Department of Electrical and Computer Engineering

Department of Mechanical Engineering

EEC 492/592 and MCE 493/593 - Prosthesis Design and Control

Fall 2014

__Homework Assignments__

__Homework 1 due August 28
__

Hand in the answers
to Questions 1-4. Question 5 will be graded during class on
the basis of your participation.

1. Visit
the web page http://en.wikipedia.org/wiki/Transverse_plane
to see the definition of the sagittal, coronal, and transverse planes.

a. In
which plane does most of the motion take place during normal walking?

b. In
which plane does most of the motion take place when rotating your head?

c. In
which plane does most of the motion take place when you lean to the side?

2. Do a Google search for the “six determinants
of gait.”

a. What are the six determinants of gait?

b. In which plane does pelvic rotation take
place? (ambiguous?)

c. In which plane does pelvic tilt take place?
(ambiguous?)

d. In which plane does lateral pelvic motion
take place? (ambiguous?)

3. Kuo and Donelan wrote a paper called “Dynamic
principles of gait and their clinical implications,” in which they discuss the
six determinants of gait.

a. What are the two hypothesized goals of the
six determinants of gait?

b. What is the name of the model that they
believe explains human gait better than the six determinants?

4. Find the paper “Energy cost of walking of
amputees: the influence of level of amputation.”

a. What is average walking speed (meters/minute)
for able-bodied persons?

b. What is the average walking speed for
vascular above-knee amputees?

c. What is the average walking speed for
traumatic above-knee amputees?

d. What is average oxygen intake
(milliliters/kg/meter) for able-bodied persons?

e. What is the average oxygen intake for
vascular above-knee amputees?

f.
What is
the average oxygen intake for traumatic above-knee amputees?

g. How does the paper explain the differences in
performance between vascular above-knee amputees and traumatic above-knee
amputees?

5. Print hard copies of the following papers.
They are all readily available on the internet, except for the last two, which
you can download using the provided links. Skim through each paper. Pick two
papers to read in detail, and be prepared to lead a class discussion on those
two papers, including some discussion of the questions following the paper
title. Collaboration with other students is encouraged.

a. “Comparative Biomechanical Analysis of
Current Microprocessor-Controlled Prosthetic Knee Joints”

·
According
to the Conclusions Section at the beginning of the paper, which prosthesis
offers the greatest safety to the amputee?

·
According
to the introduction, what are some of the advantages of microprocessor
prostheses relative to purely mechanical prostheses?

·
According
to the Study Limitations Section at the end of the paper, why might the results
reported in the paper be biased toward the C-Leg?

b. “Recycling Energy to Restore Impaired Ankle
Function during Human Walking”

·
How does
the artificial foot in this paper capture energy: with a spring, hydraulics,
pneumatics, or motor?

·
What is
the rate of work in Watts that is expended by the average person during normal
walking

·
In their
study, how many Watts were expended during ankle push-off by a conventional
foot prosthesis? How many Watts were expended during ankle push-off by their
new foot prosthesis?

·
What was
the percentage of average power increase (relative to normal) during walking
for amputees wearing a conventional foot prosthesis? What was the percentage of
average power increase for amputees wearing their new foot prosthesis?

c. “Biomechanical Energy Harvesting: Generating
Electricity During Walking with Minimal User Effort”

·
How much
average power was produced in continuous-generation mode, and how much
additional power was expended during walking? How much average power was
produced in generative braking mode, and how much additional power did was
expended during walking?

·
What
implications does this research have for prosthetic leg technology?

d. “Ankle-Knee
prosthesis with powered ankle and energy transfer for CYBERLEGs
α-prototype”

·
How do
these researchers capture knee energy: with a spring, hydraulics, pneumatics,
or motor?

·
According
to Figure 3, what is the peak torque produced by the ankle during able-bodied
walking?

·
According
to Figure 5, what is the peak torque produced by the knee during able-bodied
walking?

e. “Powered Robotic Legs - Leaping Toward the
Future”

·
How much
faster was the amputee’s walking speed with the new prosthesis?

·
How much
less energy did the amputee expend with the new prosthesis?

