O PTIMAL D ESIGN AND C ONTROL OF A
L OWER -L IMB P ROSTHESIS WITH E NERGY
R EGENERATION : A S UMMARY
H OLLY WARNER , D R . D AN S IMON , AND D R . H ANZ R ICHTER
I NTRODUCTION
G ROUND C ONTACT M ODELING
S WITCHED C ONTROLLER
Passive prostheses are above-knee amputees’ primary option for locomotion. These prostheses are not capable of
producing natural kinematics. This increases the risk of
ancillary health problems. Furthermore, amputees must
expend more energy than able-bodied individuals while
walking. A solution to these issues is an active (powered)
prosthesis. Powered prosthesis designs currently have a
limited battery life and still lack some features of natural
gait. Human gait data suggests that the knee joint produces excess energy that may be collected to drive the ankle
joint; therefore, energy regeneration could help address the
first issue. Focusing on the latter shortcoming of powered
prostheses, an improved control method should be sought.
Three steps toward the realization of an integrated knee
and ankle prosthesis with energy regeneration will be presented.
Background
Background
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Concept
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Concept
The heel in particular includes significant soft tissue as well
as bone. Noting this fact and observing the kinematic data
for the heel suggests the presence of a damping term.
0.3
0.2
0.1
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Time (Seconds)
1
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−2
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−0.88
Fvert =
kbelt
vert (1
Jm
↵
R
u
C
Motor inertia
Motor torque constant
Motor armature resistance
Power converter ratio
Capacitance
Biogeography based optimization (BBO), an evolutionary
optimization algorithm, was used for the Basic and Generalized Friction Models. Cost was computed over one gait
cycle under open loop control.
2
sat(b ˙vert
, 0, 1)).
The contact model parameters stiffness k and damping b
were defined independently for the heel and toe, forming
two functions Fvert . In addition, a threshold affecting the
magnitude of was defined. This yielded a total of five
unknowns within the model. These variables were selected
by particle swarm optimization over nine trials including
three subjects’ datasets which were composed of up to three
walking speeds each subject and up to two trials per speed.
For the depicted trial the peak heel contact force increased
by a factor of five. Heel strike timing also improved. Across
all trials the model results lacked a double peak, and the
performance degraded in cases where the heel and toe were
not level. All trials replicated the primary features of gait.
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Results
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Time (Seconds)
Heel
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Toe
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Time (Seconds)
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−0.9
−0.92
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Simulated
Reference
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Reference
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Reference
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C ONCLUSIONS
An optimal knee actuator capable of energy-regeneration
was designed. As a consequence of preparing a simulation
for controller optimization, a novel ground contact model
was defined. Finally, a control strategy termed switched
robust tracking/impedance control was developed and optimized.
In brief, the actuator system may be extended and evaluated for the ankle joint. For the ground contact model methods of further increasing the heel force should be investigated. The stability of the controller needs to be established
theoretically. Eventually, extension to continuous gain functions is desired.
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100
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Simulated
Reference
F UTURE W ORK
600
Ground Reaction
Force (N)
• Basic Model: qC = +0.3932 C
• Complex Friction Model: qC = +0.2620 C
• Generalized Friction Model: qC ⇡ +0.056 C
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Simulated
Reference
0
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Ground Reaction
Force (N)
Knee angle tracking of sufficient accuracy for human gait
was observed across all trials. Each model also resulted in
charging of the capacitor. With each consecutively greater
friction accounting, the charge gained decreased in magnitude, but the ability to regenerate energy persisted.
q1 (Meters)
Accordingly, a ground contact model is hypothesized as
Ground Reaction
Force (N)
Knee moment profile
Torsion spring constant
Crank-slider transformation
Ballnut mass
Ballscrew lead
Results
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Results
Mk (t)
K
G
m
l
Combining these controllers should improve prosthetic
gait by balancing the joint tracking and force requirements, allowing for variable human-like joint impedance
behavior, and introducing robustness. The robust tracking/impedance controller was applied to all four degrees of
freedom, hip vertical displacement q1 , hip flexion q2 , knee
flexion q3 , and ankle plantarflexion q4 . Only the gains for
q3 and q4 were discretely switched across five gait phases.
This defines 50 gains to be optimized with BBO.
Five optimization trials yielded gains with much variation.
One notable pattern from trial-to-trial is a high knee stiffness at heel strike, which is reduced during the next phase.
The tracking is sufficiently accurate. The ankle indicates the
most compliant behavior.
2
Heel Vertical
Velocity (m/s)
Heel Vertical
Position (m)
0.4
Switched: discretely varied gains across five phases
Impedance: balance tracking and force
No inertia term in impedance definition
Tested with ankle/knee prosthesis prototype in past
Human joints have dynamically varying impedance
q2 (Degrees)
Ground Reaction
Force (N)
Toe
20
Robust: handles system uncertainties
Impedance: balance tracking and force
Includes inertia term in impedance definition
Applied to ankle/knee prosthesis simulation in past
q4 (Degrees)
The bond graph, a means of multi-domain dynamic modeling, describing the Complex Friction Model is provided.
Removal of the lower R element, the friction model losses,
simplifies the bond graph to describe the other two models.
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Time (Seconds)
q3 (Degrees)
Methods
•
•
•
•
•
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•
•
•
•
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Heel
0
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1. Robust tracking/impedance control
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Background
The parameters of a crank-slider drive
system including ballscrew lead, linkage geometry, motor constant, and supercapacitor initial charge and capacitance may be optimized to accomplish the
greatest capacitor charge (energy regeneration). This was completed through three
consecutive models.
• Basic Model: Optimize for energy regeneration,
omitting all mechanical losses
• Complex Friction Model: Evaluate mechanical
losses under Basic Model optimal parameter set and
realistic screw friction model
• Generalized Friction Model: Optimize for energy
regeneration using efficiency-style accounting for
screw mechanical losses
800
Two controllers from literature:
2. Switched impedance control
Simulated
Reference
Ground Reaction
Force (N)
O PTIMAL K NEE A CTUATOR
1000
Ground Reaction
Force (N)
• Optimal energy regenerative knee actuator design
• Simulation development: Ground contact modeling
• Switched controller design and optimization
Controller design via optimization requires an accurate
simulation. A simulation of a knee and ankle prosthesis
attached to a robotic hip was obtained for this project. The
ground contact model was a simple spring for the vertical
force Fvert = kbelt vert , where is the ground penetration.
Upon optimization the contact model resulted in an early
contact period and a low heel force magnitude.
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400
R EFERENCE
200
0
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H. Warner, Optimal Design and Control of a Lower-Limb Prosthesis with Energy
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Time (Seconds)
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Regeneration, Thesis, Cleveland State University, 2015.
This work was supported by the Wright Center for Sensor Systems Engineering and National Science Foundation grant 0826124.
October 30, 2015