Inertial proprioceptive
`devices: Self-motion-
`sensing toys and tools
`
`by C. Verplaetse
`
`One of the current goals of technology is to
`redirect computation and communication
`capabilities from within the traditional computer
`and into everyday objects and devices—to make
`smart devices. One important function of smart
`devices is motion sensing. Aproprioceptive
`device has a sense of its own motion and position.
`This ability can allow pens to remember what
`they have written, cameras to record their
`positions along with images, and baseball bats to
`communicate to batters information about their
`swing. In this paper, inertial sensing is introduced
`as the logical choice for unobtrusive, fully general
`motion sensing. Example proprioceptive device
`applications are presented along with their
`sensing ranges and sensitivities. Finally, the
`technologies used in implementing inertial
`sensors are described, and a survey of
`commercially available accelerometers and
`gyroscopes is presented.
`
`A
`
`s technology redirects intelligence away from the
`desktop and into everyday objects, common
`devices such as appliances, clothing, and toys are
`given computational sensing and communication abil-
`ities. This technological movement is exemplified in
`such research initiatives as the MIT Media Labora-
`tory’s Things That Think projects and Xerox PARC’s
`concept of Ubiquitous Computing. While much of the
`associated work centers around devices that sense and
`respond to the motion, presence, or state of people
`and objects in their surroundings (examples include
`three-dimensional mice, smart tables, and smart cof-
`fee cups), this paper focuses on devices that have a
`sense of themselves, particularly a sense of their own
`motions. Embedded with inertial sensors, these
`devices are capable of autonomously sensing their
`own motions and orientations and reacting accord-
`
`ingly. As a result, they are called inertial propriocep-
`tive devices.
`
`Devices with this self-motion-sensing ability can
`monitor their motions and respond to them. Consider
`a hand-held personal digital assistant (PDA) contain-
`ing inertial sensors. Such a device could allow its user
`to move through complex information spaces by
`physically moving or tilting the PDA in the corre-
`sponding direction. To go a step further, an inertial-
`sensing user-controlled device with a sense of its own
`functionality could assess its state and give its user
`appropriate feedback. For example, a baseball bat
`could give batting tips, or juggling balls could teach a
`novice to juggle.
`
`Motion sensing is not a new idea. For years, security
`systems, weapon systems, and medical and entertain-
`ment systems have employed various forms of “exter-
`nally referenced” motion-sensing technologies such
`as infrared, radar, and video. Internally referenced,
`autonomous motion sensing has also existed for quite
`some time. Robots, aircraft, automobiles, and other
`vehicles have sensed and measured their motions for
`decades, using varying electromechanical sensors as
`well as inertial sensors.
`
`Most of the motion-sensing technologies referred to
`above are restricted in terms of where and how they
`
`©Copyright 1996 by International Business Machines Corpora-
`tion. Copying in printed form for private use is permitted without
`payment of royalty provided that (1) each reproduction is done
`without alteration and (2) the Journal reference and IBM copyright
`notice are included on the first page. The title and abstract, but no
`other portions, of this paper may be copied or distributed royalty
`free without further permission by computer-based and other infor-
`mation-service systems. Permission to republish any other portion
`of this paper must be obtained from the Editor.
`
`IBM SYSTEMS JOURNAL, VOL 35, NOS 3&4, 1996
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`Table 1 Cost, size, and performance of selected inertial sensors from the 1970s to 1990s
`
`Sensor Type
`
`Electrostatic Gyro
`(ESG), Rockwell†
`
`Expected near-term††
`navigation and military
`gyros
`
`Expected near-term††
`general consumer gyros
`
`Date
`
`1970s
`
`1990s
`
`1990s
`
`Bias Stability
`(deg/hr)
`
`Size
`(in3)
`
`Price
`($U.S./axis)
`
`0.02
`(1 naut.m/hr)
`
`0.02
`(1 naut.m/hr)
`
`50–100
`
`17000
`
`10–20
`
`5000–10000
`
`10
`
`0.01–1.0
`
`1–10
`
`† = ESG references include 1 and 2 in the cited references
`†† = With reference to Kumar et al.3
`
`are useful. Infrared, radar, and video motion-sensing
`technologies are all “externally referenced,” physi-
`cally removed from the moving object of interest. As
`a result these sensing modes are subject to occlusions
`and numerous interferences and noise sources. Al-
`though cars and aircraft measure their own motions,
`their motion sensors are both dimensionally and
`directionally limited. The motion sensor of a car
`wheel requires the friction of a road and only senses
`in one dimension; a pitot tube only works for an air-
`craft traveling forward in familiar atmospheric condi-
`tions.
