The Development of a Portable Head Perturber for
Investigation of the Vestibular-Ocular Reflex
by
Rachel Hannon Peters
B.S., Mechanical Engineering (2000)
The University of South Carolina
Submitted to the Department of Mechanical Engineering
in Partial Fulfillment of the Requirements for the Degree of
Master of Science in Mechanical Engineering
at the
BARKER
Massachusetts Institute of Technology
MASSACHUSETTS NSTITUTE
OF TECHNOLOGY
September 2002
OCT
C 2002 Massachusetts Institute of Technology
All rights reserved
Signature of Author..............................
2002
L__LIBRARIES
-.....................
Department of Mechanical Engineering
09 August 2002
C ertified by .............................................................
I
-......
/ Lynette A. Jones
IPrincipal Research Scientist
Thesis Supervisor
Accepted by .........................................
4
Ain A. Sonin
Chairman, Department Committee on Graduate Students
The Development of a Portable Head Peturber for
Investigation of the Vestibular-Ocular Reflex
by
Rachel Hannon Peters
Submitted to the Department of Mechanical Engineering
on 09 August 2002 in partial fulfillment of the
requirements for the Degree of Master of Science in
Mechanical Engineering
Abstract
The vestibular system comprises five sensory organs in the inner ear that measure
the linear and angular acceleration of the head. This information is used to maintain
balance and influences the perception of space. In addition the vestibular system controls
reflexive eye movements that stabilize images on the retina during head and body
movements. One of these reflexes is the vestibular ocular reflex (VOR), which maintains
retinal stability during head movements using the vestibular and ocular systems.
Deficiencies in the vestibular system and its reflexes cause severe dizziness, lack of
balance, nausea, and other debilitating conditions. Diagnosis of vestibular problems
requires the use of specialized equipment that is expensive and limited to specialized
clinical facilities. The objective of this research is to develop a portable head perturber
for investigation of the VOR. A portable head perturber that is able to test the VOR
using unpredictable stimuli was built for this project. The weight of the device was
limited to 2 kg after experiments were conducted to determine the maximum weight that
could be comfortably added to the head without affecting a person's ability to track a
visual target. A DC, brush pancake motor was selected that met the required torque of
0.2 Nm that could be delivered over frequencies ranging from 0 to 5 Hz. An aluminum
ring was coupled to the motor which was attached to a lightweight, adjustable helmet. A
torque sequence given to the motor perturbed the ring, which resulted in perturbations of
the head. The results from tests with a mannequin head indicated that the portable head
perturber could reach the required torque over the specified bandwidth.
Thesis Supervisor: Lynette A. Jones
Title: Principal Research Scientist
2
Acknowledgements
I would like to thank Lynette Jones and Ian Hunter for giving me the opportunity
to do research in the Bioinstrumentation Laboratory. The knowledge and experience that
I have gained will be invaluable to me in the future. I would also like to thank James
Tangorra for all of his help on this project. Thanks to all of the senior members of the lab
for their advice, especially John Madden, Peter Madden, and Patrick Anquetil. Thanks to
the entire Bioinstrumentation Laboratory. In particular I would like to thank Aimee
Angel, Laura Proctor, Michal Berris, and Wilson Chan for making me laugh and helping
me keep the big picture in mind. Thanks as well to James Celestino for being so patient
and helping me with homework.
Thanks to all of my family for loving me unconditionally. A special thanks to my
Mom and Dad for being great parents and for being so supportive of me. Thanks to Kim
and Kathryn for always encouraging and supporting me. Thanks to Kimball and Winston
for making me smile at least once a day. Thanks to Marti and Wes for your friendship,
guidance, and support. Thanks to Hamilton for always making me laugh. I would like to
thank the Card family for always being so supportive of me. Thank you Drew. I would
not be where I am today if I did not have your endless support, encouragement, and love.
I am truly grateful for you every day. I would also like to thank Hera for being excited to
see me every day when I get home.
The National Institutes of Health provided financial support for this project.
3
Table of Contents
A bstract ............................................................................................................................... 2
A cknow ledgem ents ............................................................................................................. 3
Chapter 1: Introduction ...................................................................................................... 6
1. 1 Vestibular System ....................................................................................................................... 6
1. 1. 1 Vestibular Receptor Organs ..................................................................................................... 6
1. 1.2 Vestibular Reflexes .................................................................................................................. 7
1.2 Gaze System ................................................................................................................................ 8
1.3 Vestibular Disorders ................................................................................................................... 9
1.4 Current Testing M ethods .......................................................................................................... 10
1.4.1 Caloric Testing ....................................................................................................................... 11
1.4.2 Rotational Testing .................................................................................................................. 12
1.5 Benefits of a Portable Head Perturber .......................................................................................13
Chapter 2: D esign of Portable Device ............................................................................. 15
2.1 Perturbation .............................................................................................................................. 15
2.2 Actuators ................................................................................................................................... 16
2.3 Helmets ..................................................................................................................................... 18
2.4 Ring/W eight/Inertia/Velocity/Frequency Issues ....................................................................... 19
Chapter 3: W eight Experim ents ....................................................................................... 23
3.1 Design of Experiments .............................................................................................................. 23
3. 1.1 M ethod of Adding Weights .................................................................................................... 23
3.1.2 M ethod of Presenting Target .................................................................................................. 23
3.2 Equipment ................................................................................................................................. 24
3.2.1
3.2.2
3.2.3
3.2.4
Helmet, W eights, and W eight Adapter ..................................................................................24
Electro-oculogram .................................................................................................................. 25
Angular Velocity Sensor and M outhpiece .............................................................................26
Target ..................................................................................................................................... 26
3.3 Data Analysis ............................................................................................................................ 26
3.3.1 Calibration Analysis ............................................................................................................... 27
3.3.2 W eight Trial Analysis ............................................................................................................ 28
3.4 Results ....................................................................................................................................... 29
3.5 Discussion ................................................................................................................................. 35
Chapter 4: Portable H ead Perturber Final D esign ............................................................. 36
4.1 M otor and Ring Design ............................................................................................................. 36
4.1.1 Ring Selection ........................................................................................................................ 36
4.1.2 M otor Selection ...................................................................................................................... 36
4.2 M otor M ounting ........................................................................................................................ 37
4.3 Testing ......................................................................................................................................38
4.3.1 M ethods ................................................................................................................................. 38
4
4 .3 .2 R esults....................................................................................................................................4
0
4 .3 .3 C onclusion s............................................................................................................................4
3
4.4 Future Work on the Portable Head Perturber........................................................................
References .........................................................................................................................
Appendix A........................................................................................................................
44
45
47
A. 1 MathCAD Worksheet for PRBS Generation........................................................................
47
A.2 Torque and Velocity Analysis..............................................................................................
49
A.3 PRBS Calculations for 10 Signals with seed length = 10 ..................................................
51
A.4 PRBS Calculations for 10 Signals with seed length = 12 .....................................................
54
A.5 "Sampled" PRBS and Power Spectrum ..............................................................................
57
Appendix B.......................................................................................................................
B. 1 Example of Calibration Analysis from Data Set 14 for Subject
B.2 Example of W eight Trial Analysis from Data 15 for Subject
60
1........................................
60
1 ............................................
69
Appendix C .......................................................................................................................
78
C. 1 MathCAD Worksheet for PRBS Velocity Calculations .......................................................
78
C.2 MathCAD Worksheet used for Testing ................................................................................
79
C.3 Data Analysis of Torque Sensor Output and Torque Signal Input ......................................
84
5
Chapter 1: Introduction
1.1 Vestibular System
1.1.1 Vestibular Receptor Organs
The vestibular system consists of five sensory organs in the inner ear that measure
the linear and angular acceleration of the head. The five receptor organs contained in the
vestibular labyrinth and are the utricle, saccule, and three semi-circular canals. Hair cells
within the vestibular labyrinth are deflected when the head accelerates. The membrane
potential and release of neurotransmitter in these cells changes in response to head
movement, and this in turn alters the discharge of vestibular neurons. Head velocity and
acceleration signals are carried to the brain stem by these vestibular neurons, and this
information is used to maintain balance and influence the perception of space [Goldberg
and Hudspeth, 2000].
The utricle and saccule, also known as the otolithic organs, primarily detect linear
accelerations of the head. The utricle contains about 30,000 hair cells and the saccule has
approximately 16,000 hair cells. The hair cells are localized in the macula of the utricle
and saccule. Within the maculae there are both hair cells and supporting cells. The hair
bundle at the top of each hair cell is attached to a gelatinous sheet called the otolithic
membrane, which extends over the entire sensory macula. When the head moves, the
otolithic membrane moves or slides over the hair cells stimulating them and causing them
to discharge. Utricula maculae are positioned in the lateral plane and saccular maculae
are approximately perpendicular to the utricula maculae. The utricle and saccule are
primarily responsible for the maintenance of head/body position relative to gravity, or
static equilibrium, which is essential for maintaining posture and balance. However, they
also contribute to dynamic equilibrium, or the maintenance of head/body position in
response to quick head movements. Horizontal translations are generally picked up by
the utricle, and vertical motions are detected by the saccule [Tortora and Grabowski,
1993].
The three semi-circular canals detect rotational acceleration of the head and also help
maintain dynamic equilibrium of the head/body. The three canals are perpendicular to
each other with two in the vertical plane (posterior and anterior semicircular canals) and
6
one in the horizontal plane (lateral semi-circular canal). The canals are sensitive to
rotations about the vertical and horizontal planes. There are matching pairs of canals in
each ear which are symmetric. The hair cells are contained in an area of the epithelium
called the ampullary crista. The hair bundles at the apex of the hair cells extend into the
cupula, a gelatinous diaphragm. Movement of the head causes the cupula to be displaced
as the fluid in the canals moves, and the hair bundles that extend into the cupula are
stimulated. The semi-circular canals provide information about head velocity to the
brain, as they mechanically integrate the angular acceleration information they detect
from head movements [Leigh and Zee, 1999; Tortora and Grabowski, 1993].
Semicircular Canals
Saccule
Vestibular Nerve
Auditory Nerve
\\
Cochlea
-
\
EardrurnmE
u
-Round
Window
Oval Window
Middle-Ear
Eustachian Tube
\
I
INNER EAR OR LABYRINTH
Figure 1.1 Diagram of the inner ear [VEDA, 20021.
1.1.2 Vestibular Reflexes
The vestibular system is also responsible for stabilizing images on the retina as
the head moves by reflexively controlling eye movements. There are three main classes
of vestibular reflexes. The vestibulospinal reflex compensates for head movement
through the skeletomotor system, which assists in the maintenance of posture. Second,
the vestibulocollic reflex maintains head stability relative to space using the neck
muscles. Finally, the vestibular-ocular reflexes (VOR) involve the vestibular and ocular
7
systems and are responsible for maintaining retinal stability by stabilizing the eyes in
order to keep the image on the retina still [Goldberg and Hudspeth, 2000].
There are three vestibular-ocular reflexes that result from the three components of
the labyrinth. The rotational VOR acts mainly on input from the semi-circular canals to
compensate for rotation of the head. The translational VOR maintains balance during
linear head movements. The ocular counter-rolling response compensates for head offaxis movement in the vertical plane [Goldberg and Hudspeth, 2000]. The latter two
reflexes receive input mainly from the otolith organs.
The vestibular system signals how fast the head is moving, and the oculomotor
system uses this information to control the eye muscles. Vestibular processing is faster
and more effective than visual processing for image stabilization. The VOR takes about
16 ms to inform the ocular system that the head has moved, whereas it usually takes the
eyes usually more than 70 ms to respond to head motion. Since head motion during
walking falls between 0.5 and 5 Hz, the VOR is crucial to keeping the eyes still and
images clear during motion [Leigh and Zee, 1999].
