Cleveland State University

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.

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)

Midterm Solutions

Homework 11, 13, 14

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

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 {xi}, and the fitness of xi is f (xi) = 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 -

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