 262, then stop pulse 264 on line 254 will be as ~hown, with its duration equal to the duration of one shi~t clock pulse. If the capacity shift r~gister 250 is less ~han the duration of hal~ cycle of input signal 262, then stop pul~e 264 will exhibit a down level until the first zero appears in shl~t register 250. In e~ther case, it i~ the leadlng edge of stop pulse 264! WhlCh causes the associated counter to cease its ~ount.

Microprocessor 200, knowlng the number of shift pulses required to fill shift register 250, converts that number to a time and subtracts it from the time indicated by the counter and thus obtains a direct indication of the ti~e o~ signal transmission between the acoustic receiver and tran5mitter. The circuit of Fig. 10 therefore, detects the hal~ cycle wave~orm 262 2~2~0 and determines that it is, ln fact, a signal from an acoustic transmitter.

While the signal detector ln Fig. 10 ~s implemented with a shift register, ~t ls to be unclerstood that any circuit which is capable of determining ~he presence of a return signal from incoming noise may be employed, assuming that it is reasonably economical to implement.
For instance, a counter can be substituted ~or shift re~ister 250, with the input signal's "front porch"
being used to gate stepping pulses into the counter.
When the predetermined count is reached, the presence of a return signal i5 confirmed and a "stop" pulse generated.
If a noise signal is received, and its duration is equal to or longer than the duration o~ shi~t register 250, an erroneous range output wlll occur. Thus if the invention is to be operated in a noi~y environment, a somewhat more costly, less noise susceptible circuit for noise detection i desirable and is shown ~n F~gO
11. . ' :

In Fig. 11, serial shift register 300 has, for ex~m~le any purposes, a suf~icient nu~ber o~ stages to contain an entire full cycle of a received acoustic signal when it ls clocked by shift clock over line 302. The system o~ Fig. 11 will also ~unction i~ shift regi6ter 300 includes enough stages to contain either less than or more than one cycle of a received acoustic signal.

A received signal is i~pressed upon input line 304 and - its levels are shlfted into shift regi5ter 300 as they are received from the receiver/comparator circuit 202.

212~0 lB

A replica o~ the transmitted (reference) signal is permanently fixed in reference reglster 306, with register 306 having an identical number of stages as shift register 300. At each shift interval, the levels S ln the corresponding stages of seria]. shi~t register 300 and reference register 306 are compared in a mod 2 adder circuit. For instance, the level in stage 30~3 is fed via line 310 to mod 2 adder 312 and the level from re~erence register stage 314 fed via line 311 to mod 2 adder 312. There is one mod 2 adder for each pair of register stages and, at each shift time, their outputs are collectively ~ed to a chain of accumulators ~16, which accumulators provide a sum of the resultant signals to peak detector 318.
Those skilled in the art will recognize that the circuit shown in Fig. 11 bears a resemblance to a correlation circuit which correlates the wave shape of a received signal on line 304 to the wave shape o~ a reference ignal stored in regi~ter 306. As the recPived signal begins to shift into shift register 300, the sum value ~rom accumulators 316 starts to increase as shown by waveform 320. When the received signal is fully present in shift register 300 (in ~h~se with the signal levels in re~erence règister 306), the level from accumulators 316 reaches a peak 322 (waveform 320) and then begins to decrease as the received signal shifts ~urther through register 300.
Peak 322 is detected by peak detector 31B which provides a stop pul~e to a countQr in counters and latches 206.

As with the circuit og Fig. 9, microproceSSOr 200 subtracts the time required to insert the received 212~1~0 signal into shift register 300 from the time indicated by the counter clock circuit to thl~reby derive the actual time of transmission o~ the acoustic signal.
The circuit of Flg. 11 is highly specific ~o the s transmitted ~requency and is able to differentiate that signal from all others and provides a high noise-immune detection circuit.

Microprocessor 200, in response to determining the slant ranges between transmitters 24 and 26 and receives 24, 26, 38, and 40 performs a number of additional calculations to derive the position in the workspace o~ the ~tylu~ point or puck crosshair. These calculations are described herein below.
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TWO DIMENSIONAL MATRh~lATICS. CALI13RATION AND A~:ORITHM
q The measured slant ranges must be trans~ormed to x and y coordinate values. The ~et-up and location of the receivers plays an important role in overall ~ystem accuracy.