There are two main circumstances in which the vestibular ocular reflexes may not
function effectively. Nystagmus, or the combination of slow and quick phase eye
movements, eventually slows down and stops when a person is rotated in the dark. This
is in part due to habituation in the semi-circular canals. After a period of constant
velocity rotation, the cupula return to their position of rest and the hair cells are no longer
stimulated. The time constant of the exponential decay in the semi-circular canal
response is 5 s, and this is prolonged further by the brain stem circuitry [Goldberg and
Hudspeth, 2000]. Leigh and Zee (1999) estimate this time is around 45 s. The vestibular
response is supplemented by the optokinetic system through visually mediated eye
movements in this situation. The second situation in which the VOR does not respond
well is in response to very slow head motions that are difficult for the semicircular canals
to detect. In both these situations the optokinetic system compensates for the vestibular
system by providing visual information [Goldberg and Hudspeth, 2000].
1.2 Gaze System
The gaze system moves the fovea, which is the most sensitive region at the center of
the retina, to an object that is being visually examined. It uses both the oculomotor
8
system which moves the eyes and the head movement system to accomplish this. The
fovea is stabilized on the object being viewed using six neuronal control systems.
Saccadic eye movements are rapid movements of the eyes between fixation points.
Moving targets are focused on the fovea using smooth pursuit movements. Vergence eye
movements move the eyes in opposite directions so that images can be positioned on both
foveae. Vestibular-ocular movements keep images on the retina during head movements,
whereas optokinetic movements use visual stimuli to keep images still while the head is
rotating. The eyes are stabilized during intent gaze through the fixation system, which
inhibits eye movements [Goldberg, 2000].
The gaze system also prevents movement of images on the retina by preventing the
eyes from moving when an object is motionless, and keeping the image steady when the
object or head moves. Information about head motion and head position is supplied to
the gaze system via the vestibular system where this information is processed [Goldberg,
2000].
1.3 Vestibular Disorders
The importance of the vestibular system to the maintenance of balance and
posture often goes unnoticed until there is a problem with the perception of space or
stability. When the vestibular system degenerates with age, balance and the perception of
space can become difficult and may lead to injury or even death [Lopez et al., 1997;
VEDA, 2002]. Dizziness and dysequilibrium are common symptoms in the elderly that
result in their seeking medical attention, and falling is a primary medical problem for
people over 60 [VEDA, 2002]. Vestibular problems may not be the sole contributor to
balance problems in the elderly, but some vestibular damage is usually present in elderly
people who complain of dizziness and falling. Balance problems are not restricted to the
elderly; nearly 90 million Americans have problems with balance or dizziness. These
problems may be due to vestibular disorders such as Meniere's disease which induces
vertigo and hearing problems. Meniere's disease most likely results from changing
endolymph pressure in the inner ear, however, the cause of this pressure change is not
known. Probably the most common vestibular disorder is Benign Paroxysmal Positional
Vertigo (BPPV), which results in dizziness or vertigo, lightheadedness, imbalance, and
nausea [VEDA, 2002].
9
Studies have shown that there is deterioration in the VOR as a person gets older.
The horizontal VOR has a higher phase lead at low frequencies ( ;0.1 Hz) in elderly
subjects as compared to younger subjects [Paige, 1992], and the VOR gain decreases
significantly with age, and the phase lead of eye velocity to head velocity increases
considerably in older subjects [Baloh et al., 1993]. These VOR inadequacies may be
attributed to the decrease in vestibular peripheral structures with age. As people get
older, labyrinthine hair cells, vestibular ganglion cells and nerve fibers decrease in
number [Paige, 1992]. Lopez et al. (1997) also found that the number, volume and
density of neurons in the human vestibular nuclear complex significantly decrease with
age. VOR function can not be sustained with this loss [Peterka et al., 1990a].
1.4 Current Testing Methods
The American National Standard Institute published a standard of the procedures for
testing basic vestibular function in 1999. The Basic Vestibular Function Test Battery
includes a description and guidelines for testing, including standards for measuring as
well as data analysis and reporting. Six different tests are discussed. In all tests, vertical
and horizontal eye movements are recorded using an electro-oculogram (EOG).
The Spontaneous and Gaze Evoked Nystagmus Test requires that the subject is
seated in an upright position while nystagmus is evoked for different gaze positions
without a vestibular stimulus. For spontaneous testing, eye movements are recorded with
the subject looking forward in normal lighting, with their eyes closed, and with their eyes
open in the dark. Gaze evoked nystagmus is tested under the same three conditions as the
spontaneous tests while the subject moves their eye position to 300 right, 300 left, 250 up
and 250 down and holds each position for 10 s. Slow component velocity is determined
by finding the slope of the slow component of the velocity profile recorded during
testing. This slope is divided by the calibration factor found by moving the eyes to a
known position and measuring the output plot of the EOG.
The Saccade Test involves having the subject use quick eye movements to view
specific target positions (left 200, 00 center, and right 200), while eye movements are
recorded and then analyzed for position and velocity symmetry. If the eye movements
are not the same for the left and right target positions, each eye is recorded separately for
the subsequent pursuit, positional, and caloric tests. Pursuit tests are used to determine if
10
the subject can use smooth eye movements to follow predictable, periodic targets.
Analysis includes determining if the subject can track the targets correctly, as well as
determining the ratio of eye velocity to stimulus (target) velocity. Positioning and
Positional Nystagmus Tests evaluate nystagmus responses during dynamic and static
changes in subject position with respect to gravity. Frenzel lenses are worn for dynamic
tests to prevent fixation during testing [ANSI, 1999]. The final test discussed in the
standard is caloric testing which is explained in detail below.
1.4.1 Caloric Testing
Caloric testing uses water or air to stimulate the lateral semicircular canal
of each ear which results in slow movement of the eyes away from the side stimulated,
while quick components of vestibular nystagmus are induced and point in the direction of
the side being irrigated [Furman and Cass, 1996]. Two effects of the thermal stimulus
cause this response to the caloric test: the convection currents and the effect the
temperature change has on the vestibular nerve's discharge rate [Leigh and Zee, 1999].
Caloric tests are conducted in the dark while the subject is alert. In order to get
the lateral semicircular canal as vertical as possible, subjects lie on their back with their
head tilted at a 300 angle. Two different water (or air) temperatures are used: 30* C and
440 C. Water is delivered into the ear for about 40 seconds while eye movements are
recorded. The process is repeated in the other ear after a break of 5 minutes and is then
repeated at the second water temperature. It has been recommended that individual labs
should decide on their own standards for interpreting the results since the conditions of
testing influence the responses measured [Leigh and Zee, 1999].
Peripheral vestibular function is measured using the caloric test as well as the
directional preponderance of the vestibular system (detected by a larger ocular response
to stimulation in one ear) [Leigh and Zee, 1999]. The magnitude of the vestibular
response is determined from the horizontal slow component velocity. Advantages of
caloric testing include the ability to stimulate each vestibular apparatus separately and the
ease of testing. Nausea and the inability to do many tests at once are problems with this
form of vestibular testing [Furman and Cass, 1996], however the main disadvantage is
that caloric testing depends on many variables (such as ear canal volume, temporal bone
11
thickness, and blood supply to the temporal bone) that are not related to the performance
of the vestibular system [Baloh et al., 1993].
1.4.2 Rotational Testing
Several types of vestibular testing which involve rotating the subject in a chair,
with different types of input to the chair, have been used to determine the VOR gain,
phase, and time constant. Subjects sit in the rotational chair with their eyes open in a
dark room while velocity-step stimuli are delivered. The peak eye velocity during this
stimulation may be used to measure the VOR gain, and the time constant can be
estimated from the time taken for the slow phase velocity to decrease to 37% of its
original value. A sinusoidal stimulus may also be used to determine the VOR gain and
time constant using phase shift at low frequencies [Leigh and Zee, 1999]. Pseudorandom
stimuli have the benefit of requiring a shorter testing time and stimuli with a greater
range of frequencies but need more extensive equipment and data analyses [Peterka et al.,
1990b]. In some studies, subjects actively rotate their head, but careful analysis must be
done so that eye movements are correctly differentiated from passive VOR responses
[Leigh and Zee, 1999].
Another method of rotational testing involves manipulating the visual stimulation
conditions. The subject may focus on an earth-fixed target with the lights on, then the
lights are turned off and the rotational chair is moved for a short time while the subject
fixates in the direction of the target. The vestibular system should respond to this
stimulus with a slow phase response and a gaze-adjusting saccade. After the lights are
turned on, a saccade may be seen that corrects for any insufficiencies of the vestibularsaccadic response in the dark. Vestibular imbalance may also be detected by this lightdark test method [Leigh and Zee, 1999].
An alternative type of testing currently being examined and developed is headonly rotation [Tabak and Collewijn, 1995]. A lightweight helmet may be used to hold a
rotational velocity sensor which records head velocity in conjunction with eye movement
recordings. Both active and passive head movements are used with the technician
moving the subject's head during passive testing. Most subjects are able to rotate their
heads voluntarily up to 3 to 4 Hz maximum; however, these tests are usually conducted
12
over the frequency range of 0.5 to 5 Hz, so assistance from a technician is necessary for
the higher frequencies [Furman and Cass, 1996; O'Leary and Davis, 1998].
Advantages to head-only rotational testing are that it can be conducted in the
home or clinic, assesses the VOR at high frequencies, is inexpensive, and can be repeated
several times. However, there are problems with the amount of head movement that can
be self-generated (inadequate stimulus range). The data may include small fast
components and responses at low amplitudes which can complicate data analysis.
Unwanted subject movement, in particular neck movement, can also contribute to
abnormalities in the data [Furman and Cass, 1996].
Rotational testing, involving a chair rotating a subject, is preferred to head-only and
caloric testing because the frequency and amplitude of the stimuli are easily controlled,
and there are few side effects. However, the disadvantages of rotational testing include
that both labyrinths are stimulated simultaneously, and that it is not portable due to the
instrumentation required for whole-body rotation [Furman and Cass, 1996; Hirvonen et
al., 1999]. The use of rotational chairs in general clinical settings is not practical due to
the size and cost of the equipment [Hanson and Goebel, 1998]. Another disadvantage is
that testing is limited at high frequencies due to insufficient head restraint [Goebel et al.,
2000; Hirvonen et al., 1999].
1.5 Benefits of a Portable Head Perturber
Rotational chair testing using sinusoidal inputs and rotating the whole body is
considered the "gold standard" for evaluating the vestibular system. This testing is
considered an important part of the diagnostic process for patients who complain of
dysequilibrium and dizziness. The low frequencies of most rotational stimuli are not
adequate for testing the VOR since its performance is not ideal in this low range (0.1 to 1
Hz) [Barr et al., 1976; Tabak et al., 1997]. Similar problems arise with caloric testing.
Testing is limited to low frequencies (~0.003 Hz) tested, and only the horizontal canals
are stimulated [Goebel et al., 2000]. Again, portability is not possible with caloric testing
due to the environmental requirements for the water stimulation.
There are some obvious benefits associated with using a portable head perturber to
test the VOR in preference to traditional rotational and caloric testing. Since the majority
of people with a loss in vestibular function are elderly patients, there is a need for a
13
portable device that could be taken into people's homes or used in clinics that oversee
patients' care. The present project involves the development of a portable head perturber
for measuring the VOR. The head perturber comprises a helmet with a motor and ring
attached to it. The torque input to the motor was designed using a system identification
approach which looks at the input and output to define the characteristics of the system.
These test signals are specifically designed to stimulate the vestibular and ocular systems
so that the VOR can be measured under normal operating conditions.
14
Chapter 2: Design of Portable Device
2.1 Perturbation
The perturbations that are delivered to the head must cover a certain frequency
range and apply a pre-determined torque via the helmet that the subject wears. The
frequencies of these perturbations should range from 0.5 to 5 Hz. This was determined
from the range of movements that the head experiences during normal locomotion [Leigh
and Zee, 1999]. The maximum amplitude of the torque applied to the head should be
approximately 0.2 Nm. This value is based on experiments that evaluated how the
head/neck dynamics changed during head perturbations, and on determining the torque
amplitude that was sufficient to elicit a VOR response [Tangorra et al., 2002].
