US005899963A
`5,899,963
`(114) Patent Number:
`United States Patent 55
`Hutchings
`[45] Date of Patent:
`* May 4, 1999
`
`
`[54]
`
`[75]
`
`SYSTEM AND METHOD FOR MEASURING
`MOVEMENTOF OBJECTS
`
`Inventor: Lawrence J. Hutchings, Castro Valley,
`Calif
`
`,
`.
`_
`[73] Assignee: Acceleron Technologies, LLC,
`Oakland, Calif.
`;
`;
`;
`;
`;
`This patent is subject to a terminal dis-
`claimer.
`
`;
`.
`[*] Notice:
`
`[22]
`
`[21] Appl. No.: 08/877,342
`>
`Jun. 17, 1997
`Related U.S. Application Data
`
`Filed:
`
`
`
`4,571,680
`«+ 702/160
`2/1986 Wu ........
`4,578,769
`w 702/160
`3/1986 Frederick ......
`4,627,011
`wees 701/70
`12/1986 Spenceret al.
`4,630,226
`w+ 702/103
`12/1986 Tanaka ..........
`4,703,445
`10/1987 Dassler occeeeteee ce ceeeeeee 702/160
`4,736,312
`4/1988 Dassler et al. oo. eee 702/160
`4,741,008
`4/1988 Franke ...escccccsssssesesssssesseeeeee 378/53
`
`4,763,287
`we 702/160
`8/1988 Gerhacuseretal. .
`4,787,051
`11/1988 OISOM vsesesesssseeeee
`a 364/518
`
`4,821,218
`4/1989 PStSCh vececccsssesssssseeecsseneeeen 73/514.01
`4,855,942
`8/1989 Bianco c..vccssssssesseeeseseesseeeeeee 702/160
`4,885,710 12/1989 Hersbergeret al.
`we 702/146
`
`wa. 702/160
`........
`5,033,013
`7/1991 Kato etal.
`
`.
`wo 377/24.2
`5,117,444
`5/1992 Sutton et al.
`
`1/1993 Gyn oeecssseeecssccssssseeesssccssssseeess 702/141
`5181181
`5,206,652
`4/1993 Hoyt et al. oo eeeccceeeeeeseeeens 342/52
`(List continued on next page.)
`OTHER PUBLICATIONS
`
`[63] Continuation-in-part of application No. 08/570,759, Dec.
`Herbert Goldstein, “Classical Mechanics” Harvard Univer-
`12, 1995, Pat. No. 5,724,265.
`ST] Unt, CLS cesscssssnsneninnennnnnanene GO1C 22/00_Silty, Addison-Wesley Publishing, 1959.
`
`[51]
`In
`:
`.
`!
`:
`AGARD,“Inertial Navigation Systems and Components”A-
`[52] U.S. Ch. ee eeeeeceees 702/145; 702/141; 702/142;
`:
`GARDConference Proceedings No. 43, NATO, 1968.
`:
`:
`702/149; 702/146; 364/143
`Lae
`gg
`:
`Le
`os
`Kenneth R. Britting,“Inertial Navigation Systems Analysis
`:
`[58] Field of Search oe 340/323 R, 384.71;
`Massachusetts Institute of Technology, Wiley—Interscience
`235/105; 364/143, 410.1; 128/779; 482/3,
`1971
`,
`8, 74, 902; 342/52; 324/171; 377/24.5,
`,
`24.2; 73/490; 702/101, 149, 141-142, 146,
`Primary Examiner—JamesP. Trammell
`147, 166
`Assistant Examiner—Cuong H Nguyen
`Attorney, Agent, or Firm—Sofer & Haroun, LLP
`
`[56]
`
`References Cited
`U.S. PATENT DOCUMENTS
`
`[57]
`
`ABSTRACT
`
`A device that measures the distance traveled, speed, and
`1/1974 Heywood et al. uu... 340/384.71
`3,789,402
`height jumped of a moving object or a person while running
`.. 340/323 R
`3/1974 Adleretal. .
`3,797,010
`or walking. Accelerometers and rotational sensors are placed
`3,865,305—2/1975 Sampey ...sccccsceseceseeseeretesesees 377/24
`
`in the object or in the sole of one shoe, or in a wrist watch
`10/1977 Sherrill ...........