This ~ection discusses a geometry that uses! ~h~ee receivers to determine the x a~d y coordinates. The geometry allows arbitrary receiver locatlon ~or workspace placement. The three receivers provide independent x and y coordinate measurement~ so that errors do not accumulate with the y coordinate. The three receivers al50 allow th~ calculation of stylus orientation 50 that o~set errors to the actu~
d~gitized point can be corrected ~or. Finally, i~ the receiver array i~ calibrat~d with respect to known calibration point lo~tions, the acoustic scale ~actor 2124~0 -~ .
will be less sensitive to o~fset errors, and the final accuracy of the system will be based primarily on the known calibration point locatlon accuracy. -:

Figure 12 shows the 2-D geometry. Tha rPceiver locations are de~ined ~or receivers A, B, and C. The range distances between the receivers and tran~mitter -~
(a, b, and c) are measured with the acoustic hardware, and stored for each receiver. The receivers are all located in the same plane, and the receivers can be located arbitrarily so long as they do not form a straight line~

~ Simultaneous equations can be set up ~or the slant ranges with respect to the coordinate position of a transmitter and the coordinate positions of the receivers~as follows:

a = (x - XA) + (Y ~ YA) b2 = (x - XB) + (Y ~ YB) .
c2 = (x - Xc)2 + tY ~ yc)2 ~ ~:

The complete solution ~or the above equations can be ;.
shown to be: !
x o (allb1l ~ al2b21) y = (a21bll + a22b21) where D = (XA - Xc)(YB ~ YC) (XB Xc)(~A YC) e ~ l .. ... . : .. :, , :

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21 ~ ~ ~
"~' ' ' ' ' 11 YB Yc' a = y _ Y
a - X - X 22 A C

b a R2 R2 -t c2 a2 b21 = R2B - R2C + C2 _ b2 A z coordinate can be calculated based on a slant range, and the x, y coordinate values. However, two restrictions are needed: first the transmitter must not approach the reaeiver plane since z accuracy de~eriorates quickly with small slant range dif~erences, and secondly the value is calculated with a square root function so that the sign of the coordinat~ cannot be determined. Both o~ these restxictions are eliml~ated with the 3-D geometry using four ~eceivers (di~cussed below). The z coordinate value is - : :
z = ~ Ic2 _ (x-Xc)2 ~ (Y ~ ~c)2~

TWO DIMENSIONAL CALIBR~TION ' ' Calibration of the receiver array is important to the accuracy of the systemO There are several preferred -~
ways to calibrate the ~ystem. ~i -- -: - ' :"'~'~ .
The ~irst method requires preclsely mounting the receivers at known di~tances so that theîr Cartesian ~ -coordinates are known ~or initializing the geometry. ~ ~
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Usually, placement o~ ~he receivers along symmetrical axes will reduce the complexity o~ th~ geometry, such that in the extreme case, only the distanca between them is required. The receivers can be mounted with s respect to the workspace coordinate system, or they can be mounted on a separate ha~e and re~erenced only to itself. The final alignment o~ recelver coordinates and workspace coordinates can be found by rotation and translation.
A preferred method is to set a piece of grid paper on the workspace surface, and arbitrarily set the receivers in convenient locations as shown in the Fig.
13. (An error analysis indicates the best accuracy is obtained i~ the receivers are approximately placed at right angles, and separated by a reasona~le distance.) Three known points can be digitlzed on the grid paper, and by reversing the geometry equations (i.e. the three digitized points become the receiver positions ln the original geometry and a ~ingle xeceiver location becomes the transmitter location in the original geometry), the receiver coordinate locations can be mapped. Now the rec~i~er coordinate system is completely referenced to the workspace coord~na'te system, and rotation and translation is not required to al~gn the two coordinate systems.

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2 1 ~ 0 . 23 TWo DIMENSIONA~ ALGoRIT~Ms The complete procedure for dQtermininy a 2-D positisn with three receiver~ i~ outlined below in A-E.
(See Fig. 12 for definitions o~ transmitter and receiver locations~) A ~ p~ame~$
rmu~m~um~n~ntnm~ ~ow~(~ ~) S ~e~ fi~m~ ~ o~on~ ~t) b~ ~ d~ay b~ W~t(~ ~) R ~ A ~ Y A ~ ~ a X D + Y ~ R C 3 X c + Y C
R~C--RA--RC . R;C~R,,,--RC ' ( A X CX~ ~ YC) ~ a~ J ~ XC)~A ~
e~ 2D

au J ~ C ~ C A
2 0 ~ g C X ~ X A X C. ~ -B F~o~
Re~r~Sng~ b ~' (C~mtS) ~nr~u~ ~ m~ ~ ~ n~o~ S~p5 c S~de~y(c~ mc~d~r~,w.c~
a~ s (d- b.) / b3 3 (b'- b,), c~ s (c9 b,) ~;