The torque perturbations are delivered according to a Pseudo Random Binary
Sequence (PRBS). The PRBS was chosen because it has similar properties to white noise
but is also periodic and deterministic [Ljung, 1999]. The length of the period is defined
by,
length
[2.1]
= 2 'd- 1
where sd = seed length
A PRBS can be designed to have power over a certain frequency spectrum, as defined by
Davies (1970):
f
1
N-At
to
1
3-At
Hz
[2.2]
where At is the time interval between pulses and N is the sequence length
It can be seen from Equation 2.2 that the frequency spectrum is specified by
selecting certain values for the sequence length and the time between intervals. This is
the main advantage of using a PRBS to generate the signals for the torque perturbations,
namely that the exact frequency spectrum of perturbations can be known [Davies, 1970].
If the desired frequency spectrum ranges from 0.5 Hz to 5 Hz, then Equation 2.2 can be
used to find the desired value of At and the required length of the PRBS. The time
interval, At, should be 67 ms for the highest frequency to have power at 5 Hz. When At is
15
equal to 60 ms, the sequence length, N, must be greater than or equal to 34. Using
Equation 2.1, an initial seed length of 10 generates a PRBS with a total length of 1023,
and an initial seed length of 12 generates a PRBS of 4095, so both of these sequences are
sufficiently long, and have time periods that are suitable for experimental testing. The
time period of these two sequences would be 61.38 seconds and 245.7 seconds,
respectively, with At equal to 60 ms.
A PRBS is generated by defining the initial seed length. This seed matrix is
defined to contain all Os and Is in random order. Once the seed matrix is randomly
generated, two positions in the matrix are tapped (depending on the seed length), and the
values in those positions are evaluated using the exclusive or function (XOR). Table 2.1
shows the possible combinations for XOR.
Table 2.1: All possible XOR combinations.
First Value
Second Value
XOR Result
0
0
0
0
1
1
1
0
1
1
1
0
This new value is added to the seed register and the XOR is repeated after shifting the
positions one spot over. After generating a matrix of Os and Is, the 0 values are replaced
by -1 and the matrix is now a PRBS of 1s and -Is. The PRBS is multiplied by the torque
value, and the resulting matrix contains the torque signal. A MathCAD worksheet was
written which calculated a PRBS once for a seed length of 10. This can be found in
Appendix A.1.
2.2 Actuators
Earlier research conducted in our laboratory evaluated five types of actuators that
could be used in a portable device. They were: a Coanda water jet, an inertial ring driven
by a central servomotor, a solid conductive ring driven by a Lorentz force actuator, a
liquid metal driven by a Lorentz force actuator, and a controlled braking system
(flywheel design). The torque requirement for these five actuators was initially set to
16
Figure 2.1:The Petzl Ecrin Roc helmet used in the portable head perturber(www.petzl.com).
2.4 Ring/Weight/Inertia/Velocity/Frequency Issues
In the process of designing a portable device for perturbing the head, many issues
need to be considered including the ring design, the weight of each component, the total
weight added to the head, the inertia of the ring, and the velocity that the ring must rotate
in order to follow the torque patterns generated by the PRBS. The amount of weight
added to the head must remain as low as possible so that the voluntary movements of the
head are not affected. Generally, heavier motors have lower angular velocity
specifications, which is problematic as a lighter ring must then be used due to weight
limitations. The angular velocity of the ring then increases as the ring inertia decreases.
A limitation of lighter motors is their low torque, which does not meet the requirement
for the head perturber.
A MathCAD worksheet was developed to calculate the angular velocity that the
ring will have to achieve for certain PRBS signals. The inertia of the ring plays an
important role in this calculation as does the PRBS time interval. The frequency band for
perturbation pulses ranged from 0.5 Hz to 5 Hz, and the time interval was calculated to be
around 60 ms. Appendix A.2 shows the calculation of maximum angular velocity using a
At value of 60 ms, a ring inertia of 4.649*10 3 kg*m 2 , and a torque value of 0.2 Nm.
Appendix A.2 also shows the derivation of the equations used in this calculation. Figure
2.2 shows the velocity profile for this particular PRBS with a seed length of 10
characters.
19
50
0
~-50
0
10
20
30
Time (sec)
40
50
60
Figure 2.2: The angular velocity profile of a PRBS with a seed length of 10 that was calculated in
MathCAD using a ring where J was 4.649*10-3 kg*m 2 and a torque of 0.2 Nm.
A MathCAD worksheet was developed that generated ten PRBS signals with the
same length initial seed. This was done to see how the angular velocity profiles of these
different PRBS signals changed. The maximum angular rates were compared for each
PRBS. The worksheet in Appendix A.3 has an initial seed length of 10 characters, and
the worksheet in Appendix A.4 has an initial seed length of 12 characters. These
worksheets show the algorithm used for multiple PRBS generation, as well as the
equations used to calculate angular rate and to organize all ten maximum angular rate
values.
After looking at ten generations of a PRBS, each with an initial seed length of 10,
the angular velocity profiles for the PRBS were compared and the maximum velocities
calculated. The maximum velocities that a ring with an inertia of 4.649*10- kg*m 2
reaches range from about 500 rpm to about 1000 rpm, assuming a time interval of 60 ms
and a torque value of 0.2 Nm. The PRBS signals generated from an initial seed length of
12 with the same inertial ring, time interval, and torque have maximum velocities ranging
from about 700 rpm to about 1700 rpm. These values are higher than those with a seed
length of 10 because the longer seed length allows for longer occurrences of constant
torque.
All of the signals generated have power over the required frequency spectrum
band. This can be checked by looking at a "sampled" PRBS signal and its power
20
spectrum. A "sampled" PRBS was generated by taking the original PRBS and filling in
characters as if the signal had been sampled at some sampling rate, such as 100 Hz.
Figure 2.3 shows the beginning of a PRBS and its generated "sampled" PRBS, and
Figure 2.4 shows the power spectrum of this "sampled" PRBS. Appendix A.5 shows the
MathCAD worksheet developed to generate a "sampled" PRBS and its power spectrum.
1
0
-1
0
2
1
3
- I I
1
0
-1
0
12
6
18
Figure 2.3: The original PRBS (upper figure) and the "sampled" PRBS (lower figure) generated in
MathCAD with a seed length of 10 and a sample rate of 100 Hz.
21
1
040
*
I
0
0@ 0 0
0
0.1
00-
0
0
0%6
0.01
0
0 1 -10-3
1.
-34
54
1 10
0
2
4
6
8
10
Frequency (Hz)
Figure 2.4: The power spectrum of a "sampled" PRBS with a seed length of 10 and designed power
over frequencies from 0 to 5 Hz.
The following chapter describes the effects of adding weight to a person's head.
The more the ring weighs, the higher the inertia of the ring and the lower the maximum
velocity values necessary for the generated PRBS signals. Experiments were therefore
conducted to determine the effect of added weight on gaze error.
22
1 Nm over a bandwidth of 0.5 to 10 Hz [The Home Automation and Healthcare
Consortium, 1999].
The Coanda Water Jet design could achieve the torque requirements and seemed
ideal for a PRBS of torque pertrubations, but had to be used in a waterproof environment,
which meant that it would not be portable. Another disadvantage of this system was that
the lines carrying the water became too stiff which prevented natural head and neck
movements [The Home Automation and Healthcare Consortium, 1999].
The second actuator considered, the helmet mounted servomotor and ring, did not
inhibit head and neck motions as it was light and easy to wear. It was controlled by a
PRBS, but could not achieve the torque requirements over the necessary frequency
bandwidth with the motor and ring combination. If the torque requirements were lower
than 1 Nm, the motor and ring could be chosen to meet these specifications [The Home
Automation and Healthcare Consortium, 1999].
The Lorentz force actuator had a solid conductive ring that was perturbed by
generating a controlled Lorentz force across the ring. It was difficult to produce
sufficient torque with this design, so a Lorentz force perturber with a liquid metal ring
was built. Similar to the solid copper ring, a liquid metal circulated in a horizontal path
actuated by the Lorentz force. The magnets needed to achieve the required torque were
too heavy for a portable device [The Home Automation and Healthcare Consortium,
1999].
The final actuator style considered was the braked disc perturber, which generated
torque perturbations by braking a spinning disc or a pair of spinning discs. The torque
requirements could be achieved with this actuator, but there were safety concerns about
spinning discs at high velocities around a person's head [The Home Automation and
Healthcare Consortium, 1999].
After considering this research on the five perturbation devices, two methods
were selected for further study. A flywheel, or braked disc method, was initially thought
to be the best way to perturb the helmet. Flywheel technologies have several advantages
over motor technologies; they can act as their own battery source, can be rotated at a
certain speed at which they can absorb and store kinetic energy, and this energy can then
be transferred to the helmet by braking or slowing down the flywheel [Norton, 1992].
17
However, safety concerns arose when considering spinning and braking discs at high
velocities (greater than 10,000 rpm) on top of a person's head. The safety mechanisms
needed in this design make it considerably more difficult to implement than the motor
and inertial ring design.
The second actuator type considered was a motor attached to a ring that would act
as an inertial load. The motor would perturb the ring while both are mounted on top of a
helmet. The head is in turn perturbed equal and opposite to the ring perturbations. The
major considerations in this design are the inertia, weight and geometry of the ring, as
well as the mass of the motor. The angular rates of rotation the ring would need to
achieve would also have to be closely monitored. This technology is simpler to
implement than the flywheel design and motors are available that satisfy the torque and
speed requirements. On the basis of experimental studies that indicated that a lower
torque was sufficient to stimulate the VOR [Tangorra et al., 2002], the torque
requirements were lowered to 0.2 Nm. The inertial ring actuator was therefore chosen in
preference to the flywheel because of its safety and ease of design. Further details about
the motor and ring are provided in Chapter Five.
2.3 Helmets
In addition to the frequency and torque requirements of the actuator, the helmet
must obviously be comfortable for the person wearing it. Different types of
commercially produced helmets, including bicycle and climbing helmets, were
considered and evaluated for weight and adjustability. Petzl climbing helmets can be
adjusted for most head sizes and are relatively lightweight. The Petzl Ecrin Roc helmet
(shown in Figure 2.1) was found to be the most adjustable helmet while remaining
lightweight and so was used in these experiments. It fits head diameters ranging from
approximately 0.53 to 0.63 m and weighs about 475 grams. The helmet is adjusted by
attaching the chin strap and then controlling the tightness of the straps with two knobs on
the inside of the helmet by the person's ears. These knobs control the tightness around
the circumference of the head and at the back of the helmet. When adjusted correctly this
helmet is relatively tight fitting and barely moves when the head is rotated.
18
Chapter 3: Weight Experiments
3.1 Design of Experiments
Experiments were conducted to determine if gaze error was affected by an
increase in weight added to a person's head as this would determine the weight limit of
the helmet-based system. It was hypothesized that as weight was added to the head, gaze
error would increase when the subject tracked a visual target, and that the ability to track
a target would diminish with added weight. These experiments were conducted to
determine the maximum weight of the motor and ring combination that could be used
without affecting a person's ability to track the target.
3.1.1 Method of Adding Weights
Four subjects, two males and two females, aged from 21 to 34 years old were
tested. The first two subjects were tested under the following conditions: 0 (nothing on
the head), 800 (helmet with platform), 1000, 1200, 1400, and 1600 gm. The latter four
conditions required the addition of one or two copper weights to the helmet. The second
two subjects were tested under the following conditions: 0 (nothing on the head), 800
(helmet with platform), 1200, 1600, and 2000 gm. The latter three conditions required
the addition of one or two copper weights to the helmet. The weight was increased for
the last two subjects after reviewing the data from the first two subjects and determining
that a 1600 gm weight did not affect gaze error. The maximum weight added was limited
to 2000 gm since it was determined that a portable head perturber could be built that
weighed less than this. The helmet with a nylon platform weighed 800 gm. The helmet
was tightly secured to the head by adjusting the chin strap, the band around the inside of
the helmet, and the tightness of the straps in the rear of the helmet. Weights were
randomly added to the subjects' heads and the first two subjects were given the weights
in the same order as were the last two subjects.