`
`A more tractable and generally effective type of
`motion sensor is the inertial sensor. Used in space-
`craft, aircraft, and submarines for years, this type of
`sensor attaches directly to the moving body of interest
`and gives an output signal proportional to its own
`motion with respect to an inertial frame of reference.
`Two types of sensors comprise inertial sensing: accel-
`erometers and gyroscopes. Accelerometers sense and
`respond to translational accelerations; gyroscopes
`sense and respond to rotational rates. Inertial sensors
`are desirable for general motion sensing because they
`operate regardless of external references, friction,
`winds, directions, and dimensions. However, inertial
`systems are not well-suited for absolute position
`tracking. In such systems, positions are found by inte-
`grating, over time, the signals of the sensors as well as
`any signal errors. As a result, position errors accumu-
`late. Inertial systems are most effective in sensing
`applications involving relative motion.
`
`Until recent years, inertial sensors have only found
`use in the few fields mentioned above, since their cost
`and size have traditionally been quite prohibitive (see
`Table 1). Since their inception, these sensors have
`largely been complex and expensive electromechani-
`cal devices. Accelerometers have been made of rela-
`tively large mechanical proof masses, hinges, and
`servos; gyroscopes have been built with multiple
`mechanical gimbals, pick-offs, torques, and bearings.
`Recent advances in microelectromechanical system
`(MEMS) technologies have enabled inertial sensors to
`become available on the small size and price scales
`associated with such commonplace devices as con-
`sumer appliances. These advances are largely a result
`of batch processing techniques developed by the time-
`keeping and microelectronics industries.3
`
`In this paper, several types of new motion-sensing
`applications are described along with corresponding
`sensing ranges and sensitivities. Then a brief intro-
`duction to general inertial measurement systems is
`given. Finally, the technologies used to implement
`accelerometers and gyroscopes are described, and
`representative commercial inertial sensors are sur-
`veyed.
`
`Example proprioceptive applications
`
`Motion sensing of common objects such as shoes and
`pens has long existed in one form or another. Tread-
`mills have measured people’s walking speeds and dis-
`tances. PDAs sense the path of a pen tip as a user
`
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`Figure 1 Characteristic motions of common human-controlled devices
`
`HEAD DEVICES (VIDEO CAMERA)
`PAN/TILT: < 60 deg/sec
`AVG FREQUENCY: 3.5 Hz
`FREQUENCY < 8 Hz
`
`HAND, ARM, UPPER-BODY DEVICES
`(TENNIS RACKET, BASEBALL BAT)
`ACCELERATION RANGE: 0.5 TO 9.0 g
`FREQUENCY < 12 Hz
`
`HAND, WRIST, FINGER DEVICES (PEN)
`ACCELERATION RANGE: 0.04 TO 1.0 g
`FREQUENCY < 8–12 Hz
`
`FOOT-LEG DEVICES (SHOES)
`ACCELERATION RANGE: 0.2 TO 6.6 g
`FREQUENCY < 12 Hz
`
`writes on them. And computer programs analyze the
`optical flow of digitized video to infer camera motion.
`Each of these forms of motion detection requires an
`externally displaced device to actually sense motion.
`
`Inertial sensors do not require external references, and
`since they are becoming inexpensive and smaller in
`size, they offer a new means of autonomous motion
`detection for devices that have long been dependent
`on external references (i.e., shoes and treadmills).