·
How much
does the prosthesis weigh?

f.
“Evaluation
of function, performance, and preference as transfemoral amputees transition
from mechanical to microprocessor control of the prosthetic knee”

·
What was
the first prosthetic knee to use microprocessor control? In which phase (swing
or stance) was it used?

·
What was
the first prosthetic knee to use microprocessor control in both swing and
stance phase?

·
According
to the conclusion, what seven areas of statistically significant improvement
result from the use of a microprocessor-controlled knee compared to a passive
knee?

g. “Self-Contained Powered Knee and Ankle
Prosthesis: Initial Evaluation on a Transfemoral Amputee”

·
What
type of microcontroller is used in the Vanderbilt leg?

·
The
Vanderbilt leg gain-schedules controller parameters depending on the “walking
phase.” How many sets of controller parameters (that is, how many walking
phases) does the Vanderbilt leg use?

·
What is
the average power requirement of the leg during level walking?

·
Given
the battery type that is used in the leg, how long could an amputee walk
between battery charges?

h. “Energy generation and absorption at the
ankle and knee during fast, natural, and slow cadences” - http://academic.csuohio.edu/simond/courses/prosthesis/Winter1983.pdf

·
How much
energy per stride is produced/absorbed by the ankle/knee combination during
fast walking? How much during natural walking? How much during slow walking?

__Homework 2 due September 2__

1. According to the paper “Microprocessor
Prosthetic Knees,” how long can a C-Leg be used after a 15-minute battery
charge? How long can it be used after a 4-hour charge?

2. According
to the abstract of the paper “Review of secondary physical conditions
associated with lower-limb amputation and long-term prosthesis use,” by Robert
Gailey et al., what three bone disorders can result from prosthesis use?

3. Download David Winter’s 1984 paper from http://academic.csuohio.edu/simond/courses/prosthesis/Winter1984.pdf. One of the studies reported in the paper is
an intra-subject study that quantifies the gait variation of a single
individual from one day to the next. How much variation in ankle angle and knee
angle (degrees RMS) did Winter observe? What does this imply for prosthesis
control?

__Homework 3 due September 11__

__Homework 4 due September 16 at the beginning
of class__

1. __Prosthesis motor requirement for standing up
from a squatting posture__

This will use the model from slide 11. You may assume that the knee motor is
the only source of power in each leg. Estimate the limb dimensions and weight
carried by each leg. It may be useful to do a Google search for: anthropometric
data D.A. Winter

I need from you the following:

a. (15%)
Find an expression for the motor torque M required to initiate standing up from
a squat at knee angle q. Plot M as a function of q and label the axes properly.

b. (15%) Based on a typical duration of a
standing up movement, what would be the peak angular velocity in the knee
during this movement? Note that motor angular velocity is usually expressed in
revolutions per minute (RPM). Do the
necessary unit conversion.

c. (10%) Find a commercially available motor
that has the torque and speed capacity to stand up from any knee angle. It will
probably be a geared motor. Provide manufacturer, model number, website
address, and motor specifications (rated torque, rated speed, power, weight,
size).

d. (10%) Is this motor suitable for use in a
prosthetic leg? Explain your answer.

2. __Role of series elasticity in jumping
__The following paper is
available online: Behavior of fascicles and tendinous structures of human
gastrocnemius during vertical jumping, by Kurokawa, Fukunaga, and Fukashiro.

Answer the following questions:

a. (15%) What is the maximal shortening velocity
of the muscle fibers (fascicles) during the jump?

b. (15%) If the tendon was a rigid steel cable,
how would this shortening velocity affect the force generating capacity of the
muscle fibers? (Express shortening velocity in fiber (fascicle) lengths per
second and use the force-velocity relationship presented in class.)

c. (10%) Because the tendon is elastic, the
maximal fascicle (fiber) shortening velocity is lower than the MTC shortening
velocity. What is this shortening velocity and how does this affect the
force-generating capacity of the muscle fibers?

d. (10%) How would you include this concept in a
prosthetic limb design?