3.1.2 Method of Presenting Target
All subjects were instructed to track a target that was projected on a screen
approximately 1 meter in front of them. Four different targets were used and these were
presented in the same order for all subjects. The first three targets were all sine waves
with a frequency of 0.25 Hz and amplitudes of 32.90, 39.80, and 51.6'. The frequency of
23
0.25 Hz was chosen based on initial testing that indicated that this frequency was easy to
track at the highest amplitude sine wave. The final target was made up of a sum of sines
signal with the following equation,
y(t) = 0.9 * (2.7 * Sin(0.314 * n * t) + 0.25 * Sin(1.257 * n * t + 17)
+ 0.25 * Sin(1.885 * n * t + 3.14159) + 0.25 * Sin(2.51 * n * t + 2) +
[3.1]
0.25 * Sin(3.142 * n * t + 0.75) + 0.5 * Sin(4.71 * n * t + 7))
where t = the time in seconds
n = a factor used to control the frequency of the signal (n = 0.9)
Subjects tracked each of the four targets under the different weight conditions.
For each target all five or six weights were added to the head before the next target was
presented. Data were collected on eye position, head velocity, and target position during
all trials. There were rest periods and a calibration trial between each of the trials. The
calibration trial consisted of a target 200 to the right, 00 center, and 200 to the left.
Subjects were instructed to keep their head still and use their eyes only to track the target
during the calibration trial. These data were used to calibrate the electro-oculogram,
which detected eye movements and therefore the eye position of the subject. During
experimental trials, subjects were instructed to track the target using head and eye
motions. These directions were given to encourage the subjects to move their heads as
much as possible so that the added weight could have a maximum effect on the ability to
track the target.
3.2 Equipment
3.2.1 Helmet, Weights, and Weight Adapter
A Petzl Ecrin Roc climbing helmet was adapted to hold the weights used in these
experiments. A platform was made from PC-Il Marine Power Epoxy so that there was a
flat surface on which the weights were mounted. A rectangular piece of nylon was
attached to the top of the epoxy to increase its strength and ensure that the surface was
flat. An M6 x 90 mm bolt was put in a center hole in the nylon before it was attached to
the epoxy piece. Four 4 mm holes were drilled and tapped in the nylon/epoxy piece and
drilled in the corresponding places on the helmet in order to attach the nylon/epoxy piece
24
to the helmet. The nylon/epoxy piece weighs 329 gin, and together with the helmet the
weight is 800 gm. Figure 3.1 shows the helmet with the nylon/epoxy piece attached to it.
Figure 3.1 The Petzl helmet and nylon/epoxy attachment used for weight experiments.
Four weights were made out of copper plate, and their masses were: 197, 394,
597, and 799 gin. They were attached to the helmet using the bolt on the nylon.
3.2.2 Electro-oculogram
An electro-oculogram (EOG) measures eye movements based on the potential
difference between the cornea and retina. The amplitude of this potential difference is
proportional to eye position over approximately a
300 range. EOGs are accurate to
within 1 of eye movement. The EOG outputs zero when the eyes are looking directly
forward [Clark, 1995]. Electrodes were placed on the outer-canthus of the eye orbit of
each subject and a ground electrode was placed in the center of the forehead. The skin
was lightly abraded (Nuprep Abrasive Skin Prepping Gel) prior to applying pre-gelled
Ag-AgCl electrodes (10.5 mm inner diameter, Hydrotrace). The subject sat in the dark
with the electrodes in place for 20 minutes before testing began in order to minimize the
drift associated with the EOG measurements. The EOG was passed through a signal
conditioning module consisting of an instrumentation amplifier with programmable
gains, and a low pass filter prior to sampling. The module was custom-built in the
Bioinstrumentation Laboratory.
25
3.2.3 Angular Velocity Sensor and Mouthpiece
The angular velocity of the head was measured using a Watson angular rate
sensor (model number ARS-C141-1AR8D). The sensor was attached to a piece of delrin
that fit into a mouthpiece (Everlast). Subjects had their own mouthpieces which were
molded to fit their top and bottom teeth. They were allowed to remove the mouthpiece
between trials. Figure 3.2 shows a subject set up for testing with the velocity sensor,
helmet, weights, and electrodes in place.
3.2.4 Target
The visual target was displayed on the screen approximately 1 m in front of the
subjects using a laser that was reflected by a mirror whose position was controlled by a
galvanometer. The signals were output to the galvanometer using a National Instruments
DAQCard-6062E and BNC-2 110 connector block. A program written in Visual Basic
6.0 was used to interface with the DAQCard.
Figure 3.2 Test subject equipped with helmet, weights, velocity sensor, and EOG electrodes.
3.3 Data Analysis
Angular velocity of the head (HEAD), target position (TARG), and eye position
(EOG) were sampled using a National Instruments PCI-MIO- 1 6XE- 10 data acquisition
board and BNC-2080 connector block which was controlled with a Visual Basic program
26
(written by James Tangorra). All data were sampled at 200 Hz and were then imported
into MathCAD for analysis.
3.3.1 Calibration Analysis
The first step in the data analysis was to calibrate the EOG signal using each
calibration trial. Head velocity data were corrected for the gain set in data acquisition,
the data were then median filtered, and the first and last ten data points were removed.
The head velocity data were then converted from volts to degrees per second. The slope
and y-intercept of a line fit to the data were found, and this line was subtracted out to
remove the linear drift. The specified linear drift was in the order of 2.6 mV over 10
minutes of sampling, which converts to about 1.3*10- deg/sec per second of sampling.
The linear drift subtracted out of the head velocity data was around this order of
magnitude. After removing the linear drift, the head velocity data were converted from
velocity to position by integrating. An algorithm was written based on the trapezoidal
rule to integrate the data. This algorithm is located in Appendix B. 1 together with a
sample calibration analysis MathCAD file
The target data were also adjusted for the gain setting during sampling; they were
then run through a median filter, and the first and last ten data points were removed. The
target data had an offset associated with them that was removed. This was done by
looking at the data where the target position was known to be zero and finding the mean
offset value at these points. This mean offset was then subtracted out and the sampled
data were converted from volts to degrees using Equation 3.2. This was derived using
the distance that the subject was from the screen and the distance the mirror was from the
screen.
dm
0 = arcta n--tan(10.65-Voltago)
where 0 = the angle in degrees
dm = the distance from the mirror to screen = 1660 mm
ds = the distance from the subject to the screen (measured for each subject)
Voltage = the sampled output voltage
27
[3.2]
The head position was then subtracted out of the target position (which was assumed to
be the gaze position), so that the eye position could be calibrated while accounting for
any head movement that may have occurred.
The eye position data were corrected for the gain set during the sampling, run
through a median filter, and the first and last ten data points were removed. The offset
and drift of the EOG were removed by subtracting out a line that was fit to the data. The
EOG data were then fitted to the target minus head position data using a least squares
method shown in Appendix B.2. The calibration factor found using this method was then
multiplied by the eye position data.
3.3.2 Weight Trial Analysis
Once the calibration factor was found for the EOG data, the data from the weight
trials were analyzed. The eye position data were initially analyzed using the same
procedure as in the calibration analysis, and were then multiplied by the calibration factor
found in the calibration data analysis. The target position data were analyzed the same
way as in the calibration analysis, using the zero positions at the beginning and ending of
each data set to remove the offset. The head velocity data were also analyzed following
the procedure in the calibration analysis, except that the head and eye position were now
added together to get the gaze position. The gaze, target, head, and eye position data
were all shortened to contain a fixed number of cycles.
The means of the gaze and target position data were subtracted out from each data
set. This was done so that the mean gaze error could be found by subtracting the gaze
from the target and finding its mean. The variance and standard deviation of the gaze
error were also calculated. The ratio of the gaze over the target at the peak amplitudes
was determined and averaged to give the gain. The lag was found by calculating the
sample correlation between the target and gaze. The ratio of head position over gaze
position was calculated using the algorithm shown in Appendix B.2. This ratio shows the
percentage of head usage during the trial. The percentage of head usage as a function of
weight and inertia were both examined in the results, together with the mean and standard
deviation of the gaze error, gain, and lag.
28
3.4 Results
Subjects were able to track targets very well as shown in Figure 3.3. Subject one
undershot each peak of the sine wave, as did almost all subjects on this trial. The head
and eye positions are plotted together with the target in Figure 3.4. The head and eyes
compensate for one another and together enable the subject to track the target accurately.
60
*0
0
I
I
I
I
I
I
I
I
0
-60
0
I
I
5
10
2( )
15
Time (sec)
I
I
25
30
35
Figure 3.3 Subject 1 tracking a 39.8 degree sinusoidal target. The target position is shown in red,
and the gaze position is shown in black.
60
0e
0
0
0
-60
0
I
I
5
10
I
I
2( )
15
Time (sec)
I
I
25
30
35
Figure 3.4 Subject 1 tracking a 39.8 degree sinusoidal target. The target position is shown in red,
the head position is shown in aqua, and the eye position is shown in blue.
29
Each subject's mean gaze error ranged from 2.3' to 16.10 with an overall mean of
4.60. As can be seen in Figure 3.5, there was no systematic change in gaze error with
added weight.
1
Subject 2
-
Subject
15
0
15
~0
10 1
0
p
5
0
10
5
0
500
1000
0
1500
0
500
1000
Weight (gm)
Weight (gm)
Subject 4
Subject 3
I
1500
I
-
I
15
I
I
15
10 I-
0
10
0
5
5
~
-e--0
I
0
500
1000
I
1500
I
0
2000
Weight (gm)
I
0
500
I
1000
Weight (gm)
I
1500
2000
Figure 3.5 Gaze error as a function of added weight for each subject. The sine signal with an
amplitude of 32.9* is shown in red, the sine signal with an amplitude of 39.8* is shown in blue, the
sine signal with an amplitude of 51.6* is shown in green, and the sum of sines signal is shown in
magenta.
30
The standard deviation of gaze error is shown in Figure 3.6 and ranged from 1.4'
to 4.9' with a mean of 2.40. The variability of the subjects' gaze error did not increase
with added weight.
1
Subject
U
Subject 2
I
I
4
U
0
.4
0
U
0
2
-
-
2
cj~
0
U
~0
0
500
1000
0
1500
0
500
Weight (gm)
Subject 3
Subject 4
4
U
0
1500
1000
Weight (gm)
4
0
U
U
0
2
0
0
0
500
1000
1500
0
2000
Weight (gm)
0
500
1000
1500
2000
Weight (gm)
Figure 3.6 Standard deviation as a function of added weight for each subject. The sine signal with an
amplitude of 32.9* is shown in red, the sine signal with an amplitude of 39.8* is shown in blue, the
sine signal with an amplitude of 51.6* is shown in green, and the sum of sines signal is shown in
magenta.
31
The gain, defined as the ratio of the gaze position to the target position, was found
for all subjects for the three sinusoidal signals, but not for the sum of sines signal because
it consists of more than one sine wave. The gain values ranged from 0.788 to 0.962 with
a mean of 0.875 as shown in Figure 3.7, and did not change consistently as the weight
increased.
