Coupled Spiking Oscillators Constructed with Integrate-and-Fire Neural Networks

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Coupled Spiking Oscillators Constructed with
Integrate-and-Fire Neural Networks

• Ralph Etienne-Cummings, Francesco Tenore, Jacob
  Vogelstein
• Johns Hopkins University, Baltimore, MD
• Collaborators
• M. Anthony Lewis, Iguana Robotics Inc, Urbana, IL
• Avis Cohen, University of Maryland, College Park,
  MD
• Sponsored by
• ONR, NSF, SRC

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Why do we need coupled Oscillators?

• The Central Pattern Generator is the heart of
  locomotion controllers

• What is a Central Pattern Generator for
  Locomotion?
• Collection of recurrently coupled neurons which
  can function autonomously
• All fast moving animals (Swimming, running,
  flying) use a CPG for locomotion

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Applications Biomorphic Robots
(IS Robotics, Inc.)
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Applications Physical Augmentation

• Neural prosthesis for spinal cord patients
• Artificial limbs for amputees
• Exoskeletons for enhanced load carrying, running
  and jumping

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Applications Physical Augmentation

• Neural prosthesis for spinal cord patients

Cleveland FES Center, Case-Western Reserve U.
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CPG Control Locomotion Across Species
Lamprey Swimming Mellen et al., 1995
Complete SCI Human Dimitrijevic et al., 1998
Spinal Cat Walking on Treadmill Grillner and
Zangger, 1984
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Lamprey with Spinal Transections
After Complete Transection of SC Cohen et al.,
1987
Dysfunctional Swimming after Regeneration Cohen
et al., 1999
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Determining the Structure and PTC/PRC of the CPG
Simple Lamprey CPG Model Lasner et al., 1998
Schematic of Spinal Coordination Experiment
Complex Lamprey CPG Model Boothe and Cohen, 2003
Neural Stimulators, Recording Control Set-up
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Implementation of CPG Locomotory Controller
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Locomotory Requirements

• A self-sustained unit for providing the control
  timings to limbs. (CPG)
• Adaptive capability to correct for asymmetries
  and noise in limbs. (Local adaptation)
• Reactive capability to handle non-ideal
  environmental conditions. (Reflex recovery from
  perturbation)
• Local sensory network to asses the dynamic state
  of the limbs. (Joint and muscle receptors)
• Descending control signals to include intent,
  long-term learning and smooth transitions in the
  behaviors. (Motor, cerebellum sensory cortex)

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Adaptive and Autonomous Control of Running Legs
Set the frequency of strides
Set the center of the limb swing
Set the angular width of a stride
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Sensory Adaptation Implementation
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Hardware Implementation Integrate-and-Fire Array
Basic neuron element Integrate-and-fire
Synapse Array
Neurons
10 Neurons, 18 synapse/neuron
Neuron architecture
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CPG based Running
Reality Check
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CPG Controller with Sensory Feedback
Passive Knee joint Driven Treadmill Mechanical
Harness
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CPG based Running
 
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Experiments
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Experiment 1 Lesion Experiments
Sensory Feedback is Lesioned Light ON Sensory
Feedback intact Light OFF Sensory Feedback Cut
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Does 1.5 Mono-peds One Bi-ped?
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Serendipitous Gaits

• Ballet Dancer

• Strauss

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Other Gait

• Night on the town

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Two Mono-peds -- One Bi-ped
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Two Mono-peds to make One Bi-ped
Uncoupled Right - Bad gait Left - Good gait
Coupled Inhibition Asymmetric Weights
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Sensory Feedback Mediated Motor Neuron Spike Rate
Adaptation (A1 Reflex)
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How do we couple these oscillators Spike Based
Coupling
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Membrane Equation and Spike Coupling
Membrane equations
Direct Coupling
Weight of Impulse L
Phase update due to coupling
Spike Coupling
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Geometry of Coupling ..Single Pulse coupling
Via Analysis
Collected Data on CPG Chip
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Geometry of Coupling .. 2 Spike Coupling
Measured Data
Theoretical Prediction
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Multiple Spike Coupling
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Measured PTC and PRC for Lamprey SC
J. Vogelstein et al, 2004 (unpublished)
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Measured PTC and PRC for Lamprey SC
J. Vogelstein et al, 2004 (unpublished)
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Hardware Implementation Integrate-and-Fire Array
Basic neuron element Integrate-and-fire
Synapse Array
Neurons
10 Neurons, 18 synapse/neuron
Neuron architecture
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Coupling with Linear and Non-Linear Synapses

• Uncoupled neurons
• Excitatory linear or nonlinear synaptic current
  inputs
• Discharging currents

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Coupling with Linear and Non-Linear Synapses
Membrane potential
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Firing Rates
Firing rates versus current inputs for linear and
nonlinear synapses
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Coupled Neurons

• Mutually coupled neurons using linear and
  nonlinear synapses
• Firing rates versus strength of the coupling
• Nonlinear synapse provides a larger phase
  locking region

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Entrainment using Spike Coupling and Non-Linear
Synapses

• Purpose
• to make two oscillators of different frequencies
  sync up
• to be able to control the phase delay between
  them at will

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Entrainment

• Phase delay function of weight
• Strong weight --gt small delay
• Weak weight --gt large delay
• 0 - 180 attainable
• Finer tuning possible for lower phase delays

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Emulation of waveforms required for biped
locomotion

• Using described technique, waveforms for
  different robotic limbs can be created

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Emulation of waveforms required for biped
locomotion

• Using described technique, waveforms for
  different robotic limbs can be created

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Summary

• An integrate-and-fire neuron array is used to
  realize a CPG controller for a biped
• Sensory feedback to CPG controllers allows a
  biped to adapt for mismatches in actuators and
  environmental perturbation
• Individual CPG oscillators per limb are coupled
  to create a biped controller
• Spike based coupling offer a more controlled and
  faster way to synchronize oscillators
• Non-linear synaptic currents (as a function of
  membrane potential) allow robust phase locking
  between oscillators
• Arbitrary phase locking between oscillators can
  be realized for CPG controllers
• Spike coupled oscillators can be used to generate
  control signals for more bio-realistic biped and
  quadrupeds
• We are conducting the early experiments to
  control spinal CPG circuits which will allow us
  to bridge the gap between two pieces of
  transected spinal cord.

Iguana Robotics Snappy
Iguana Robotics TomCat
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Summary
Lewis, Etienne-Cummings, Hartmann, Cohen, and Xu,
An In Silico Central Pattern Generator Silicon
Oscillator, Coupling, Entrainment, Physical
Computation Biped Mechanism Control,
Biological Cybernetics, Vol. 88, No. 2, pp
137-151, Feb. 2003. URLs http//etienne.ece.jh
u.edu/ http//www.iguana-robotics.com http//www.l
ife.umd.edu/biology/cohenlab/ http//www.ine-web.o
rg