`Both the automobile and computer industries have
`quickly found uses for inertial sensing. In the automo-
`tive market, car navigation and air-bag control are the
`main inertial applications; the consumer computer
`market is seeing new input devices that can be used in
`three-dimensional space such as inertial mice and
`head trackers for virtual reality. The inertial market
`for these two industries is estimated to be in the range
`
`of four billion dollars a year over the next several
`years.1
`
`Current work at the MIT Media Lab is focused on giv-
`ing ordinary devices autonomous motion-sensing
`capabilities, via inertial sensing, so that as pens write,
`shoes walk, and cameras move, these objects sense
`their own motions without need for external refer-
`ences. The following subsections describe several
`example applications of human-controlled motion-
`sensing devices and the characteristics of their related
`motions. Figure 1 summarizes the characteristic input
`motion levels for general user-controlled devices. For
`each application, estimated motion data ranges are
`given along with experimentally recorded ranges. The
`experimental motion data were gathered both from
`video analysis and from a three-axis accelerometer-
`based inertial measurement unit (IMU) with a range of
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`–10 g s, where g is the acceleration constant due to
`gravity. This IMU used Analog Devices’ accelerometer
`model ADXL05, a type of capacitive pendulous accel-
`erometer to be described later.
`
`Pen. Personal digital assistants and signature verifica-
`tion devices both employ forms of handwriting recog-
`nition—each analyzes the path of a pen tip on a
`writing surface. If a pen is given inertial sensors and
`on-board computation and memory resources, it can
`sense its motions while it writes and use those motion
`data to estimate its time-varying position. By employ-
`ing a pattern recognition method such as a neural net-
`work or hidden Markov model4 on its time-varying
`pen tip position, the pen can know and remember
`what it has written. Such a “smart” pen could not only
`save notes and letters but also send electronic mail (e-
`mail), solve mathematical problems, check for spell-
`ing errors, and carry out other standard computer
`operations.
`
`video cameras are not used to record static scenes. If a
`video camera can sense its own motions inertially and
`record its motion data along with the video, subse-
`quent camera motion analysis can be performed
`solely by using the inertial data, or a joint inertial-
`optical motion estimator7 can be implemented with a
`state-estimation scheme such as an extended Kalman
`filter.
`
`The required sensing capabilities for a motion-sensing
`camera can be estimated by looking at the rates of
`movement of typical camera maneuvers. Camera
`movement rates were experimentally found by moni-
`toring the pan and tilt motions of a hand-held video
`recorder throughout a series of shooting sequences.
`An average rotational rate of about 36 degrees per
`second (deg/sec) was observed. Pan rates varied from
`near zero deg/sec up to about 60 deg/sec. These rota-
`tional rates determine the input range for gyroscopes
`used in a motion-sensing camera.
`
`An estimated range for pen tip accelerations was
`found by videotaping the pens and papers of several
`people as they signed their names. Pen tip velocities
`and radii of curvature of a number of characters were
`used to calculate the corresponding centripetal accel-
`erations, which ranged from 0.1 g to 1.0 g.
`
`Characteristic camera motion frequency can be esti-
`mated as that of human head motion. Head motion
`frequency averages about 3.5 Hz and rolls off around
`8 Hz.8 Inertial sensors used for tracking a video cam-
`era should thus have optimal frequency response in
`the 3 to 8 Hz range.
`
`Pen tip accelerations in the two-dimensional writing
`plane were also recorded using the aforementioned
`IMU attached to a pen tip. Recorded handwriting
`accelerations ranged, with uniform distribution, from
`0.04 to 0.66 g.
`
`The frequency of motion for handwriting will be esti-
`mated as the approximate natural frequency of the
`wrist and hand, 8 to 12 hertz (Hz), and should not
`exceed 20 Hz.5 When the relative size and motion
`scales are considered, the handwriting characteristic
`frequency described here will act as the frequency
`limit for other applications such as foot-, leg-, and
`arm-controlled devices.