3 O D CalCUIate C~ CO~L~Ia~ (~nCh~:
~U 5 R A~ b~ 2 r~;c t c 2 x - (a~ b~ + a",b7J~ c y ~3 ~a?~ b~ bv) ¢
3s ~ Tr;~s~towor~p~ceco~e~ys~ DyxO,yO~) ~reqr~ed:

2124~80 THREE DIMENSIONAL MATHEMATICS CALI~RATION AND ALGORITHM

The measured slant ranges must be trans~ormed to x, y, and z coordinate values. The set-up and location of the receiverS plays an important role in the overall system accuracy.

The following sections discuss a geometry that uses four receivers to determine the x, y, and z coordinates. The geometry allows arbitrary receiver location for easier workspace placement. The four receivers provide independent x, y, and z coordinate measurement so that errors do not accumulate with the z coordinate. If the receiver array is calibrated with respect to known calibration point locations, intrinsic functions are not required to rotate the coordinate system to workspace coordinates. Finally, if the receiver array is calibrated with respect to known calibration point locations, the scale factor will be less sensitive to of~set errors, and the final accuracy o~ the system will be based primarily on the known calibration point location accuracy.

T~REE DIM~NSIONA~ SLANT RANGE CONVERSION ' ' Four rece~vers are used to determine the x, y, and z Carte~ian coord~nates. The four receivers also allow the use of the two transmitter stylus ~or accurate projection of the coordinate value to the tip o~ the stylus ~or minimal of~set error. Flg. 14 shows the 3-D geometry.
The receiver locations are shown for receivers A, B, C, and D. The range distances between the receivers and transmitter (a, b, c, and d) are mea~ured and stoxed for each receiver. Three o~ the receiver~ are located in the . . ., : , .

,;, : : ., , . . .;
- , :; .:. ~ ,., ,: , ~, ~ . , :

2124~0 ~ame plane and the ~ourth i8 0~8et ~rom this plane. The receivers can be located arbitrarily as long as they are not all ln the same plane.

Simul~aneous equation~ ~or the slant ranges can be set up with re~pect to the coordlnat~ posi~ion o~ a transmitter and the coordlnate positions o~ th~ receiver as follows~

a2 = (x - X~ ~ ty YA)2 + (z ZA)2 . c2 B)2 B)2 ~ ( ZB)2 2 C 2 C 2 ~ ( ZC)2 ~' d = (X ~ XD) ~ (Y YD) ( D

The abo~e equations can be ~hown to lead to the rollowing solutions~

x =- (a~lb~ + ~1"b" + a~b~)c .Y=tO,Ib~+a2~b" I a~b,l)c z a~a,lb" + a~b3 + a~b,~)c ~1 ~ X ~ ~ X ~ ~ y~ a ~ D ~ I ~, D i ~ :
Xl--X~--XO ~ Y1 ~ D ~ ZO ZD .
x~ Xc XO ~ Y~ Yc Y~ ~ Y~ Zc ZD ! '~

D ~ xly~s~ + x~y~r~ x~y~ Ys~l ~ x~y~- say~

3 0 ql ~ y~Z~ - y~ al, aU o y~ 2l - Y~ ' y~S~ -~a~ - x~ x~ xlz~--x~ a~ 31 X~2 y~ y~, ax~ ~ x~y~ - XJy~ IY~- x~yl bl~ 3 R ,, - R D + d - a~ , :
b,~ R,--R D+ d -b b" ~ Rc ~ R D~ d - c~

21241~0 T~REE pIMENSION~h C~LIBRAT~ON

The cali~ratlon o~ ~he three dimension ~ystem is much the same a~ for the two dlmensional system. Three known locations on a grid paper can be digitized to establish receiver coordinate po~itions. An additional technique makes it pos~ible to extend the concept o~ digitizing known locations on a grid paper. A reference array of precisely ~ixed transmitter po3itions can be located at a convenlent po~ition in the workspacQ. I~ the reference transm~tter array i~ not mo~ed, the receiver array can be relocated at any time ~y simply re-init~alizing the Rystem wi~h the fixed re~erence array.