1
Subject
Subject 2
I
-
0.95
0.95
0.9
0.9
0.85
0.85
0.8
0.75
I0
0.8
500
1000
0.75
1500
0
Weight (gm)
Subject 4
Subject 3
I
0.95
0.95
0.9
0.9
0.85
0.85
0.8
0.8
5
0
500
1000
1500
1000
500
Weight (gM)
1500
A7I
2000
Weight (gm)
I
0
500
I
I
1000
I
I
1500
2000
Weight (gm)
Figure 3.7 Gain as a function of added weight for all subjects for the sine wave targets. The sine
signal with an amplitude of 32.9* is shown in red, the sine signal with an amplitude of 39.8* is shown
in blue, and the sine signal with an amplitude of 51.6* is shown in green.
32
The lag, or time delay between the gaze and the target, was found for all four
subjects for the three sinusoidal targets. Again this was not calculated for the sum of
sines signal. The lag ranged from 0 to 0.045 s with a mean of 0.008 s as shown in
Figure 3.8.
Subject
0.06
1
Subject 2
0.06
0.037
0.037
C.)
0.0 13
0.013
-0.01
I-I
-4-
-0.01
'
I
0
500
1000
1500
0
I
Subject 4
I
0.06
I
-
I
1500
Weight (gm)
Subject 3
0.06
1000
500
Weight (gm)
0.037
0.037
0.013
0.013
C.)
I
-A1 Al
0
500
I
1000
Weight (gm)
1500
-
-
-n A i
I
0
2000
500
1000
1500
2000
Weight (gm)
Figure 3.8 Lag as a function of added weight for all subjects for the sine wave targets. The sine
signal with an amplitude of 32.9* is shown in red, the sine signal with an amplitude of 39.8* is shown
in blue, and the sine signal with an amplitude of 51.6* is shown in green.
33
The percent of head used during tracking the target was found by dividing the
head position by the gaze position. The amount of head usage decreased with increasing
weight particularly for subject 2 as shown in Figure 3.9. The percent of head usage
ranged from 48.4% to 110.3% with a mean of 74.4%. The percent of head usage was
above 100% for the sum of sines signal for subject one due to a significant increase in
gaze error as seen in Figure 3.5. The plots of percent head usage versus inertia look very
similar to the figures below.
Subject I
115
0
Subject 2
115
97.5
97.5 r-
-
-
F
80
80
62.5
62.5
-
-
0
500
1000
1500
500
Weight (gm)
Subject 3
115
I
I
I
1500
Subject 4
115
I
1000
Weight (gm)
U
U
97.5
U
80
-I
97.5
80
----
U
--
U
62.5
62.5
I
A5
0
500
I
1000
Weight (gM)
I
1500
I
4AC
2000
0
-I
500
1000
Weight (gm)
1500
2000
Figure 3.9 Percent head usage as a function of added weight for all subjects. The sine signal with an
amplitude of 32.9* is shown in red, the sine signal with an amplitude of 39.8* is shown in blue, the
sine signal with an amplitude of 51.6* is shown in green, and the sum of sines signal is shown in
magenta.
34
3.5 Discussion
Gaze error was not significantly affected by an increase in the weight supported
by the head for any of the subjects tested. However, there was a trend of increasing gaze
error with increasing target amplitude in most subjects, especially subject one and two.
The sum of sines signal produced the highest overall gaze error in all subjects. This
suggests that as the target moved to greater distances across the screen, the subjects had a
harder time tracking it. The sum of sines signal also resulted in more variability in the
gaze error for the four subjects. The standard deviation of the gaze error was overall
higher for subject twp, but there was no consistent increase with weight across subjects.
The gain remained relatively constant as more weight was added to the subjects' heads.
Subject two, however, had an overall lower gain than the other three subjects. This may
be due to the fact that she was physically the smallest subject or it could be attributed to
fatigue or inattention. The weight added to the head did not affect the lag. The
percentage of head usage decreased slightly from a group mean of 76.8% at no weight to
a mean of 73.2% at maximum weight.
Since there was no significant effect of added weight on any of the variables
analyzed, it was determined that an added weight of 2000 gm does not affect a person's
ability to track a target. Therefore, the helmet, ring, and motor design were limited to
weigh less than 2000 gm in their preliminary design.
35
Chapter 4: Portable Head Perturber Final Design
4.1 Motor and Ring Design
The head perturber was limited to weighing less than 2000 gm. In addition it
could not inhibit voluntary head movements nor impair vision. The inertia of the ring,
the velocities that it had to reach, and the characteristics of the motor were all factors
considered in developing the portable VOR testing device.
4.1.1 Ring Selection
The first ring considered for the head perturber had been built for the mounted
servomotor by James Tangorra [The Home Automation and Healthcare Consortium,
1999]. This ring consists of aluminum square rod bent and made into a ring. This ring
weighs 413 gm and has a rotational inertia of 4.649*10 3 kg*m 2 . Using this inertia, a
time interval of 60 ms, and a torque of 0.2 Nm, a MathCAD worksheet (shown in
Appendix C. 1) was created to calculate the angular velocity necessary to follow a
previously generated PRBS. This PRBS was used for design purposes because the
highest angular velocity necessary, under the previously stated conditions, was found to
be 567 RPM for a 60 s trial, which seems reasonable for the ring velocity. This ring was
used in the final design since it was already constructed and had an appropriate weight
and inertia for the portable system.
4.1.2 Motor Selection
The major criteria for the motor were that it had to be able to maintain a
continuous torque of 0.2 Nm while reaching a velocity of approximately 1000 RPM, it
had to weight less than 1112 gm, and be mounted safely on the helmet when considering
its size and heat sink requirements. The motor weight limit was calculated by subtracting
the weight of the helmet (475 gm) and the weight of the ring (413 gm) from the
maximum possible weight of 2000 gm. A number of motors met the torque, velocity, and
weight requirements, and of these three were seriously considered (see Table 4.1).
36
Table 4.1 Motor characteristics for three motors.
Manufacturer
& Model(gas
Koford
Brushless
Koford
Brushless
Max. Cont.
Speed at
Cont. Stall
Peak
Diameter
Weight
Power @
Rated Power
Torque
Torque
25C (W)
(RPM)
(N*m)
(N*m)
154
?
0.36
0.833
425
413
?
0.346
1.67
425
?
3000
0.29
3.38
1000
& Length
(mm)
41.4
65.25
41.4
65.25
Kollmorgen
Ferrite Series
ServoDisc
151.9
20.3
12F
The Kollmorgen Ferrite Motor was chosen as the most promising motor due to its
size and shape. This is a pancake motor and so could lay flat on top of the helmet
whereas the other two motors would sit up on the helmet.
4.2 Motor Mounting
The motor was mounted on the helmet by machining four feet that were attached
to the motor through the four holes in its outer flange. The four feet were attached and
altered as necessary until the motor was level on the helmet. The motor mounted on the
helmet is shown in Figure 4.1.
37
Figure 4.1 The motor mounted on to the helmet via four aluminum feet.
The ring was attached to the shaft of the motor with a piece of delrin that was
machined to act as a coupling between the shaft and the motor.
4.3 Testing
4.3.1 Methods
A test stand was made so that the helmet with the motor mounted on it could be
attached to a mannequin head while torque was applied. The mannequin head weighed
1777 gm. The test stand consisted of two metal pieces separated and connected with four
M1O x 80 mm socket cap screws. The shaft rigidly attached to the mannequin head was
placed in a ball bearing that was press fit into the center of the top plate. A torque sensor
(Omega TQ-202-100Z) was attached to the bottom plate such that the shaft of the sensor
was aligned with the shaft in the mannequin head. At first a flexible coupling
(McMaster-Carr Helical Beam Coupling) was used to connect the two shafts, but after
initial testing a rigid shaft coupling (McMaster-Carr Two-Piece Clamp-On Coupling) was
used to minimize the unwanted vibrations of the test stand. The test stand was clamped
to a desk during testing as shown in Figure 4.2.
38
Figure 4.2 Test stand and mannequin with the helmet, ring, motor, coupling and torque sensor set up
for testing.
The torque output of the portable perturber was tested using a PRBS with a seed
length of 10. The velocity profile for a 60 second trial with a 0.2 Nm torque and a ring
inertia of 4.649*10-3 kg*m 2 shown in Figure 4.3, was generated using a MathCAD
worksheet very similar to the one in Appendix A.2.
I
I
I
I
I
I
I
I
10
20
30
40
50
0
0
-50
0
50
Time (sec)
Figure 4.3 The velocity profile of the PRBS used in testing.
39
60
The voltage required to drive the motor was calculated from the torque constants
of the motor, the torque profile of the PRBS, and the velocity profile of the PRBS using
the following algorithm in MathCAD.
voltage:=
for i e 0..11- 1
(Torq).+ T
K d'*i
1000
it
[4.1]
Vi<- 0.625 -Ii
V
where 11 = the length of the sequence
I = the calculated current for the motor
Torq = the PRBS torque sequence
Tf= 2.1 N*cm
Kd = 0.5 N*cm/Krpm
co = the PRBS velocity sequence
Kt= 4.78 N*cm/Amp
V = the calculated voltage for the amplifier
The signal was sent out at 200 Hz while the output from the torque sensor (tsensor) and
the input torque signal (tout) were sampled at 400 Hz using the MathCAD worksheet
located in Appendix C.2 in conjunction with a National Instruments PCI-MIO-l6XE-10
data acquisition board and BNC-2080 connector block
4.3.2 Results
Analysis of the torque output (sensor) and torque input (motor) data was done
using the MathCAD worksheet shown in Appendix C.3. The power spectra of tsensor
and tout should be similar to the predicted power spectrum in Figure 2.4, since the same
PRBS was used to generate this spectrum and to calculate the voltage output signal. The
desired power should be near 1 for frequencies 0 to 5 Hz since these are the frequencies
of interest. The power is sufficient over the desired frequencies as shown in Figure 4.4.
40
I
I
I
1'J
10
S
000 0
.0
1
-
00000
0
@
ee
,
0
0
0,
0
0
0
0
0
-
0.1 0
0.01
.4
1-10
0
2
4
6
8
10
Frequency (Hz)
10
1
1
1
4
6
Frequency (Hz)
8
0.1.0
0.01
1 -10-3
1-10
-
00
C.4
_
0
2
10
Figure 4.4 The power spectra of the torque output (red) and torque input (blue).
The torque sensor data contained some noise which was most likely due the
dynamics of the test stand used for testing. Even with the rigid coupling, the test system
vibrated if a torque was applied and quickly released. A torque of 0.196 Nm was applied
using weights at a known distance and then quickly released while the torque sensor
output was sampled. The vibrations in the system died out after about 1 s as shown in
Figure 4.5.
41
0.1
t-0
F-
0
o|
1
2
Time (sec)
3
4
Figure 4.5 Torque sensor data after applying and removing a 0.196 Nm torque.
The output torque and input torque data were filtered using a median filter and a
moving average filter to smooth out aberrant data points and noise. The overall shape of
the output torque data is similar to the shape of the input torque with some spikes and low
points oscillating around the input torque value as shown in Figure 4.6.
42
I
I
I
0.2
S
0
0
-0.2
S
0
I
I
1
2
3
4
5
2.8
3
Time (sec)
I
I
I
I
I
I
2.2
2.4
2.6
-
0.2
S
0
-0.2
-
0
2
Time (sec)
Figure 4.6 Output torque in red and input torque in blue. The top figure is the full 5 seconds test and
the bottom figure is the 2 - 3 sec window of the full test.
4.3.3 Conclusions
The goal of developing a portable head perturber was to be able to test the VOR
using an unpredictable torque with a bandwidth from 0 to 5 Hz and a maximum value of
0.2 Nm. The data from the torque sensor show that the required frequency spectrum was
achieved at the desired torque value using a PRBS input. The oscillations in the torque
sensor data are most likely due to the vibrations in the test set-up and noise. The motor,
helmet, and ring combination are able to meet the requirements for a portable head
perturber.