`.. 702/160
`4,053,755
`or the waist of the user, along with an electronic circuit that
`6/1978 Holdrenetal.
`.. 73/514.22
`4,094,199
`
`12/1979 DeCrescent....
`. 250/222.1
`4,180,726
`
`performs mathematical calculations to determine the dis-
`. 702/160
`4,220,996
`9/1980 Searcy.....
`tance and height. A microprocessor calculates an output
`... 600/483
`1/1982 Barney...........
`4,312,358
`speed based upon step-distance and elapsed time, and the
`
`wo. 324/171
`6/1982 Sochaczevski .
`4,334,190
`
`distance traveled from the sum of all previous steps. The
`« 702/160
`4,371,945
`2/1983 Karr et al.
`.....
`output of the microprocessor is coupled to a display that
`6/1983 Lowreyet al. ww.ee 702/160
`4,387,437
`showsthe distance traveled, speed, or height jumped.
`5/1984 Meher .a..ccsccssssssssssseesseseseeeeeee 702/94
`4,449,191
`
`7/1984 Ruehlemann ..
`... 235/105
`4,460,823
`12/1985 Kato et al. ccssssssssessseseeeeen 235/105
`4,560,861
`
`35 Claims, 7 Drawing Sheets
`
`APPLE 1102
`
`APPLE 1102
`
`1
`
`

`

`5,899,963
`
`Page 2
`
`5,471,405
`11/1995 Marsh ..eesssesesessessnenneeeeneens 702/41
`
`5,516,334
`5/1996 Easton...
`.-. 482/8
`
`5,524,637
`5,245,537
`6/1996 Erickson ..
`.. 600/592
`9/1993 Barber ..cececeesssesseseeeneneees 364/410.1
`
`5,574,669
`5,396,510
`..
`.- 702/149
`
` 3/1995 Wilson ....eeeeeseeeeceeteeeeetereeneeenees 372/38
`11/1996 Marshall
`
`
`5,452,216—G/1995 MOunce wrsecsecsecsserserssessesseseeees 701/214 5,583,776 12/1996 Levi et al. o.eeeeeeeeeeeeeeeeees 701/217
`
`U.S. PATENT DOCUMENTS
`
`2
`
`

`

`5,899,963
`
`U.S. Patent
`
`May4, 1999
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`Sheet 1 of 7
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`3
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`U.S. Patent
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`May4, 1999
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`Sheet 2 of 7
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`5,899,963
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`FIG. 3
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`4
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`U.S. Patent
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`May4, 1999
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`Sheet 3 of 7
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`5,899,963
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`FIG. 4
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`5
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`U.S. Patent
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`May4, 1999
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`Sheet 4 of 7
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`5,899,963
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`FIG. 5
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`6
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`U.S. Patent
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`May4, 1999
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`Sheet 5 of 7
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`5,899,963
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`9S
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`
`OLSOTNY
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`
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`HOSSIOOHdOHIINUSLUIANODWIISIGpe
`
`YSLLIWNSNVYLgca1931S
`
`JOON
`
`pS
`
`JOTYNY
`
`40SS300Ud
`
`9‘9I4
`
`cS
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`co
`=r
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`7
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`U.S. Patent
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`May4, 1999
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`Sheet 6 of 7
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`5,899,963
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`128
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`= [=p)
`‘ om [i m
`go A :
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`wo
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`124
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`8
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`U.S. Patent
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`May4, 1999
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`Sheet 7 of 7
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`5,899,963
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`FIG. 9
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`9
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`

`5,899,963
`
`1
`SYSTEM AND METHOD FOR MEASURING
`MOVEMENT OF OBJECTS
`
`CROSS-REFERENCE TO RELATED
`APPLICATIONS
`
`This application is a continuation-in-part of application
`Ser. No. 08/570,759 entitled SYSTEM AND METHOD
`FOR MEASURING MOVEMENTOF OBJECTSfiled by
`Lawrence J. Hutchings on Dec. 12, 1995, now US. Pat. No.
`5,724,265, the contents of which are incorporated herein by
`reference.
`
`FIELD OF THE INVENTION
`
`This invention relates generally to the field of measuring
`instruments and is particularly directed to a system and
`method for determining the speed, distance and height
`traversed by a person or an object while in motion.