`
`Camera. Many current video analysis schemes
`attempt to extract camera motion from optical flow.6
`Optical flow is the apparent motion of image intensity
`on the image plane of the camera over time. A number
`of models exist that relate this two-dimensional opti-
`cal flow motion with its corresponding three-dimen-
`sional camera motion. Such optically based motion
`estimation schemes are best suited for static scenes,
`where the only motion on the image plane is that
`caused by camera motion. In most cases, however,
`
`Shoes. Just as most types of vehicles have speedome-
`ters and odometers, shoes should also be able to sense
`and track their motions. The medical and athletic
`fields have relied on various forms of externally refer-
`enced walking rate and distance sensors for some
`time. Shoes embedded with an inertial-sensing system
`would allow walking-sensing to be carried out unob-
`trusively and in any setting. An inertial shoe pedome-
`ter system would work much like the pen and camera
`described above; inertial sensors would record shoe
`motion components, and an on-board computer would
`estimate speed and distance traveled. Given sufficient
`computational, memory, and sensing resources, a
`proprioceptive shoe system could not only tell its
`wearer how far and fast he or she is walking, but could
`also diagnose gait abnormalities or alert the wearer
`that it is time to replace the shoe soles.
`
`For a benchmark estimate of the shoe accelerations
`associated with walking, consider an average person’s
`walking speed of 3.5 miles per hour (mph) (5.13 feet
`per second, or fps) or 2 steps per second.9 The centrip-
`etal acceleration of a shoe traveling 5.13 fps about an
`average adult’s knee of radius 2.17 ft10 is 12.1 ft/sec2
`(about 0.4 g).
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`General inertial measurement systems
`
`Motor-cognizant devices like those mentioned in the
`preceding sections can independently track their
`motions using inertial sensors. As mentioned earlier,
`inertial sensing is accomplished with two types of
`sensors: accelerometers and gyroscopes. Typically,
`both of these sensors are sensitive to only one axis of
`motion. Inertial navigation systems (INSs) used in air-
`craft, spacecraft, and other vehicles are ordinarily
`based on an inertial measurement unit that consists of
`a set of three orthogonal accelerometers and three
`mutually orthogonal gyroscopes. Such a device is sen-
`sitive to the full six degrees of freedom of motion
`(three translational and three rotational). It should
`also be noted that rotation can be measured inertially
`without gyroscopes, using the differential linear ac-
`celerations measured by two (or more) accelerometers
`undergoing the same rotational motion but located at
`different distances from the center of rotation.
`
`INSs determine position and orientation from the basic
`kinematic equations for translational and rotational
`motion. The orientation of an object, given a sensed
`rotational rate, w
`, during each time step, t, is given by
`q q
`=
`t+
`(1)
`where q equals the orientation angle, and t equals the
`time step. The output of a gyroscope is the rotational
`rate w
`. Similarly, position is found with the transla-
`tional kinematic equation
`
`0
`
`(2)
`
`at2
`
`12---
`
`x
`
`=
`
`x0
`
`+
`
`v0t
`
`+
`
`where x equals position, v equals velocity, and a
`equals acceleration, the output of an accelerometer.
`
`A schematized inertial measurement system for a gen-
`eral proprioceptive device is shown in Figure 2. This
`system consists of a set of sensors whose signals go
`through an analog-to-digital converter to a microcon-
`troller. The sensors include accelerometers and gyro-
`scopes as well as a temperature sensor (because the
`signals of most inertial sensors are temperature-
`dependent) and any other sensors called for by a given
`application. The microcontroller either stores the sen-
`sor data for later use, or it performs some type of real-
`time analysis and invokes the appropriate output.
`
`Several types of computation and analysis may be
`performed with the data of the inertial sensors by the
`microcontroller of the system. The most basic micro-
`
`Experimental values of walking foot accelerations
`were obtained with the previously mentioned IMU fas-
`tened to a shoe near the ball of a foot while walking.
`Recorded accelerations ranged from 0.19 to 6.57 g,
`with nearly all the acceleration activity located near
`the mean of 1.59 g.
`
`Given the estimated walking accelerations, inertial
`sensors used for shoe motion tracking should have an
`input range of about –10 g s.