43
4.4 Future Work on the Portable Head Perturber
Suggestions for future design changes to the portable head perturber include
changing the helmet used in the device. This helmet was adjustable and relatively light
weight, however if a custom helmet was designed and manufactured, the entire device
could be lighter. A custom helmet would not have to be a helmet at all, provided it was
adjustable and able to support the weight of the motor and ring. The mounting of the
motor to the helmet could also be improved to be variable for different people, for
example by using a stage instead of feet to mount the motor. A stage could have many
positions for the motor so that it would be balanced on the subject's head (front to back
and side to side) prior to testing. The ring could also be redesigned to have a higher
inertia which would decrease the speeds that it would have to reach for the PRBS. An
enclosure around the ring should also be considered to prevent subjects from seeing it
spinning while they track visual targets.
Future suggestions regarding testing the torque capabilities of the motor and ring
combination include making the test set-up more rigid. A rigid coupling was used, but
there was still some vibration in the system. The ideal testing situation would be to
directly couple the torque sensor to the helmet removing the mannequin, bearing, and
coupling all together. Further testing should be done with human subjects once more
safety features have been incorporated into the head perturber. There is a cut-off switch
on the motor power supply that can be subject controlled, but some sort of clutch or
torque limiting mechanism should be included in the device to prevent excessive torque
from being applied to the subject's head.
44
References
American National Standard: Procedures for Testing Basic Vestibular Function. ANSI
S3.45-1999. New York: 1999.
Baloh, R. W., Jacobson, K. M., Socotch, T. M. The effect of aging on visualvestibuloocular responses. ExperimentalBrain Research 1993;95:509-516.
Barr, C. C., Schultheis, L. W., and Robinson, D. A. Voluntary, non-visual control of the
human vestibulo-ocular reflex. Acta Otolaryngologica 1976;81:365-375.
Clark, J. W. Jr. The origin of biopotentials. Webster, J. G., (editor). Medical
Instrumentation:Application and Design. 2 "ded. John Wiley and Sons. New
York: 1995. pp. 193-194.
Davies, W. D. T. System Identificationfor Self-Adaptive Control. John Wiley and Sons.
New York: 1970.
Furman, J. M. and Cass, S. P. Laboratory evaluation. I. electronystagmography and
rotational testing. Baloh, R. W. and Halmagyi, G. M., (editors). Disordersof the
Vestibular System. Oxford University Press, Inc. New York: 1996. pp. 191-210.
Goebel, J. A., Isipradit, P., and Hanson, J. M. Manual rotational testing of the vestibuloocular reflex. The Laryngoscope 2000;110:517-535.
Goldberg, M. E. The control of gaze. Kandel, E. R., Schwartz, J. H., and Jessell, T.
M., (editors). PrinciplesofNeural Science. 4th ed. McGraw-Hill. New York:
2000.
Goldberg, M. E. and Hudspeth, A. J. The vestibular system. Kandel, E. R.,
Schwartz, J. H., and Jessell, T. M., (editors). PrinciplesofNeural Science.
McGraw-Hill. New York: 2000.
4h
ed.
Hanson, J. M. and Goebel, J. A. Comparison of manual whole-body and passive
and active head-on-body rotational testing with conventional rotary chair
testing. Journalof Vestibular Research 1998;8:273-282.
Hirvonen, T. P., Aalto, H., Pyykko, I., and Juhola, M. Comparison of two head
autorotation tests. Journalof Vestibular Research 1999;9:119-125.
Home Automation and Healthcare Consortium, The: Phase 2, Report No. 2-3.
d'Arbeloff Laboratory for Information Systems and Technology. Department of
Mechanical Engineering, MIT. March 1999.
Leigh, R. J. and Zee, D. S. The Neurology ofEye Movements.
University Press. New York: 1999.
45
3rd
ed. Oxford
I1
Ljung, L. System Identification: Theoryfor the User.
New Jersey: 1999. pp. 418-422.
2 "d
ed. Prentice Hall PTR.
Lopez, I., Honrubia, V., and Baloh, R. W. Aging and the human vestibular
nucleus. Journalof Vestibular Research 1997;7:77-85.
Norton, R. Design ofMachinery. McGraw-Hill, Inc. New York: 1992.
O'Leary, D. P., and Davis, L. L. Spectral analysis of low-frequency, active-head
vestibulo-ocular reflex responses. Journalof Vestibular Research
1998;8:313-324.
Paige, G. D. Senescence of human visual-vestibular interactions: 1. vestibulo-ocular
reflex and adaptive plasticity with aging. Journal of Vestibular Research
1992;2:133-151.
Peterka, R. J., Black, F. 0., and Schoenhoff, M. B. Age-related changes in human
vestibulo-ocular reflexes: sinusoidal rotation and caloric tests. Journal of
Vestibular Research 1990a; 1:49-59.
Peterka, R. J., Black, F. 0., and Schoenhoff, M. B. Age-related changes in human
vestibulo-ocular and optokinetic reflexes: pseudorandom rotation testing.
Journalof Vestibular Research 1990b;1:61-71.
Tabak, S. and Collewijn, H. Evaluation of the human vestibulo-ocular reflex at high
frequencies with a helmet, driven by reactive torque. Acta Otolaryngologica
1995;520;4-8.
Tabak, S., Collewijn, H., Boumans, L. J. J. M., and Van der Steen, J. Gain and delay of
human vestibulo-ocular reflexes to oscillation and steps of the head by a
reactive torque helmet. Acta Otolaryngologica 1997; 117:785-795.
Tangorra, J. L., Jones, L. A., and Hunter, I. W. Dynamics of the human head-neck
system in the horizontal plane: joint properties with respect to a static torque.
2002. Submitted for Publication.
Tortora, G. J. and Grabowski, S. R. Principles ofAnatomy and Physiology. 7'h ed.
HarperCollins. New York: 1993.
Vestibular Disorders Association, The (VEDA). 2002. Retrieved July 02, 2002 from
http://www.vestibular.org/
46
Appendix A
A.1 MathCAD Worksheet for PRBS Generation
Pseudo-Random Binary Sequence
Formulating the Sequence
sd:= 10
sd = seed length
This is the length of the initial sequence.
k := 0.. sd - 1
k is the individual place in the sequence.
L:= 2sd -2
L is the length of the sequence minus one.
L = 1022
j:=L.. L - sd + 1
xj
round(md(1))
j :=L - sd.. 0
xj
j+7 @ Xj+10
j is the value of L for the place where you are in
the sequence within the initial seed length.
x1 is the value assigned randomly to the initial
seed length sequence.
j is defined here as the part of the sequence excluding
the initial seed length part. It goes from the first 'new'
part to zero.
xi is the equation for the 'new' value to be put into
the sequence. It is defined as the exclusive or of
the seventh number from the most recent new
value with the tenth number from the most recent
new value. XOR mean either or, but not both.
k
xk
0.. L
2.(xk - 0.5)
k is defined as the length of the sequence
xk is the x value in the kth position. Since we want
either +1 or -1, it is multiplied by two after having 0.5
subtracted from it.
47
This is the plot of the PRBS, with values adjusted to be from +1 to -1. These are the
values that the motor will be given. (cw or ccw)
2
xk
0
-20
20
60
40
k
48
80
100
A.2 Torque and Velocity Analysis
Torque and Velocity Analysis
J = inertia, T = torque, ( = angular velocity
T = d-Jo)
dt
do
T = J-dt
I
Tdt = J.{
-
dt
dt
T-At = J-Ao
Ao =
1
*T-At
--
J
Tk-At
(Of - (00 =
per step k
where
torque is the torque value defined for the motor
torque := 0.2
T
At
torque-x
0.06
J is the total inertia of the rotating piece in kg*m
J = 4.649 x 10- 3
k
1.. L
Tk I-At
+
Ok := Ok-1
J
49
2.
Torque Profile (Nm)
0.2
(T)k
0
-0.2
60
40
20
0
80
100
k
Angular Velocity Profile (rad/sec)
50
0
I
I
I
I
-50
-100
0
200
600
400
800
k
These rotational velocity values are in rad/sec.
miio) = -67.108
max(o) = 49.04
These values are in revolutions per minute.
mi4(o).60 = -640.833
2-7
max(0)- 60= 468.301
2-n
50
1000
A.3 PRBS Calculations for 10 Signals with seed length = 10
Calculation of PRBS with seed length of 10.
Found 10 PBRS sequences.
n := 10
n is the number of PRBS to generate.
sd := 10
sd is the seed length.
2
L is the total length of the sequence.
for ie0.. n - 1
seed gives you the initial seed length of
random numbers, either 0 or 1. Fills the entire
first column with 1. Because if seed becomes
all zeros (essentially all -1) then it is possible
for the sequence to be all -1's.
2 sd
seed :=
m i, O - 1
for
je
1 .. sd - 1
mi,' j+<- 1 round(md(1))
m
prbs(m) :=
prbs fills in the entire sequence with
0 or 1 using exclusive or and the intial
seed length. First puts seed in all spots in
matrix to define it. Starts at the end of the
matrix and fills in the beginning with PRBS.
for iE0..n- 1
k +- 0
for j e 0.. L
Vi, j +- mi, k
k*<-k+ 1
k +- 0 if k > 10
for iE0..n- 1
for j e L - sd.. 0
Vi, j +- vi, j+7 @ vi, j+10
V
normaliz(m) :=
normalize makes the sequence consist
of either -1 or 1.
for ie 0.. rows(m) - 1
for j e 0.. cols(m) - 1
mi, j<- -I
if mi, j = 0
m
x := normaliz(prbs(seed))
51
Velocity and Torque Analysis
torque is the torque value defined for the motor
torque := 0.2
T := torque-x
time interval in seconds.
At := 0.06
J
4.649-10
i
0.. n - 1
()
i, 0
3
ring inertia in kg*m 2.
k:= 1..L-1
initial angular velocity = 0 rad/sec.
0
Oi, k =
i,(k
+ Ti,(k-1) At
J
max(o) = 85.18
mir(o)
=
These rotational velocity values are in rad/sec.
-100.667
max(o) 60 = 813.405
2-n
These values are in revolutions per minute.
0 ---6602 = -961.297
mi mi~)
2-7t
52
Maximum angular velocity calculations for each of 10 PRBS signals.
absolute(z) :=
absolute finds the absolute value of each
velocity.
for ie 0.. rows(z) - 1
for j e 0.. cols(z) - 1
zi
j
Z
abso := absolutdo)
absAi := max(submatridabsoi,i,0,m- 1))
absA finds a matrix of the maximum values
in each row of the absolute o values.
These values are in rad/sec.
These values are in rpm.
absAi =
64.53
77.436
85.18
82.598
98.086
67.111
74.855
98.086
100.667
85.18
absAi.
60
=
2-7c
616.216
739.459
813.405
788.757
936.649
640.865
714.811
936.649
961.297
813.405
max(absA)
=
60
max(absA) 6- = 961.297
2-n
100.667
mir(absA)-60 = 616.216
mir(absA) = 64.53
2-7c
53
A.4 PRBS Calculations for 10 Signals with seed length = 12
Calculation of PRBS with seed length of 12.
Found 10 PBRS sequences.
n := 10
n is the number of PRBS to generate.
sd := 12
sd is the seed length.
L := 2sd - 2
L is the total length of the sequence.
seed gives you the initial seed length of
random numbers, either 0 or 1. Fills the entire
first column with 1. Because if seed becomes
all zeros (essentially all -1) then it is possible
for the sequence to be all -1's.
for iE0 ..n- 1
seed :=
n, 0 <-
for
je
1
1 .. sd - 1
mih, j +- 1 roundmd(1))
m
prbs(m) :=
prbs fills in the entire sequence with
0 or 1 using exclusive or and the intial
seed length. First puts seed in all spots in
matrix to define it. Starts at the end of the
matrix and fills in the beginning with PRBS.
for iE 0..n- 1
k +-0
for j e 0.. L
vi, j <
mi, k
k+-k+ 1
k <- 0 if k> 10
for ie0..n-1
for je L-sd..0
Vi, j <- vi,j+7 E vi,j+10
V
normalizom) :=
normalize makes the sequence consist
of either -1 or 1.
for ie 0.. rows(m) - 1
for j e 0.. cols(m) - 1
mi, j ---I
if mi,
0
m
x := normalizoprbs(seed))
54
Velocity and Torque Analysis
torque is the torque value defined for the motor
torque := 0.2
T := torque-x
At := 0.06
time interval in seconds.