THREE-DIMENsI~oNAL ALGORITH~S

The complete procedure ~or determin~ng a 3-D position with four receiver~ i8 outllned in ~A-D) below.
(See Fig. 14 for deflnitions of transmitter and receiver location~.) ~a~ pa~
r,~ = maxilTIum slant~ ge allowod (COL~tS) s ~ scale fae~ om ~cc~ c~nx~on ~n/colmt) 3 o ~5 ~ dC~Iy bia~ cons~nt (colm~) RA3 XA ~ ~A~r Z~ ~ R~ ~ + YX ~za R~ 3 XC ~ Yr ~ Ze C RD' XD ~ YO~ ZD
~ocRA~RD~ R~D~R~ D ~ R~ ~~D

2~12~1~0 A X D Y~ A D ~ Zl = Z,~-- æD
X1= X~_ ~D Y2 Y~ O ~ 2 ~ D
9 C D ~ Y~ Y C D ~ 9 ZC ZD :

5D= XIY1Z~ X~YIZ1~ XaY~ Y~
c~ 2D : . . -.a~l= YaZ~--Y9Z~,a"= Y~l--Y~ 2~ ' y~I~--Y"~l :
a~ a X~ ~ X~Z~, a~ -x~z~ -x~z~ !aa~ = X1ZI- X~Z1 a~l = x~y~- x7y~, ~ = X~YI - X1Y~ X1Y~- X1YI

B Fmo the cmi~:
Re~d~ange~ a b G d' (COUn~

Sub~act delay (co~ nd scalo uho mcsur~d sl~ ~ (lnches)~
a= 5 ta!- b8), b~ s (~'--b,) c=s(c'-~"), d=~(d'-b,) 0 c ~ C~ C~:5 (~he~
bu c R~ - a2 2 5 b .~ da ~a b ~ ~ R ~ +

x = t4l b l + 4aba + ~b~) ~
3 o y c ~aa b~ a b~, + ~, bD ) C
b~ ;u + a" b3,) C

T~ansla~ ~o wo~space coordin~o sSrste~l (by xO, yO, zO) if n~quired:
x = x ~,x, . i , . ., , , , ~ , .

2 1 2 ~

RATIO SCALING CORRECTION

Range measurement accuracy is affected by the acoustic medium in the workspace. Factors such as temperature, humidity, and air flow affect the speed of sound, and therefore measurement accuracy. If temperature is used to correct the speed of sound constant, then the correction factor at 70 F is V = 13,574 inches/second.

I~ the digitizer counters run at 10MHz, the length per coun~ is:

K = 3~574 ln./sec. = .001357 inches/count.
10 x 10 counts/sec.
''~

Prior art units correct for the speed of sound with a temperature probe. The problem with temperature compensation by a probe is that the probe and circuitry have to be extremely accurate and not susceptible to bias or drift. Additionally, temperature is only one of the ractors that affect the speed of sound. , , ~ -This invention uses a method of measuring the reference range with each coordinate measurement, and correcting with a ratio scale factor. The speed of sound constant is not required, and scaling ratios provide the systems acoustic correction, A reference correction transmitter 400 (see Fig. 15) is permanently mounted at a precisely ~nown location with respect to a receiver, and fired periodically so that the 21241~

range values can be rescaled ~or temperature and other ~ :~
environmental condi~ions. The ~ollowing approach is used : -: :
~or range scaling:

r;mL~e (inclles) = me~rScufreer(ln~efed~Stcccre (iLneC(~co) nts) x men~ured ~nE:e (coun~s) ~ : -.. ~;'' ~ :' or in mathematical form, ~ -- ~
r' = actual reference range distance ~`:
r = measured reference range corresponding to r' bc = constant delay bias of circuitry r' ! ~: :
r bc . , ' , ' , ~
Correct the range measurement for each receiver: -~ I

a=s(a-b ) b=~ (b-bC~
c=s(c-bc) d=s(d-bc) ' This invention uses a method of measuring the reference :
range with each coordlnate measurement, and correcting I -with a ratio scale ~actor. The speed o~ ~ound constant is not required, a~d scaling ratios provide the systems acoustic correction.
The steps ~or sy~te~ calibration are as ~ollows: !

. Place the grid paper on the work~pace ~fla~ table top).
.
~:

: :',, ` ~

2~2~1~0 ~o 2. Place the receiver array anywhere to one side of the workspace 3. Digitize the calibration points Oll the grid pajer.