`
`Bats, rackets, and batons. The final example appli-
`cation area includes toys and tools that are swung or
`waved expressively by their users. A baseball bat or
`tennis racket that senses its motions can tell a player
`how fast he or she is swinging, and if used with other
`sensors and a microprocessor, could give feedback
`information about a player’s performance.
`
`An application with similar motion-sensing require-
`ments is the “Digital Baton,”11 which was developed
`at the MIT Media Lab. This device, using an orthogo-
`nal accelerometer triad for motion sensing and several
`pressure sensors for analog finger inputs, allows its
`user to “conduct” and control computer music orches-
`trations simply by being moved and gripped in differ-
`ent ways.
`
`Using the test IMU, hand accelerations were recorded
`during athletic arm- or hand-swinging motions. An
`acceleration range of 0.49 to 9.02 g was found. Most
`of the acceleration activity was concentrated near the
`mean value of 2.2 g.
`
`Baseball bat accelerations for the typical swing of a
`youth (bat speed of 40 mph, 58.7 fps)12 are estimated
`as the centripetal acceleration. These accelerations
`will serve as an upper limit. If a swinging arm length
`of 2 feet and a distance of about 10 inches from the
`hands’ position to the center of mass of the bat is
`assumed, the bat will experience a maximum acceler-
`ation of (58.7 fps)2/2.8 ft = 1230 ft/sec2 = 38 gs! At the
`same time, the handle of the bat will undergo an
`acceleration of about (29.3 fps)2/2 ft = 429 ft/sec2 =
`13 gs.
`
`Given the motion range estimates for these athletic
`and expressive hand and arm applications, any inertial
`sensors measuring the motion of a user’s hand or arm
`needs to have an upper input limit of near 10 to 15 gs.
`If the motion of an object extending from the user’s
`body (like a baseball bat) is to be sensed, a greater
`input range (about 50 g) is necessary.
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`Figure 2 Schematic of general proprioceptive system
`
`X-ACCELEROMETER
`
`Y-ACCELEROMETER
`
`Z-ACCELEROMETER
`
`X-GYROSCOPE
`
`MICROCONTROLLER
`
`Y-GYROSCOPE
`
`ADC
`
`MULTIPLEXER
`
`Z-GYROSCOPE
`
`TEMPERATURE SENSOR
`
`OTHER SENSORS
`
`OTHER SENSORS
`
`....
`
`OUTPUT
`DEVICES /
`ACTUATORS
`
`OUTPUT
`DEVICES /
`DISPLAYS
`
`COMMUNICATIONS
`INTERFACE
`
`SYSTEM
`CLOCK
`
`MEMORY
`
`EXTERNAL SYSTEMS
`
`controller computational function is to estimate
`motion and position with Equations 1 and 2. A more
`sophisticated method for estimating motion and posi-
`tion is to use a Kalman filter state-estimation algo-
`rithm. Once
`the
`time-dependent motions and
`positions of the system are estimated, a pattern recog-
`nition scheme such as a neural network, hidden
`
`Markov model, or matched filter may be performed
`with that motion data. These pattern recognition
`schemes are useful for identifying certain segments of
`the motion of a system. Those motion segments might
`be caused by a baton moving through the upbeat of a
`conducting gesture, a pen signing its user’s signature,
`or a pair of dancing shoes stepping through a samba.
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`After estimating the motion and position of the device
`and recognizing any appropriate patterns, the micro-
`controller of the system may accordingly store system
`state data, activate output media, or communicate
`with external devices.
`
`It was mentioned earlier that IMUs cannot be used for
`absolute position tracking. Since an INS calculates
`position by multiplying the output of an accelerome-
`ter by t2, any errors in the output of the accelerometer
`are also multiplied by t2; accelerometer errors propa-
`gate by Equation 2. This leads to huge position errors:
`in just 60 seconds, a one-dimensional IMU using an
`accelerometer with an output noise level of just 0.004
`g yields a position uncertainty of about 70 meters.