J := 4.649*-10~
ring inertia in kg*m 2.
i:= 0..n- 1 k := 1..L- 1
oi, o:
initial angular velocity = 0 rad/sec.
0
Ti, (k-1) -At
+
O~i~k :O=i,(k-1)
max(o) = 121.316
mir(io)
=
These rotational velocity values are in rad/sec.
-100.667
max(o) 60 = 1.158 x 103
These values are in revolutions per minute.
2 -ii
mio). 60
=
-961.297
2 -7
55
Maximum angular velocity calculations for each of 10 PRBS signals.
absolute(z) :=
absolute finds the absolute value of each
velocity.
for ie 0.. rows(z) - 1
for je 0.. cols(z) - 1
(zi,j<-
Izij)
z
abso := absoluto)
maxsubmnatiiabsoj,O,,m- i))
absAi:
absA finds a matrix of the maximum values
in each row of the absolute o values.
These values are in rad/sec.
These values are in rpm.
absAi
absAi*
67.111
90.342
61 .949
64.53
121 .316
87.761
80.017
108.41
100.667
77.436
max(absA)
60
-
=
2 -R
640.865
862.703
591.568
616.216
1.158-103
838.054
764.108
1.035-103
961.297
739.459
=
max(absA)--
121.316
60
= 1.158 x 103
2.r
mir(absA). 60 = 591.568
2 -c
mir(absA) = 61.949
56
A.5 "Sampled" PRBS and Power Spectrum
"Sampled" PRBS
Generation of "Sampled PRBS" by filling in values using algorithm.
t
ts :
k
i
time between PRBS executions
0.06
ts is the time between samples
0.01
t
k is the number of sprbs for every one prbs.
k = 6
ts
length of x PRBS
0.. L
lengtl(x) = 1.023 x 10 3
L = 999
j
0.. k-N - 1
N = 1 x 103
p :=0.. k
sprbs(x) :=
sprbs is the algorithm to generate the "sampled"
PRBS
j +-- 0
for ie 0.. L
for pe0..k-1
Yj +
xi
j +- j + 1
x is the original PRBS
y
0
1
2
3
4
sprbs(x) =
5
6
7
-1
-1
-1
-1
10
2
3
4
-1
-1
5
1
7
6
8
8
9
0 -~1
1
9
10
11
57
-1
-1
-1
1
-1
-1
"Sampled PRBS"
y := sprbs(x)
Original PRBS
1
0
-1
0
2
3
I I
"Sampled" PRBS
1
0
-1
0
6
12
18
Torque associated with PRBS.
yy:= 0.2-y
Frequency Range of PRBS:
1
N-At
1
-
ff := -
fj
=
0.016
lowest effective frequency present in PRBS
=
5.556
highest effective frequency present in PRBS
58
Power Spectrum
n:= 10
n = subdivisions of the input signal
r := 0.5
r = fractional overlap (typically 0.5 for random data)
S := pspectrun(yy,n,r) k := 0.. lengtl(S)
1
lengtl(S) = 1.09 x 103
= 9.174 x 10
lengtl(S)
Smallest frequency the power spectrum can pick up is 1/length(S).
Power Spectrum
0.4
A'i
.
0.3
0.2
0
0
0.1
0
0
80
60
40
20
100
Frequency (Hz)
Power Spectrum
1
-OI
0.1
0.01
~L)
0
1
1 -C5
4
1
-10-4
0
5
10
15
~
20
Frequency (Hz)
frequency at 3dB - 7.6923 Hz
This value was found by looking at the ratio between Sk values. When SO/Sk is less than or
equal to -2. (2 - 3dB drop)
59
Appendix B
B.1 Example of Calibration Analysis from Data Set 14 for Subject 1
Data Analysis from Calibration Data 14
Subtract Head Position from Target Position and fit EOG to this using least squares
Head Data from Calibraton
h
D:\..\Head14.dat
Correction for gain (20X during calibration)
hg :=
-
hl
median filter
hg:= medsmootl(hg, 7)
At :=
samp:= 200
samp
N := lengtl(hg) N = 9.001 x 13
n:= 0.. N - i
hg:= submatri(hg, 1o, lengtl(hg) - 10,0,0)
convert from volts to deg/sec
hv:= (hg) -29.99
Watson Sensor Factor: 29.99 deg/sec/volt
Correct for offset and drift
Fit a line to the head velocity data and subtract it out - account for drift in the watson
sensor.
B := lengtl(hv)
(
in~hx, hv)
=
y:= b0+ 1 1 -hx
b := o.. B - i
-7.219
6
l3.409x 10-6
1 := in~hx,hv)
hv:= hv-y
60
hxb := b
Conversion from velocity to positon:
Integrate the velocity to get the position: first try using trapezoidal rule
samp:= 200
At :=
At = 5 x 10- 3
N := lengtl(hv)
samp
integra(h,N,At)
for
je
I .. N
N = 8.982x 101
-
n := 0.. N - I
initial area is
zero (p0).
2
P0 4- 0
P
0
pj+
hj +
-(hj+1
hj) -At + pj_ I
p
lengtl(hp) = 8.981x 103
hp:= integra(hv,N,At)
Head Position vs Time
I
10
0
Z0
-1
0
I
I
I
10
20
30
n-At
Time (sec)
61
40
50
Target Data
Ct
D:\..\Targl4.dat
Ct
correct for gain
-
ctg :=
2
median filter
ctg
medsmootl(ctg, 7)
ctg
submatri(ctg, 10,lengtl(ctg) - 10,0,0)
Need to correct for offset:
for target - when 0 was being sent out, find mean value and subtract off
mean target value at first zero step
k := 0
xl := 200-4 x2 := 200.5
x2
ctga
n = xl
tk :
x2 - xl
to= 0.022
mean target value at second zero step
k := i
xl := 200-9
x2 := 200-10
x2
tk
Ctg:
n = xI
tk x2 - xI
62
mean target value at third zero step
k := 2
x3
200-14
x4 := 200-15
x4
tgn
I
n = x3
tk :
x4 -- x3
mean target value at fourth zero step
k := 3
x3 :200-18.5
x4 := 200-19.5
x4
Sctgn
n = x3
tk :=
x4- x3
mean target value at fifth zero step
k := 4
xl := 200-23.5 x2 := 200-24.5
x2
ctgx
tk :=
x2 - xl
mean target value at sixth zero step
k := 5
xl := 200-28
x2 := 200-29
x2
ctgn
tk --
n = xl
x2 - xI
63
mean target value at seventh zero step
k := 6
x3
x4 := 200-34.5
200-33.5
x4
Z
tk
ctgn
n = x3
x
x4 - x3
mean target value at eighth zero step
k := 7
x3 :200-40
x4 := 200-42
x4
ct&n
tk :
n = x3
x4 - x3
0.022
0.022
0.022
t
0.022
0=
0.022
0.022
0.022
(0.022)
meant = 0.022
meant:= mear(t)
ctO = offset corrected
cto := ctg- meant
-
Change target voltage values into angle values in degrees sing relationship between mirror
screen and subject - screen distances.
Ctp
t
ata
_
1.
7T
I
10. 6 5 -- -(cto)
_
180
_
6 6 -tan
180
7
64
ctp = (offset, gain, degrees)
Target Postion vs Time
I
I
I
20
ctpn
0
0
U
-20
0
I
I
I
10
20
30
50
40
n-At
Time (sec)
Target position minus head position (th)
lengtl(hp) = 8.981x 103
lengtl(ctp) = 8.982x 103
tp := submatri:ctp,0,lengtk(hp) - 1,0,0)
th:= tp - hp
At :=
At = 5x I-3
N := lengtl(th)
-
fsamp:= 200
&amp
N = 8.981 x 103
n =
.. N - I
Target minus Head Position (deg)
I
I
I
I
20
thn
0
-20
0
I
I
I
I
10
20
30
40
n-At
Time (sec)
EOG
65
50
&
ce
D:\.\EOG14.dat
ceg :=
i
correct for gain
median filter
ceg := medsmoott(ceg, 7)
ceg := submatri(ceg, 1o,lengtl(ceg) - 10,0,0)
fsamp := 200
At :=
N := lengtl(ceg)
N = 8.982x 10,
samp
n := 0.. N - 1
Fit a line to the eog data and subtract it out - account for drift in the eog
exie := le
le := o.. E - i
E := lengtl(ceg)
1.226
lin~ex, ceg) =
y := b + 11 -ex
1:= lin~ex,ceg)
2.575x 10- 6)
lep := ceg - y
Eye Position in Volts
0.2
lepn
0.1
0
0
-0.1
-0.2
0
I
I
I
10
20
30
n-At
Time (sec)
66
40
50
Least Squares Difference
N
x
I
samp
At :=
samp:= 200
lengtl(lep)
N = 8.982x 103
M:= lengtl(th)
n:= 0.. N - 1
M = 8.981 x 103
Moved EOG over by 50 data to try
to match up the eog with target
y := submatriLth,0, M - 51,0,0)
submatriX lep,50, M - 1,0,0)
N := lengt(x)
N-i
N-1
N
xi
I
Iyi
i=0
i=0
N- -i
b:=
N-I
N-i
(xi) 2
xi
0
i=0
i=0
-0.224
*b
c:=A
158.07
simplified method (from James Tangorra)
P := lengtl(lep)
lengt(lep) = 8.982x 103
lengtl(th) = 8.98Ix io3
xx:= submatriX lep,50,P - 1,0,0)
ss :=
(T
xx
T
\- I
xx
-xx -yy
yy:= submatri(th,0,P - 51,0,0)
ss = (158.072)
Both cl and ssO are very close in value. To be consistent Iwill use ss because it is simpler than
my LS calculations. Need to multiply by ss to get into degrees from volts.
lep := sso-lep
67
Eye and Target minus Head Position (deg)
25
20-
lepn
0
- 25 -20
"
-
thn
I
I
0
10
0.
30
20
n-At
40
50
50
Time (sec)
eye
target-head
68
IVV
B.2 Example of Weight Trial Analysis from Data 15 for Subject 1
Analysis of data set #15- 2.5V, 0.25Hz sine wave - helmet, delrin
EOG Data
e
:=
D:\..\EOG15.dat
lengtl(eg) = 7.601 x 10 3
I)
eg:=
gain corrected eog
median filter
eg := medsmootl(eg, 7)
N = 7.601 x 10 3
N := lengtl(eg)
I
1
s amp
At :=
samnp:= 200
eg :=submatri:(eg, 10 ,lengtl(eg)
-
10 , 0,0)
n:= 0.. N - 1
take out first 10 data and last 10 data
to get rid of spikes
Fit a line to the eog data and subtract it out - account for drift in the eog
calibration ratio from Calibration 14
b := 158.072
E
exe := e
e := 0..E- 1
lengtl(eg)
1.213
fin~ex, eg) =
lep:= (eg - y)-b
+ li -ex
y:
x := 0.. lengtl(eg) - 1
1:= Iin4ex, eg)
1.099 X 10- 6
Eye Position in Degrees
20
lepn
0
yn
0
I
-20
-40
0
-
5
10
15
20
n-At
Time (sec)
69
25
30
35
40
-r
Target Data
:
t
D:\..\Targ15.dat
tg :
t
gain corrected target
2
median filter
tg:= medsmootl(tg, 7)
At
samp := 200
1
N := lengtltg)
take out first 10 target data and last 10 data
mean target value at beginning
xO:= 0.200
xI := 1.0-200
X1
~tgn
ttk :=
n = xO
tto = 0.022
X1 - x0
mean target value at end of experiment
xO := 36-200
k := 1
I
ttk:=
n:= 0.. N - 1
samp
tg := submatri:(tg, 10,lengtl(tg) - 10, 0, 0)
k := 0
N = 7.601 x 10
x:
37-200
tgn
n ==x0
AO
tti = 0.022
x1 - x0
meantt:= mear(tt)
meantt= 0.022
Correct for offset
tpo := (tg - meant)
70
-
Change target voltage values into angle values in degrees using relationship between mirror
screen and subject - screen distances.
tp :=atan 1.66 -ta4
180
7C
10.65-- .(tpo)
180
--_ __7T
Eye and Target Position in degrees
50
lepn
0
-50
I
0
5
I
I
I
I
I
I
10
15
20
25
30
35
40
n-At
Time (sec)
Head Data
h
=
D:\..\Headl5.dat
h
Correction for gain
-
hg:=
2
hg := submatrihg,10,N - 10, 0,0)
Take out first 10 data and last 10 data
hg:= medsmootl(hg, 7)
Median filter data to smooth it out.