`
`BACKGROUND OF THE INVENTION
`
`In recent years many individuals have turned to their own
`fitness program of regular jogging. As used herein, jogging
`is also intended to include running and walking and the
`words are used interchangeably. Jogging has long been
`recognized for its therapeutic effects on the body. It pur-
`portedly increases cardiopulmonary fitness, helps to lower
`blood pressure, decreases cholesterol and triglyercides asso-
`ciated with heart disease and reduces weight. Jogging is also
`one of the easiest exercises to do. It requires no athletic
`ability and can be done almost any time and any place with
`a minimum of equipment and without assistance. In more
`recent times, jogging has also gained acceptance for its
`recreational value as well and is recognized as a positive
`factor in promoting psychological well-being.
`The popularity of jogging today is well documented by
`the large numbers of products and literature available to the
`public. As in many exercise and sporting endeavors, there
`exists in the prior art a wide variety of devices for aiding
`those who jog. Many people whorun,jog or walk regularly
`desire to know their progress over time. Therefore,
`it is
`desirable to know the accurate distance and speed traveled
`during an exercise session. This information allows a jogger
`to monitor his or her progress and accordingly pursue a
`regular course of exercise designed to enhance performance.
`Further, it has becomedesirable to accurately measure the
`speed of amateur and professional runners, both in training
`and during competition. In the prior art, such measurements
`were made with a stop watch timing the runner over a known
`distance. Heretofore,
`it has not been possible to obtain
`accurate instantaneous speeds of runners or height jumped
`using the measuring devices currently knowninthe priorart.
`The simplest jogging aids for measuring movements are
`basic pacing timers such as those disclosed in U.S. Pat. No.
`3,540,344 to Veech and U.S. Pat. No. 3,882,480 to Greber.
`Pacing timers generate a repetitive audio tone signal at
`selected intervals for pacing the strides of the jogging, where
`the length of the interval between tonesis adjusted to suit the
`pace of the individual jogger.
`There are other running aids knownin the prior art such
`as pedometers as disclosed in U.S. Pat. No. 4,053,755 to
`Sherrill. These devices usually count the numberof steps
`taken and for a particular stride length,
`the approximate
`distance traversed can be determined.
`
`Human speedometers and odometers that measure the
`speed and distance traveled by a person include devices that
`utilize ultrasound to measure the distance between each foot
`
`10
`
`15
`
`20
`
`25
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`30
`
`35
`
`40
`
`45
`
`50
`
`55
`
`60
`
`65
`
`2
`such as disclosed in U.S. Pat. No. 4,736,312 to Dassler. Also
`used is a device that measures the elapsed time of shoe in
`contact with the ground and converts this to the length of
`step and speed as disclosed In U.S. Pat. No. 4,578,769 to
`Frederick.
`
`While pacing timers, pedometers, ultra sound, and
`elapsed foot-time-distance devices are useful to the runner
`and walker, they are deficient in several areas. For example,
`while ultra sound devices can measure the distance between
`two feet, this is not equivalent to the length of a step or a
`stride, which is defined as the distance traveled by the same
`foot from the beginning of a stride till the end of the same
`stride. For example, the difference between (1) separation
`between feet, as measured by the ultra sound device, and (2)
`stride length, is different for each person and will vary for
`different speeds of running.
`Furthermore, devices that employ elapsed-foot-contact-
`time measurements, have significant errors in measuring
`stride length. It is known that above a certain speed,stride
`length begins to increase as speed increases, and the rela-
`tionship ofstride length to speed is not directly proportional,
`and moreover,is different for each runner. In addition, most
`of the devices mentioned above require calibration, which
`may proveto be a difficult task. For example, manyof these
`devices need to be calibrated by the manufacturer or by
`specially designed equipment.
`It is, therefore, a difficult task to determine the correct
`stride length for an individual runner at various speeds.
`Thus, pacing timers can provide no more than a constant
`running pace, and pedometer measurements are only useful
`as an approximation of distance traversed. Also, ultra sound
`and elapsed-foot-time-distance devices provide only a rough
`approximation of actual distance traveled and speed of the
`person. Also, none of the prior art includes a measurement
`of height jumped. Running and walking aids known in the
`prior art are often deficient and cumbersometo use and they
`often add weight to the runner or walker while providing
`only marginalutility in terms of the amount of information
`available and its accuracy.
