1. Modeling The Spino- Neuromuscular System Terence Soule, Stanley Gotshall, Richard Wells, Mark DeSantis, Kathy Browder, Eric Wolbrecht

2. Goals/Motivation Build a biologically accurate model of (a small piece of) the spino-neuromuscular system Biological modeling – Hypothesis Testing – Injury modeling Better Robots

3. Physical Model Biceps equivalent Gravitational force  Biceps’ applied force Triceps equivalent Triceps’ applied force

4. Neural Model High Level Neural Networks (12 total) I User controlled input Renshaw Inhibition Muscle Fibers (6 per muscle)

5. Neural Model Detailed 52 Synaptic Connections x 6 Motor Units Per Muscle x 2 Muscles = 624 Synapses!

6. Some Feedback Loops Gamma MN Alpha-MN Renshaw Cell Intrafusal Fibers Extrafusal Fibers 1a Afferent

7. Neurons Neurons are ‘pulse coded’ Time Neuron Potential Threshold Input Signals Neuron Fires Refractory period

8. Goal: Desired Behavior

9. 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

10. Problem Anatomy/network is ‘known’ – Reflex pathways – Neuron types – Inhibitory/excitatory connections Strength of connections is unknown

11. 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.

12. Evolutionary Training Need 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

13. 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.

14. Crossover and Mutation 0.23 | 1.43 | 2.3 | 0.32 | 1.3 | … | 0.21 0.43 | 0.14 | 2.3 | 1.67 | 1.5 | … | 1.32 0.23 | 1.43 | 2.3 | 1.67 | 1.3 | … | 1.32 0.43 | 0.19 | 2.3 | 0.32 | 1.5 | … | 0.21 Crossover Mutation New solutions (offspring) based on ‘parent’ solutions.

15. Results - Behavior

16. Results - Training

17. Co-activation, Tonic Tension

18. Recruitment

19. Results –  motor neuron

20. Stability Altering weight

21. Stability Altering arm weight 0.65kg approaches the peak faster than 0.55kg

22. Results - Generalizability Training on multiple cases improves behavior on ‘out of sample’ test cases.

23. Stability Altering speeds/frequencies

25. Training Algorithms

26. 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

27. 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