__Homework 5 due September 18__

__Homework 6 due September 23__

__Homework 7 due September 30__

__Homework 8 due October 2__

See slide 19 of 2014-09-25 Measurements 1.pdf

** Homework 10 due October 7 at the beginning of
class** (we skipped
homework 9)

http://academic.csuohio.edu/richter_h/courses/prosthesis/

__Midterm Solutions__

Dr.
van den Bogert’s questions

__Homework 11, 13, 14__

http://academic.csuohio.edu/richter_h/courses/prosthesis/

__Homework 12 due October 28__

See slide 2 of 2014-10-21 Kinematics Kinetics 2.pdf

Solution - Assignment
12 solution.pdf

__Homework 15 due November 6 at the beginning
of class__

1. Write a random mutation hill climbing
algorithm to optimize an impedance controller for a prosthetic knee during mode
2. See Dr. van den Bogert’s slides for details about the human gait data that
you should use, and for the definition of “mode 2.” For the cost function, use
the RMS error between the controller knee torque and the human knee torque.
Hand in the following.

a. A clear description of the problem
formulation, including the form of the impedance controller that you decided to
use

b. Your Matlab code

c. A convergence plot for a typical optimization
run

d. A plot of the best torque output of the
impedance controller that you obtained, along with the human knee torque

e. How many generations do you have to run the
algorithm to get convergence for most simulations?

2. Repeat for mode 1, except for the cost
function, use the maximum absolute error between the controller knee torque and
the human knee torque.

Solution – RandomMutationHillClimbingImpedance.m

__Homework 16 due November 13 at the beginning
of class__

1. Suppose you have a GA with 10 individuals {x_{i}},
and the fitness of x_{i} is f (x_{i}) = i for i =1, …, 10.
Suppose you use roulette wheel selection to select 10 parents for crossover.
Two parents are selected to mate to create two children; then two more parents
are selected to mate to create two more children; and so forth.

a. What is the probability that the most fit
individual will mate with itself at least once to create two cloned children?

b. Repeat for the least fit individual.

2. Write a computer simulation to confirm your
answers to problem 1.

3. Use a genetic algorithm to optimize knee
impedance control parameters. Use the GA software that was discussed during
class, which has an elitism parameter of 2 and a mutation rate of 0.02. Change
GA_Impedance.m so the GA runs for 200 generations. Change ImpedanceControl.m so
that the entire initial population is randomly initialized. What is the minimum
cost value obtained by the GA, averaged over 20 Monte Carlo simulations?

4. Repeat problem 3 with an elitism parameter of
1. Repeat with an elitism parameter of 10.

5. Set the elitism parameter back to its default
value of 2. Repeat problem 3 with a mutation rate of 0. Repeat with a mutation rate
of 0.2.

6. __500-Level
Students:__

a. Perform a statistical test (for example, a
t-test) to determine the probability that the differences in the average
minimum cost values obtained with different elitism parameters reflect a
fundamental difference in GA performance for the impedance control problem.

b. Perform a statistical analysis to determine
the probability that the differences in the average minimum cost values
obtained with different mutation rates reflect a fundamental difference in GA
performance for the impedance
control problem.

Solution - GAHomeworkSolution.zip

__Homework 17 due November 18 at the beginning
of class__

Write a gradient
descent program to optimize knee impedance control parameters during the first
mode of Winter’s data, which is the first 55 samples of the gait data.

1. Hand in your Matlab program.

2. Tune the gradient descent parameters
DeltaTheta and eta to give steady convergence to a local optimum. Run your
program a few times with randomly initialized values for the impedance control
parameters. Is the gradient descent program converging to a local minimum?
Based on your results, what do you conclude about the number of local minima
for this problem?

3. Run your program with initial impedance
control parameters k1 = 0, k2 = 0, b = 1, theta_e = 50, k3 = 0.04, theta_a = -3. How much
improvement in the cost function do you obtain with your gradient descent
program? How much do the impedance control parameters change from their initial
values? What do you conclude about the sensitivity of the output torque to the
impedance control parameters?

__Homework 18 due November 20 at the beginning
of class__

Modify the basic PSO
algorithm from Section 10.1 in the slides to include acceleration sharing
between particles. Implement your algorithm on one or more benchmark problems.
Discuss your results.

Last Revised: November 21, 2014