`Gyroscope errors increase linearly with time, via
`Equation 1, and are therefore typically less “harmful”
`than accelerometer errors. Because of their inherent
`accumulation of absolute positional errors, inertial
`sensors are much better suited for relative motion
`sensing or tracking. The accelerometer with 0.004 g
`noise gives a positional uncertainty of about 0.2 milli-
`meter (mm) per cycle in a system as slow as 10 Hz;
`the uncertainty falls to about 80 micrometers per
`cycle in a 50-Hz system.
`
`Pure inertial measurement systems are best suited for
`relative motion-sensing applications or for short-dura-
`tion position-tracking applications. The smart-pen
`application is an example of a system where absolute
`position tracking of the pen tip would be desirable,
`but relative position tracking still allows a highly use-
`ful system. Given absolute position tracking, the IMU
`of the pen could essentially store analog “carbon”
`copies of what the pen had written. Due to inertial
`errors, the pen system could never accurately track the
`position of the pen tip on the paper for a useful dura-
`tion, but in tracking the relative motions of the pen tip
`and continuously checking for verifiable characters,
`the IMU of the pen can recognize written characters
`and store the corresponding ASCII characters in mem-
`ory.
`
`Inertial navigational systems suffer most from the
`inherent buildup of positional errors associated with
`inertial sensors because INSs need to operate indefi-
`nitely for the duration of their “missions.” For naviga-
`tion and other applications where system accuracy is
`more important than system autonomy, hybrid inertial
`motion-sensing systems are common. An inertial-
`optical motion estimator was discussed previously in
`the context of a proprioceptive video camera. Other
`hybrid inertial systems include inertial stellar missile
`
`navigation systems2 and inertial GPS (global position
`system) airplane guidance systems.
`
`Applications requiring absolute rotation (orientation)
`tracking and relative translation tracking can accom-
`plish this with a pure inertial system. In such a sys-
`tem, orientation is computed from the gyroscope
`outputs as usual—with a slightly growing time-
`dependent error as usual. Provided that the system is
`at rest occasionally, the accelerometers can accurately
`sense the orientation of the 1 g gravity acceleration
`vector. Given these occasional gravity-orientation
`updates, the system can correct its gyroscope-induced
`orientation errors for an indefinite duration. This is an
`example of a “zero velocity update.” Note this scheme
`will only work if the accelerometers being used are
`DC responsive (sense both steady-state and changing
`signals), that is, if they sense constant accelerations.
`
`Accelerometers. This subsection provides an over-
`view of the accelerometer, the translational-motion
`inertial sensor. Accelerometers sense and respond to
`translational accelerations; their outputs need to be
`integrated once with respect to time to get velocity
`and integrated twice to get position. Numerous tech-
`nologies are used to implement today’s accelerometer
`designs, including piezoelectric, piezoresistive, and
`capacitive technologies. Here these technologies are
`described, and representative commercial accelerom-
`eter models are surveyed (see Table 2).
`
`Regardless of sensing mechanism, the vast majority
`of modern accelerometers are of the pendulous type.
`Pendulous accelerometers feature an inertial proof
`mass, a segment of the sensor with known mass, that
`is mechanically coupled to the rest of the sensor by a
`spring-like hinge or tether—a cantilever structure is
`an example of a pendulous system. In this type of
`accelerometer, when the sensor is accelerated from
`rest, its proof mass tends to stay at rest, and the spring
`is deformed. It is this deformation of the spring (or the
`corresponding displacement of the proof mass) that is
`transduced to become the output signal of the sensor.
`
`Piezoelectricity is a primary transducer technology
`used for pendulous accelerometers. Piezoelectric
`materials develop distributed electric charges when
`pressed or subjected
`to forces—they
`transform
`mechanical work to electrical output and vice versa.
`Piezoelectric accelerometers, like those made by AMP
`Inc., employ a cantilever design (Figure 3) with a
`piezoelectric film attached to the beam of the cantile-
`ver. When accelerated, the proof mass causes the
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`Table 2 Summary of selected accelerometers
`
`Make/Model
`
`Type
`
`Input Range
`(g)
`
`3 dB Frequency
`Response (Hz)
`
`Output Noise
`@ 12 Hz(g)
`
`Price Range
`($U.S.)