Correct for Offset
hv:= (hg) .29.99
convert from volts to deg/sec
Watson Sensor Factor: 29.99 deg/sec/volt
71
Head Velocity vs Time
100
(U
50
hvn
0
-
-
0
-501
-100
20
15
10
5
0
25
30
35
40
n-At
Time (sec)
Fit a line to the head velocity data and subtract it out - account for drift in the watson sensor.
b := 0..B- I
B := lengtl(hv)
hxb := b
-6.649
lin~hx,hv) =
-6.247 x 10
y:=10 +11-hx
1:= lin~hx,hv)
5i
hv:=hv-y
Conversion from velocity to positon:
Integrate the velocity to get the position: first try using trapezoidal rule
fsamp:= 200
At
At = 5 x 10- 3
N
integra(h,N,At) :=
&amp
lengtl(hv)
for
N = 7.582 x 103 n:= 0.. N - 1
j e 1.. N - 2
P0
<-
Pj+
initial area is
zero (pO).
0
hj + -.(hj+1 - hj) -At + pj- I
1
1 2
P
72
lengtl(hp) = 7.581 x 10 3
hp := integra(hy, N, At)
Head Position vs Time
50
1-1
-
I
hpn
0
0l
-'
0
30
20
10
40
n-At
Time (sec)
Gaze = head position + eye position
i := 0.. lengtl(hp)
gaze(hh, e) :=
for iE 0.. lengtl(hh) - 1
gi+- hhi + ei
g
lg:= gaze(hp,lep)
I
50
Gaze and Target Position in degrees
I
I
I
I
lgn
tpn
0
0
-50
0
5
10
15
20
n-At
Time (sec)
73
25
30
35
Clip to make whole number of cycles.
shorten signals, then zero mean.
Ig:= submatriXlg,259,6227,0,0)
lep:= submatriXlep,259,6227,0,0)
hp := submatrihp,259,6227,0,0) tp
submatritp,259,6227,0,0)
lg:= 1g- mea(lg)
ltp:= tp - mear(tp)
P := lengtl(lg)
p := O..P- 1
lgeffor := Iltpp
-
1gI
mean(1gerroi) = 3.067
Head, Eye, and Target Positon (deg)
60
hpn
lepn
II
I
0
0
-60
0
5
10
20
15
n-At
Time (sec)
head
eye
target
zero
74
25
30
35
Gaze and Target Position (deg)
60
lgn
ltp0
0
0
-60
I
0
5
I
I
I
10
15
20
I
I
25
30
35
n-At
Time (sec)
gaze
target
zero
Ratio of gaze over target at amplitudes
36.84
= 0.905
40.712
-35.375
-40.706
-36.692
= 0.901
-40.706
33.861 =
40.712
35.264
=
40.712
36.897
=
40.712
37.354
=
40.712
38.087 =
40.712
-36.181 = 0.889
-40.706
38.705 = 0.951
40.712
-37.24
-
0.915
-40.706
-38.79
-40.704
= 0.953
-37.742
-40.704
= 0.927
-35.013
-40.706
= 0.86
0.832
0.866
0.906
0.918
0.936
0.905 + 0.832 + 0.866 + 0.906 + 0.918 + 0.936 + 0.951
7
0.869 + 0.915 + 0.953 + 0.927 + 0.901 + 0.889 + 0.86
= 0.902
7
75
= 0.902
0.902)
Gain:= (0.902 +
2
Gain= 0.902
Gaze Error: 800 grams
20
15
gerrorn
10
5
0
0
5
15
10
I
I
20
25
n-At
Time (sec)
mear(lgerroi) = 3.067
mean gaze error amplitude in degrees
var(lgerroi) = 3.482
stdev(lgerroi) = 1.866
lctg:= lcori(ltp, 1g)
I
I
I
I
I
I
I
0.995
1Ctgn
0.99 I
0
I
I
I
I
I
I
I
0.01
0.02
0.03
0.04
0.05
0.06
0.07
n-At
using trace: the lag appears to be 0.015 sec.
76
30
What percentage of gaze positon is head position?
Divide head vector by gaze vector at peak amplitudes and take average value.
Head, Eye, and Gaze Positon
60
hpn
lepn
lg
0
I
I
I
I
15
20
25
0
-60
0
5
10
n-At
Time (sec)
%head(h, g) :=
for j e 0.. 6
hh<- submatriih,j.800,(j + 1)-800,0,0]
gg+- submatrijg, j-800,(j + 1).800,0,0]
ma) <-max(hh)
max(gg)
mi(hh)
mi(gg)
.hm
ph <- stack(phmax, phmi)
13
ZphA
mean+-
n=0
14
mean
%head(hp,lg) = 0.908
77
30
35
Appendix C
C.1 MathCAD Worksheet for PRBS Velocity Calculations
Calculation of Angular Velocities for PRBS Signal
PRBS generated in tenseedlO.mcd
D:\..\sd10_567.txt
lengtl(x) = 1.023 x 103
sd := 10
N := 1000
L:= lengtl(x) - 1
J
At
current ring rotational inertia in kg*m 2
4.649-10- 3
time interval in seconds
0.06
torque in Nm
torque:= 0.2
T
torque-x
k
1.. N
Tk I-At
Ok := (Ok-i
+
J
Angular Velocity (rad/sec)
100
I
I
I
200
400
600
50
(Ok
0
-50
-100'
C
800
1000
k
miido) = -59.368
These rotational velocity values are in rad/sec.
max(o) = 54.205
miio) .
=
-566.919
These values are in rpm.
2 7c
maxo).-0=
517.622
2 .7
78
C.2 MathCAD Worksheet used for Testing
Using PRBS from sd10_567.dat, run through sample algorithm to get less time between points
while maintaining the frequency of original prbs.
N = length of original PRBS used in testing
N := 83
L
N-1
t
0.06
time between executions
tt
0.005
time between new points
t
-
k
tt
k
=
12
k is the number of samp for every one signal
length of x signal
i :=0.. L
L = 82
j
0.. k -N - 1
p
0.. k
samp(x) :=
j +- 0
samp is the algorithm to generate the "sampled"
signal
for ie0..L
for pe0..k-1
yj +-xi
j*-j+1
Y
D:\..\sd10_567.txt
x := submatri(x, 1 ,N,0,0)
lengtl(x) = 83
X:= samp(x)
lengt(X) = 996
79
I I
Original PRBS
1
xi
9
0
-1
1
0
2
3
24
36
Sampled PRBS
I
(
Xi
Q
-1I
0
12
80
Calculation of Angular Velocities for sampled PRBS
ll:= lengtl(X)
11= 996
J
2
current ring rotational inertia in kg*m
4.649-10 -3
new time interval
tt= 5 x 10- 3
torque in Nm
torque:= 0.1
Torq := torque-X
k := 1.. 11- 1
Torqk- -tt
Ok := O)k-1
+
J
Angular Velocity (rad/sec)
30
I
I
I
I
20
10
-I
-
0
-10
0
200
400
600
800
1000
k
mir(co) = -1.2906
These rotational velocity values are in rad/sec.
max(0o) = 21.9402
mi o) --6 = -12.32432
21n
These values are in rpm.
max(0) -60= 209.5135
2-n
81
Voltage Output to Amplifier for Motor
N -cm
N-cm
Tf := 2.1
Kd:= 0.5
Krpm
N-cm
Amp
Kt:= 4.78
60
convert to N*cm
Torq:= Torq-100
(0 := ( --
2-7c
voltage:=
for ie 0..11- 1
Kdoi
(Torq).+ Tf+
Ii+-
1000
Kt
Vi - 0. 6 2 5 -Ii
V
2
1
voltagek
0
0
1
U
I
. i
-1
3
2
k-tt
82
4
5
Output to Ampifier
NN := 1992
OutputRate:= 400
Hz
sample rate
At
At = 2.5 x 10- 3
sec
OutputRate
0.. NN
tor :=
time+- timeAt)
for kc= 0.. NN- I
timei(0)
errO <- da 0, voltagekJ
if mod(k,2) = 0
2)
torquek
+-
1000-ad(0)
tk +- ad(1)
tor +- augmen(torque, t)
errO +- da(0,0.0)
tor
83
tol
.
C.3 Data Analysis of Torque Sensor Output and Torque Signal Input
D:\..\28June_a2.dat
At := 0.0025
tsensor:= submatri(tor,O,NN - 1 ,0,0)
out:= submatri3(tor,0,NN - 1 , 1 , 1)
calibration offset from 28Junecal2.mcd
tsensor := -[tsensor - (-1.544)]
torque sensor in mVdc
50
tsensorj
0
-50
0
2
1
4
3
5
j-At
input in Volts
4
outi
I ..
I
j
-
-
-
2
0
-2
-4
I
II
0
1
3
2
j-At
84
I
4
5
Get back sampledo
60
2.7r
11= 996
length of x signal
tt
k :
At
k is the number of samp for every one signal
k= 2
i:= 0.. 11- 1
b
0.. k-11- 1
p
0.. k
samp(x) :=
b <- 0
samp is the algorithm to generate the "sampled"
signal
for ie 0..11- 1
for pe 0 .. k- 1
Yb <- Xi
b<-b+ 1
Y
w := samp(Go)
lengti~o) = 1.992 x 103
generate "sampled" o
NN = 1.992 x 103
85
Power Spectrum of Torque Sensor
subdivisions of the input signal
n := 2
n
=
r := 0.1
r
=
S := pspectrunitsensor,n,r)
k := 0.. lengtl(S)
fractional overlap (typically 0.5 for random data)
= 9.551 x 10O
lengtl(S) = 1.047 x 10 3
lengtl(S)
N = 1.992 x 10 3
At = 2.5 x 10 -3
Power Spectrum: Torque Sensor
lu
1
1
10
15
01
W
01
-
0**
0
0.
-
0
1 10
3
_
S
S
1 -10
5
0
20
Frequency (Hz)
S.
es
01
Power Spectrum: Torque Sensor
**g*
-
*
6
4
0
2
0
0
100
300
200
Frequency (Hz)
86
400
Power Spectrum of Torque Input
nn := 2
nn = subdivisions of the input signal
r := 0.1
r = fractional overlap (typically 0.5 for random data)
SS := pspectrug~tout,nn,r)
kk := 0.. lengtl(SS)
= 9.551 x 10-
lengtl(SS) = 1.047 x 10
lengtl(SS)
N = 1.992 x 10 3
At = 2.5 x 10 -3
10
1
-*
-
5
*
,
..
*
.
.
e
0.1
0
,0
*
.
0.01
-*
~*S.
0
-*
.5
0
..
1.- 4
0
,.
'eS*
_
1-10-3
0
15
10
5
20
Frequency (Hz)
Power Spectrum: Sampled PRBS
3
2
00
0i
0
90
1
0
I
0
100
I
~
200
300
Frequency (Hz)
87
400