`With the foregoing in mind,the ideal running aid should,
`therefore: be light
`in weight; serve a number of useful
`functions; be inexpensive; provide measurements that are
`readily available to the user; be reliable and easy to use; and
`provide accurate measurements of speed,distance traversed,
`height jumped, and other useful information.
`OBJECT OF THE INVENTION
`
`It is the overall objective of this invention to provide a
`new and improved running and walking measuring system,
`which overcomes the disadvantages of the prior art devices
`and substantially increases the amount and accuracy of
`information available to the jogger.
`A specific objective of this invention is to provide a new
`and improved running and walking measuring system, in
`which the speed of the runner can be easily and accurately
`determined.
`
`A further specific objective of this invention is to provide
`anew and improved running and walking measuring system,
`in which the distance traversed by the runner can be easily
`and accurately determined.
`Another specific objective of this invention is to provide
`anew and improved running measuring system, in which the
`height jumped by the runner or jogger can be easily deter-
`mined.
`
`A still further objective of this invention is to provide a
`new and improved running and walking measuring system
`
`10
`
`10
`
`

`

`3
`having the above advantages which is light
`relatively inexpensive and convenient to use.
`SUMMARYOF THE INVENTION
`
`in weight,
`
`5,899,963
`
`4
`FIG. 5 is a vector diagram illustrating output acceleration,
`velocity and displacement of one embodimentof the inven-
`tion during running.
`FIG. 6 is a block diagram ofthe electronic units necessary
`to solve equations for step length in accordance with the
`invention.
`
`In accordance with one aspect of the invention, a device
`for measuring the performance of a runnerutilizes acceler-
`ometers and rotational sensors to measure the speed, dis-
`FIG. 7 illustrates the reference frame andaplot of the path
`tance traveled, and height jumped of a person. It may be
`of the motion of a wrist during walking or jogging, and the
`measurementofthe distance traveled in accordance with one
`preferably placed in the sole of a shoe and information
`embodimentof the invention.
`signals may be transmitted to the user’s watch for display.
`An indication signal may be configured to reset measure-
`mentvalues to zero coordinates with each step taken, and the
`system recordsaccelerationsrelating to the movementof the
`foot to the next step. The accelerations and angels of rotation
`of the foot recorded are transformed to a reference frame of
`
`10
`
`15
`
`the ground, and integrated twice to obtain displacement of
`each step. Time is incorporated with the acceleration to
`perform the integration. Once the length of steps is
`determined, the elapsed time is used to obtain the speed of
`the person, and the sum of the step lengths is used to obtain
`the distance traveled. The maximum value of the vertical
`
`displacement is used to determine the height jumped. One
`set of three-componentlinear accelerometers and oneset of
`three-component rotational sensors may be employed to
`resolve the absolute motion of a person from the motion of
`the foot.
`
`According to another aspect of the invention, substan-
`tially satisfactory measurements may be obtained with two
`accelerometers and onerotational sensor; or the system may
`be attached to the top portion of the user’s shoe, instead of
`installation inside the sole of the shoe.
`
`In accordance with another embodimentof the invention,
`the measuring system maybe located at any part of the body,
`such as the waist or the wrist of the user, instead of the shoe.
`In order to alleviate the measurement errors caused by
`employing the measuring system at different parts of the
`body, the system sets a reference frame that maintains the
`same orientation during a predetermined cycle. The accel-
`erometers and the rotational sensors employed by the mea-
`suring system, measure the distance traveled by the user.
`Preferably, in order to alleviate the effects of gravitational
`field on the accelerometers, the system initiates a new cycle
`at a time whenthe velocity of the user is constant and the
`measured acceleration is influenced substantially by gravity.
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`The subject matter regarded as the invention is particu-
`larly pointed out and distinctly claimed in the concluding
`portion of the specification. The invention, however, both as
`to organization and method of operation,
`together with
`features, objects, and advantages thereof may best be under-
`stood by reference to the following detailed description
`when read with the accompanying drawings in which:
`FIG. 1 illustrates one embodiment of the invention as
`
`employed bya user.