`
`Size
`(in)
`
`AMP ACH-04-08
`
`piezoelectric
`
`–– 2 to – –30
`
`Entran EGAX
`
`IC sensors 3021
`
`piezoresistive
`
`piezoresistive
`
`Silicon
`microstructures 7130
`
`capacitive
`
`Silicon designs 1210
`
`capacitive
`
`Analog Devices
`ADXL05
`
`Analog Devices
`ADXL50
`
`differential
`capacitive
`
`differential
`capacitive
`
`0 to –– 10
`
`0 to –– 10
`
`0 to –– 10
`
`0 to –– 10
`
`0 to –– 5
`
`0 to –– 50
`
`† = These sensors have customized bandwidth
`†† = Includes linearity, hysteresis, and repeatability
`
`7 to 3300
`
`0 to 240
`
`0 to 400
`
`0 to 500
`
`0 to 800
`
`0 to 20†
`
`0 to 20†
`
`0.02
`
`0.00013
`
`.33 mg
`
`0.1
`
`0.002
`
`0.002
`
`0.13
`
`25–50
`
`500
`
`100
`
`100
`
`100
`
`15–30
`
`15–30
`
`.4·
`.14·
`.6·
`
`.4·
`.06
`.14·
`.6·
`
`.2
`
`.3
`
`.8· 1·
`.3
`.35·
`.35·
`.1
`0.4D· 0.2
`
`0.4D· 0.2
`
`beam to deflect, which in turn causes the piezoelectric
`film to stretch, resulting in an electric charge differ-
`ence (the output of the sensor). Piezoelectric acceler-
`ometers are called active devices because they
`generate their own signals and theoretically do not
`need to be powered. Since these sensors require a
`time-varying input (physical work), they do not
`respond to steady-state inputs such as the acceleration
`of gravity, hence they are called AC responsive (sense
`only changing signals).
`
`Another common transducer technology used for ac-
`celerometers is piezoresistivity. Piezoresistive materi-
`als have the property of changing their electrical resis-
`tance under physical pressure or mechanical work. If
`a piezoresistive material is strained or deflected, its
`internal resistance will change and will stay changed
`until the original position of the material is restored.
`Piezoresistive accelerometers can sense static signals
`and are thus called DC sensors; they also require exter-
`nal power, so they are passive. Common piezoresis-
`tive pendulous accelerometers are made
`from
`micromachined silicon and are situated in a “double
`cantilever” manner, with proof mass suspended on
`two sides by piezoresistive springs. It should be noted
`that piezoresistive materials are also temperature-sen-
`
`sitive (they are used in thermistors). This is often cor-
`rected by arranging the piezoresistors of a sensor in a
`Wheatstone bridge circuit.
`
`Perhaps the most common type of consumer acceler-
`ometer is the capacitive pendulous accelerometer.
`Accelerometers with capacitive sensing elements typ-
`ically use the proof mass as one plate of a capacitor
`and the base as the other. When the sensor is acceler-
`ated, the proof mass tends to move, and the voltage
`across the capacitor changes; this change in voltage
`corresponds to the applied acceleration. These sensors
`may be operated open-loop or closed-loop. Capacitive
`accelerometers are primarily made of micromachined
`silicon (like the piezoresistive type) and generally
`have higher sensitivities than piezoresistive models.
`The two piezoresistive accelerometers listed in Table
`2 have sensitivities of about 10 millivolts per gram
`(mV/g), and the capacitive accelerometers in the same
`table have sensitivities an order of magnitude higher.
`
`In terms of the self-motion-sensing applications
`described in the previous section, it is evident that the
`accelerometer market is approaching the desired size,
`price, and performance. Table 2 surveys representa-
`tive commercially available accelerometers.
