modeling the spino- neuromuscular system terence soule, stanley gotshall, richard wells, mark...
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![Page 1: Modeling The Spino- Neuromuscular System Terence Soule, Stanley Gotshall, Richard Wells, Mark DeSantis, Kathy Browder, Eric Wolbrecht](https://reader030.vdocuments.net/reader030/viewer/2022032800/56649d4e5503460f94a2e94b/html5/thumbnails/1.jpg)
Modeling The Spino-Neuromuscular System
Terence Soule, Stanley Gotshall, Richard Wells, Mark DeSantis, Kathy Browder, Eric Wolbrecht
![Page 2: Modeling The Spino- Neuromuscular System Terence Soule, Stanley Gotshall, Richard Wells, Mark DeSantis, Kathy Browder, Eric Wolbrecht](https://reader030.vdocuments.net/reader030/viewer/2022032800/56649d4e5503460f94a2e94b/html5/thumbnails/2.jpg)
Goals/Motivation
• Build a biologically accurate model of (a small piece of) the spino-neuromuscular system
• Biological modeling– Hypothesis Testing– Injury modeling
• Better Robots
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Physical Model
Biceps equivalent
Gravitational force
Biceps’ applied force
Triceps equivalent
Triceps’ applied force
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Neural Model High Level
Neural Networks (12 total)
I
User controlled input
Renshaw Inhibition Muscle
Fibers (6 per muscle)
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Neural Model Detailed
52 Synaptic Connections x 6 Motor Units Per Muscle x 2 Muscles = 624 Synapses!
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Some Feedback Loops
GammaMN
Alpha-MN
RenshawCell
Intrafusal Fibers
Extrafusal Fibers
1aAfferent
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Neurons• Neurons are ‘pulse coded’
Time
Neu
ron
Pote
ntial
Threshold
Input Signals
Neuron Fires
Refractory period
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Goal: Desired Behavior
0
1
2
3
0 200 400 600 800 1000 1200Time Step
Jo
int
An
gle
(R
ad
ian
s)
Trained
Target
(1:2)
(1:3)
(0)
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Inputs??
• What input do you use to tell the arm to move up? Down? Move fast? Hold still?
• Encoding problem• Arbitrary solution:
– Up -> high frequency input ~60 Hertz– Down -> lower frequency input ~30 Hertz
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Problem
• Anatomy/network is ‘known’–Reflex pathways –Neuron types–Inhibitory/excitatory connections
• Strength of connections is unknown
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Representation of Connections
Array of connection strengths & muscle fiber strengths:0.23 | 1.43 | 2.3 | … | 0.21 631 Total Values
Need to find a set of values that allows the model to behave properly.
Inter-relation between values is very complex, i.e. non-linear.
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Evolutionary TrainingNeed to adjust the strengths of inter-neuron connections & muscle fiber strengths & …
Population New Population
Selection by fitness
Crossover and
Mutation
Insert
When the new population is full, evaluate the individuals and repeat
(potential) solutions w/ fitnesses
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Fitness
• Root mean squared error• Square root of the sum of the squared errors
between actual and target motion at a series of points along the desired trajectory.
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Crossover and Mutation
0.23 | 1.43 | 2.3 | 0.32 | 1.3 | … | 0.210.43 | 0.14 | 2.3 | 1.67 | 1.5 | … | 1.320.23 | 1.43 | 2.3 | 1.67 | 1.3 | … | 1.320.43 | 0.19 | 2.3 | 0.32 | 1.5 | … | 0.21
Crossover
Mutation
New solutions (offspring) based on ‘parent’ solutions.
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Results - Behavior
0
1
2
3
0 200 400 600 800 1000 1200Time Step
Jo
int
An
gle
(R
ad
ian
s)
Trained
Target
(1:2)
(1:3)
(0)
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Results - Training
-300
-250
-200
-150
-100
-50
0
0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000
Iteration
Fitn
ess
Best w/ Renshaws Avg. w/ RenshawsBest w/o Renshaws Avg. w/o Renshaws
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Co-activation, Tonic Tension
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Recruitment
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StabilityAltering weight
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StabilityAltering arm weight
0.65kg approaches the peak faster than 0.55kg
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Results - Generalizability
1
10
100
1000
10000
0.5 0.55 0.6 0.65 0.7 0.75 0.8
Lifted Weight (kg)
Fit
nes
s -
Mat
ch t
o D
esir
ed B
ehav
ior
Training points
Test Points Training on multiple cases improves behavior on ‘out of sample’ test cases.
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StabilityAltering speeds/frequencies
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StabilityAltering speeds/frequencies
![Page 24: Modeling The Spino- Neuromuscular System Terence Soule, Stanley Gotshall, Richard Wells, Mark DeSantis, Kathy Browder, Eric Wolbrecht](https://reader030.vdocuments.net/reader030/viewer/2022032800/56649d4e5503460f94a2e94b/html5/thumbnails/24.jpg)
Training Algorithms
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Conclusions• Model is trainable• Trainable with mixed variable types (connection
strengths and muscle fiber strengths)• Model produces fundamental biological
behaviors• Increasing complexity produced better behavior• Model is robust, proper training helps
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Future Work
• Train more complex behaviors• Generalized movement• Adaptation to injury • Real robots ( w/simpler networks and neurons)
– Non-pulse coded neurons– One `fiber’/actuator per muscle– Simpler networks– Known angles