`FIG. 2 illustrates the location of the system’s components
`in the sole of the shoe, in accordance with an embodiment
`of the invention.
`
`FIG. 3 is a coordinate system for the reference frame of
`the stationary ground,andthe vectorsoflinear and rotational
`motion that are necessary to determine motion of the foot in
`accordance with one embodimentof the invention.
`
`FIG. 4 is a side view diagram of the foot during running,
`illustrating information employed to resolve step length in
`two dimensions in accordance with one embodimentof the
`invention.
`
`20
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`25
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`30
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`35
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`45
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`50
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`55
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`60
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`65
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`11
`
`that explains possible errors
`FIG. 8 illustrates a plot
`caused by locating the measuring system in the wrist of a
`user.
`
`FIG. 9 illustrates the coordinate system utilized to mea-
`sure the distance traveled by a user employing the measuring
`system in the wrist or other areas of the body.
`DETAILED DESCRIPTION OF THE
`INVENTION
`
`FIG. 1 shows an embodiment of a measuring system 10
`as employed by a user, although the inventionis not limited
`in scope to the location of different components of the
`system as illustrated herein. For example, the components of
`the measuring system may be located at other parts of the
`body, such as the wrist and the waist area. In accordance
`with the embodiment illustrated in FIG. 1, the shoe of the
`user may include interrelated elements such as linear accel-
`erometers; rotational sensors; a microprocessorto calculate
`the distance and height of each step; a foot impact switch;
`battery; and a radio transmitter 12, as will be explained in
`more detail below.
`
`As shown in FIG. 1, the user may wear a hand display
`having a radio receiver 14. The radio receiver may alter-
`nately be located at a remote site so that the performance of
`the runner can be monitored by another person. Incorporated
`into the receiving unit may be a microprocessor for process-
`ing the received signals into the speed of the runner, the
`distance traversed and the height jumped. The processed
`information may beselectively displayed on display 18. The
`hand display may also perform other functions, for example,
`it may selectively display normal watch functions, such as
`time of day, date, alarm and stop watch signals.
`FIG. 2 shows one possible location of different compo-
`nents of the measuring system in the sole of the user’s shoe.
`However,
`the invention is not
`limited in scope in this
`respect, and various components of the system in accor-
`dance with the present invention may be implemented in a
`variety of arrangements. Accelerometers 2, rotational sen-
`sors 4 and a contact switch 8 are preferably placed in the
`ball-of-the-foot portion of the sole of the shoe so that they
`may come in contact with the ground for each step during
`either walking or running. As it will explained in more detail
`below, the measuring system in accordance with the present
`invention may also operate without contact switch 8. Mea-
`suring system 10 may include three rotational sensors 4,
`each configured to measure the angle of the user’s foot with
`respect to a reference frame as will be explained in more
`detail below. Rotational sensors 4 are well known, such as
`those provided by AMP model numbers ACH-04-08. Each
`rotational sensor converts the measured angle into a corre-
`sponding signal, which is employed by a microprocessor 6
`to calculate information related to the user’s movements,
`such as user’s speed, distance traveled and the height
`jumped. It will be appreciated that the present invention is
`not limited in scope to the componentsillustrated in FIG. 2.
`For example, instead of contact switch 8, other means may
`
`11
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`

`

`5,899,963
`
`to indicate the
`
`5
`be employed so as to generate a signal
`beginning of each step.
`Measuring system 10 preferably includes three acceler-
`ometers 2, each configured to measure the acceleration of
`the user’s foot with respect to a reference frame as will be
`explained in more detail below. The accelerometers may
`also be located in the sole of the user’s shoe. Accelerometers
`2 are well known,such as those provided by Analog Devices
`model ADXLO5. Each accelerometer may convert the mea-
`sured acceleration into a corresponding signal, which may
`be preferably employed by microprocessor 6 to accomplish
`movement measurements.
`
`Also, other components may be separated and placed in
`another portion of the shoe. For example, the measuring
`system may be placed at another location of the shoe or
`another location in the body of the user.
`FIG. 3 illustrates a plot of the coordinate systems neces-
`sary to resolve step length and height. In the present context,
`a first coordinate system, suchas(x, y, z) 22, is referred to
`as the reference frame coordinate system of the stationary
`ground.(Y,, Yy> 2) are the rotational coordinates about the x,
`y and z axis of the reference frame. In one embodiment of
`the invention, rotation about the z axis may not be measured.