4. The scaling transmitter mounted OTI the array base is fired for a re~erence range.

The computer calibration and scaling procedure employs the above derived data as follows:

l. The systems constants are initialized.
2. For each point measured above, the ranges are scaled and two ra~e values (from two transmitters on the puck) are used to calculate the ranges to the center o~ the crosshair ~or each calihration point.
3. The measured range values ~rom above are stored: 3 digitized points, and 4 recelvers for a tot~l o~ 12 ranges.
4O The x, y, z coordinate for each receiver is calculated.

5. Based on the receiver coordinates, ~atrix coe~ficients are calculated (these coe~ficients are used in the ~inal solution ~or normal digitizing).
Now the user can digitize any point in the workspace, and get an x, y, z coordinate value (and stylus orient~ion if required). The user simply place~ the stylus tip on the point to be digitized. The steps below outllne what the computer ~oftware does to convert and scale the coordinate values~

1. The computer polls the stylus and waits for it ~o be i~
activated (e.g. by the user pressing a switch on the stylus). ~`

212~18~

. . .
-2. ~hen ready to dlgitize, a ~irst t:ransmitter on the stylus is fired and the ~our range dis~ances to the receivers are stored.
3. A second transmitter on the stylus i6 ~ired, and the ~.
S four range distances to the receivers are stored.
4. The reference transmitter on the base of the receiver array ifi fired, and the range distance to the receiver is stored.
- 5. The actual reference range is divided by the scale range measurement from the reference transmitter on the receiver ~ase to ~orm the final scale correction factor. The range values are multiplied by the scale ~actor to provide the corrected range values.

6. Range measurements ~rom the transmitters on the stylus are used to calculate the x, y, z coordinates at the stylus tip, and ~tylus orientation angl~s.

It is to be noted that the speed o~ sound constant is never Used in this procedure, only ~callng ratios.
SCALE RATIO ALGORITHM
:
A-D below show the algorithms which allow the conversion of a binary range number to inches while scali~g~ the range to correct ~or enviro~mental changes that effect the speed o~ 30und.

212~80 . 32 Sonic Ca~o~:
R~l IaIIge r (16 bit c~) Ir ~ rm,~ ;~en ~cpcat a~ove B Damino s~le f~ctor (i~ch~/comlt):

~
r -b, ' r ~ mu~d cam:~i~ cespoDdi~g tor 'tcnm~
~ ~c~ tdeIay ~a~ afc~y (COUDtS) C StaIt dlgi~ng ~c~81 da~

2o R~ra~ c ~ (16bit~t) - , - , D Sub~actthedday(c~ts~ dscalethod~g~; (~chEs): ~ ~ :
a- :; (a'- bo) , b- s (b - bs) c~ s(c'-b,~
d = s ~d--b,) . . ~
,:: ..
.,.

- ' i : :

212~:180 33 - ~.
:-It should be understood that the foregoing description is only illustrative of the invention. Various alternatives and modifications can be devised by those skilled in the art without departing from the invention. For instance, while the acoustic transmitters have been shown as parts of a stylus or puck, they could be attached to any moving body in the work space, e.g., to a human's arm, for instance, when it is desired to study the arm's movements under predetermined conditions. With one acoustic transmitter, single point coordinates can be determined for three coordinate space tracking of point or object positions. With two acoustic transmitters, the invention is able to determine position, pitch and yaw. If a ~hird acoustic transmitter is added, roll can be determined, so long as the third transmitter is not located in the same line as the other two transmitters. Additionally, while a single set o~ acoustic receivers has been described, added sets of receiver groups may be positioned about the work space tl) to accommodate barriers which may block the signals to one group of receivers, and not another or (2) to accommodate too great attenuation of received signals due to the distance between receivers and transmitters. Accordingly, the present invention is intended to embrace all such alternatives, modiflcations an variances which fall within the scope of the appended claims.

,

Claims

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

1. An acoustic transmitter comprising:
a housing having an inner space and an aperture communicating with said inner space, said aperture being sized to approximate a point source for said transmitter;

transducer means mounted in said housing for generating, in response to an energizing voltage, ultrasonic acoustic signals which pass through said aperture and create a uniform beam pattern;
and means for applying energizing voltage pulses to said transducer means, each said energizing voltage pulse exhibiting a voltage which substantially exceeds the rated continuous voltage for said transducer means, the duration of said pulses and the voltage level of said voltage pulses not exceeding the maximum power rating for said transducer means.