`
`646
`
`VERPLAETSE
`
` IBM SYSTEMS JOURNAL, VOL 35, NOS 3&4, 1996
`
`SCEA Ex. 1020 Page 8
`
`

`

`Figure 3 A piezoelectric pendulous three-degrees-of-freedom inertial sensor
`
`Y2 BEAM AND ELECTRODE
`
`Z BEAM AND ELECTRODE
`
`Z
`
`Y
`
`Y1 BEAM AND ELECTRODE
`
`X
`
`Gyroscopes. This subsection briefly discusses the
`gyroscope, or gyro, the rotational-motion inertial sen-
`sor. There are two main branches of gyroscope
`design: mechanical gyros that operate using the iner-
`tial properties of matter, and optical gyros that operate
`using the inertial properties of light. Mechanical
`gyros, at present, are more commonly available for
`the types of applications discussed in this paper. Opti-
`cal gyros are typically more expensive than mechani-
`cal gyros and are currently developed primarily for
`navigational applications.
`
`Original gyro designs, called gimbaled systems, were
`based on the preservation of rotational momentum
`and consisted of a spinning disk or rotor connected to
`the moving body of interest by low-friction gimbals.
`When the body underwent rotation, the spinning rotor
`maintained its original orientation (preserving its
`angular momentum). Today’s mechanical gyroscope
`designs are more commonly of the vibrating type.
`Instead of using angular momentum to sense rotation,
`vibrating gyroscopes use Coriolis acceleration effects
`to sense when they rotate. This is accomplished by
`establishing an oscillatory motion orthogonal to the
`input axis in a sensing element within the gyro. When
`
`the sensor is rotated about its input axis, the vibrating
`element experiences Coriolis forces in a direction tan-
`gential to the rotation (orthogonal to the vibratory and
`rotating axes).
`
`The double tuning fork gyro (Figure 4) is a popular
`vibrating gyro design. This sensor has two pairs of
`tines, with each pair having the same orientation. The
`double tines are made to oscillate antiphase, which
`yields no net motion but provides a varying radius
`about the input axis. When a tuning fork gyro is made
`to rotate about its input axis, its tines undergo sinusoi-
`dally varying Coriolis forces in the direction normal
`to the driven motion of the tines. When the tines are
`subjected to these Coriolis forces, they oscillate in the
`same direction as the forces. These oscillations are
`detected by the sensing elements of the gyro. Tuning
`fork gyros may use piezoelectric, piezoresistive, mag-
`netic, or other types of sensing elements.
`
`A gyro design using principles similar to the tuning
`fork design is a vibrating gyro whose cross section is
`an equilateral triangle. Murata Electronics Corpora-
`tion’s vibrating gyroscope, the Gyrostar**, employs
`this design. Figure 5 shows cross-sectional views of
`
`IBM SYSTEMS JOURNAL, VOL 35, NOS 3&4, 1996
`
`VERPLAETSE 647
`
`SCEA Ex. 1020 Page 9
`
`

`

`Figure 4 A tuning fork gyro
`
`DRIVE TINES
`
`SENSING TINES
`
`DRIVING OSCILLATION
`
`BODY ROTATION, w
`
`RESULTING CORIOLIS ACCELERATION
`
`Figure 5 Murata’s Gyrostar
`
`AT REST
`
`UNDER ROTATION
`
`SENSING
`ELEMENTS
`
`RESULTING SENSED
`OSCILLATORS ARE
`UNEQUAL
`
`B
`
`B
`
`A
`
`C
`
`A
`
`C
`
`DRIVING
`ELEMENT
`
`DRIVING
`OSCILLATIONS
`
`RESULTING SENSED OSCILLATIONS
`CANCEL EACH OTHER
`
`DRIVING
`OSCILLATIONS
`
`CORIOLIS
`OSCILLATIONS
`
`the gyro while at rest and while rotating. This design
`uses
`three piezoelectric ceramic elements, one
`attached to each outer wall. One driving element, C, is
`made to oscillate and the two other, A and B, act as
`sensors. The output signal of this device is the differ-
`ence between A’s signal and B’s signal.
`
`output(t) = a(t) – b(t)
`
`648
`
`VERPLAETSE
`
`When the gyro is at rest, the signals at A and B are
`equal, and therefore there is zero output, but under
`rotation, C experien