`These values advantageously indicate the slope of the
`groundat the beginning of the step. Preferably, the reference
`frame coordinate system is reset at the initiation of a new
`step and remains stationary throughout the time the same
`foot leaves and touches the ground again. The orientation of
`the reference frame coordinate system with respect to the
`foot is arbitrary, but it is preferably selected so that at the
`beginning of the step the positive x direction may be aligned
`with the axis of the sole of the shoe, the positive y axis may
`be in the same plane as the sole and at right angles to the x
`axis, and the positive z axis may be normalto the plane of
`the sole of the shoe. The arrows in FIG. 3 indicate the
`
`direction of positive motion. The length and height of each
`step with respect to this coordinate system may be measured
`in accordance with the present invention as explained in
`more detail hereinafter.
`
`FIG. 3 also illustrates a second coordinate system, such as
`(x, y, Z) 24, referredto as the translational coordinate system
`of the linear accelerometers. This coordinate system moves
`with the foot and may be centered at the location of the
`sensors. FIG. 3 further illustrates rotational coordinates,
`such as (0,, 0,, 0,) about the axes X, Y and Z. These
`rotational coordinates may be employed advantageously to
`keep track of the orientation of the (X, Y, Z) coordinate
`system relative to the (x, y, z) coordinate system, as will be
`explained below, and to resolve the accelerations along the
`reference frame.
`
`In FIG. 3, an exemplary foot is shown part way through
`a step that moves along a trajectory r such as 25. The
`orientation of the translational coordinate system with
`respect to the foot is the same as described for the reference
`frame, but moveswith the foot. Preferably, the reference and
`translational coordinate systems may be aligned together
`every time a new step is initiated. Furthermore, in accor-
`dance with another embodiment of the invention as
`explained in reference with FIGS. 7-9, the orientation of the
`reference frame and the translational coordinate system may
`be aligned at a beginning of a cycle which may comprise
`more than onestep.
`FIG. 4 illustrates an example of a motion of the foot and
`how the length of the step is resolved for a motion in one
`plane, along two dimensions(here, the plane of the paper),
`and for a step along a horizontal surface. The reference
`
`10
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`15
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`25
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`40
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`45
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`50
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`55
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`60
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`65
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`6
`frame coordinate system 26 is that described as 22 in FIG.
`3, and the translational coordinate system 28 is that
`described as 24 in FIG. 3. The foot is shown part way
`through a step having moved along trajectory r such as 29.
`The translational coordinate system is moving along trajec-
`tory r 29, as described in FIG. 3.
`FIG. 4 also illustrates acceleration vectors (Ax, Az) in the
`translational coordinate system. These accelerations are rep-
`resented by arrows aligned along the X and Z axes of the
`translation coordinate system, respectively. The length of the
`arrowsrepresent the amount of acceleration for each com-
`ponent (30 and 32, respectively). The angle of rotation about
`the y axis relative to the reference frame coordinate system
`is 0,. From these components of motion the acceleration
`relative to the reference frame coordinate system can be
`resolved. This is shown as ax and az in the reference frame
`(34 and 36, respectively).
`The amount of acceleration and its direction (a vector
`solution) is preferably employed to keep track of forward
`and reverse motions of the foot. For example, if motion
`remainsin the (z,x) plane and the surfaceis horizontal (FIG.
`4), then
`
`ax=Ax cos 0,+Az sin 0,
`
`az=—Ax sin 0,+Az cos 0,-g
`
`@)
`
`2
`
`Where g is the acceleration due to gravity, which is prefer-
`ably considered as a factor due to the use of accelerometers.
`This follows because typically the accelerometers that may
`be employed by the measuring system areof the type that are
`affected by gravity. However, the invention is not limited in
`that scope. For example, if an accelerometer that is not
`influenced by gravity is employed then the g factor in
`equation (2) may be omitted.
`Gravity may be assumedto be a constant as explained in
`more detail below. Here, acceleration az is assumed to be
`vertical and aligned with the orientation of gravity.
`However, the invention is not limited in that scope. For
`example, acceleration az may be aligned at an angle from the
`direction of gravity, such as on a hill, as explained in more
`detail below. The -g factor added to the az component of
`equation (2) is to balance the effect of gravity on the
`accelerometers. For example, if the user of the system is
`standing still, 0,=0 and Az=+g, then az=0. If the user is
`moving up at g, Az will read 2g, and az=g. If the user moves
`down at g and 9,=180, Az=0, and az=-g. For forward
`horizontal motion, with, for example, 9,=45°, Az and Ax
`would be positive and substantially equal from motion, but
`there would be an added positive component g cos@,, added
`to Az and an added negative g sin 0, component added to
`Ax, and their sum would be such that az=0. The length of the
`step is obtained by integration as discussed in reference with
`FIG. 5.
`
`FIG. 5 shows the elements that may be employed to
`obtain a complete solution of the foot motion in three
`dimensions. The reference frame is established from the foot
`
`contact at the beginning of a step 40. However the invention
`is notlimited in scopein that respect, and in accordance with
`other embodiments of the invention,
`the reference frame
`may beestablished in other manners as explained in more
`detail below and in reference with FIGS. 7-9.
`The reference frame z axis may be chosen such that it is
`not aligned with gravity. For example, the reference frame z
`axis may not be aligned with the direction of gravity if the
`ground(x,y plane) is not horizontal. y, 42 is the angle of the
`x axis from the horizontal plane, and y,, 44 is the angle of the
`
`12
`
`12
`
`

`

`5,899,963
`
`7
`y axis from the horizontal plane. These values are unknown,
`as they depend on the orientation of the reference frame in
`relation to the gravity, such as for example, the slope of the
`ground at the beginning of each step, and are calculated by
`measuring system 10, as explained below. At any point
`along the trajectory r,
`the components of motion in the
`reference frame can be determined from the linear acceler-
`ometers and rotational sensorsin the translational coordinate
`system 46.
`
`ax=AxC,-AyC,+A2C3-g sin y,
`
`ay=AxC,tAyCs-AzC,-g sin Y,
`
`az=-AxC;tAyCgtAzCg-g COS Y,, COS Y,
`
`3)
`
`(4
`
`(5)
`
`Where the C,—C, are transformation coefficients that are
`determined from the output signals generated by translation
`and rotation sensors. These signals represent, for example,
`the angles 6 or incremental changesin the angles 0, shown
`in FIG. 5. In accordance with another embodiment of the
`
`the angles may be determined from rotation
`invention,
`sensors that either measure rotation angles of the
`embodiment, such as with rotation accelerometers or mea-
`sure rotations relative to the reference coordinate system
`directly, such as with magnetic field sensors. There are
`several methods established in prior art to determine the
`values of the coefficients, such as described by Britting,
`Kenneth R. Inertial Navigation Systems Analysis, Wiley-
`Interscience, a Division of John Wiley & Sons, Inc. (1971
`Library of Congress no. 70-168635) and incorporated herein
`by reference; Goldstein, Herbert Classical Mechanics, ch. 4,
`Addison Wesley Publishing, Reading Mass. (1956) and
`incorporated herein by reference.
`In accordance with one embodiment of the invention, an
`exemplary solution to equation (3) though equation (5)
`employs the angles (0,, 9,, 8.) as shown in FIGS. 3-5 and
`described in more detail in Van Bronkhorst, A. Euler Angle
`Strapped-Down Computer, Advisory Group for Aerospace
`Research and Development (AGARD),Inertial Navigation
`Systems and Components, North Atlantic Treaty Organiza-
`tion (May 1968) and incorporated herein by reference. To
`this end, the components of motion in the reference frame
`can be determined as follows:
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`40
`
`45
`
`ax=[Cos 0, Cos 0, Cos 0,-Sin 0, Sin 0,JAx-[Sin 6, Cos 0, Cos
`6,4+Cos 6, Sin 6,|Ay+Sin 6, Cos 6,Az
`(6)
`
`ay=[Cos 0, Cos 0, Sin 0,+Sin 6, Cos @,JAx-[Sin 0, Cos 0, Sin
`6,-Cos 6, Cos 6,JAy+Sin 0, Sin 6,Az
`
`az=—Cos 6, Sin 0,Ax-Sin 0,Sin @,Ay+Cos 0,Az
`
`50
`
`(7)
`
`8)
`
`As explained in reference with FIG. 4, the terms involving
`gravity g counteract the accelerations in gravity recorded by
`the linear accelerometers. The valuesfor y,. and y, may be
`determined at the initiation of each step, and are substan-
`tially equal to zero for a substantially horizontal surface. At
`this time the proportion of gravity recorded by the acceler-
`ometers is related, among other things, to the angle from the
`vertical coordinate (as resolved by an accelerometer such as
`the ADXLO5, from Analog Devices).
`
`55
`
`60
`
`e=Sin™ (Ax/g)
`
`yy=Siny/g)
`
`2)
`
`(10)
`
`65
`
`In order to assure accurate measurements, the accelerom-
`eters employed in the present invention are desired to be
`
`8
`properly calibrated. The embodiments described herein may
`be conveniently calibrated in accordance with the present
`invention. This follows because gravity g only varies by less
`than 0.3% throughout the surface of the earth, and provides
`a substantially constant value in a direction substantially
`aligned towards the center of the earth. Therefore, an accel-
`erometer employed in accordance with the present invention
`must generate an acceleration signal substantially equal to
`gravity g, when the user’s foot is resting on a surface. It will
`be appreciated that an embodiment in accordance with the
`present invention may be configured so as to advantageously
`reset the value generated by the accelerometers to substan-
`tially represent gravity, g, when the user’s foot is resting on
`a surface. As such, the accelerometers employed in accor-
`dance with the present invention may remain substantially
`calibrated at all times.
`Since the accelerometers and rotation sensors are con-
`
`nected to a timing device, their values may be known as a
`function of time. The horizontal and vertical displacement
`may then be obtained by integrating by timeas they traverse
`the path:
`
`Lx= ax(fd?
`
`Ly= ay(bdi?
`
`Lz= az(t)d?
`
`(11)
`
`(12)
`
`(43)
`
`The integration is performed twice to obtain Lx, Ly, Lz
`shown in the equations. Lz would be zero if the ground
`remained at the slope of the beginning of the step, and would
`be significant if a person, for example, climbed a step. To
`obtain the length of the step,
`
`L=Vie+Lp+1e
`
`(4)
`
`The maximum height H jumpedis,
`
`H=max(Lz)
`
`the height
`If L, is not aligned with the vertical axis,
`jumped can be obtained by resolving its component in the
`direction of gravity, as described below.
`FIG. 6 is a block diagram of the components employed to
`solve the equations, although the invention is not limited in
`scope in this respect. Therefore, any hardware or software
`system configured to solve the above equations to measure
`the length of each step and the height jumped may be
`employed. In FIG. 6, unit 48 may preferably contain the
`linear accelerometers employed to measure accelerations
`Ax, Ay and Az and frequencyfilters (not shown). Suchfilters
`may be used to reduce high frequency components in
`measured acceleration signals. The linear accelerometers are
`configured to measure accelerations in three dimensions,
`along the direction of the foot as it travels during each step.
`Unit 50 may preferably contain rotational sensors
`employed to measure 0x @y and 0z signals. Thus the
`rotational sensors provide the angle of rotation along each
`axis of the translational coordinate. The output terminals of
`units 48 and 50 are coupled to input terminals of a processor
`52. Processor 52 may be employed to makethe calculations
`necessary to solve equations 3-5 and 9-10 mentioned
`above. For example, the sine and cosine of each measured
`angle may be computed by processor 52. The sine and cosine
`value signals are then coupled to input terminals of umit 54.
`Unit 52 may contain multipliers and adder processors to
`solve equations 3-5 and 9-10 in analog format. In accor-
`
`13
`
`13
`
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`

`5,899,963
`
`9
`dance with another embodimentof the invention, processor
`52 may process the received signals digitally by employing
`an analog to digital converter and a microprocessor that
`calculates equations 3-5 and 9-10. Yet, in accordance with
`embodiments of the invention, the output terminals of units
`48 and 50 may be coupled directly to a microprocessor 56,
`via an analog to digital converter 54. Analog to digital
`converter 54 may be a separate integrated circuit, such as
`one provided by Linear Technology LTC 1098. In another
`embodimentof the invention, analog to digita