coupled spiking oscillators constructed with integrate-and-fire neural networks

Computational Sensory Motor Systems LabJohns Hopkins University

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

Ralph Etienne-Cummings, Francesco Tenore, Jacob VogelsteinJohns Hopkins University, Baltimore, MD

Collaborators:M. Anthony Lewis, Iguana Robotics Inc, Urbana, IL

Avis Cohen, University of Maryland, College Park, MD

Sponsored byONR, NSF, SRC


Why do we need coupled Oscillators?

• 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

• The Central Pattern Generator is the heart of locomotion controllers

MotorOutput

Non-LinearSensoyFeedback

Non-LinearSensoyFeedback

MotorOutput

Descending signals


Applications: Biomorphic Robots

(IS Robotics, Inc.) (Star Wars, Lucas Films)


Applications: Physical Augmentation

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

jumping


Applications: Physical Augmentation

• Neural prosthesis for spinal cord patients

Cleveland FES Center, Case-Western Reserve U.


CPG Control Locomotion Across Species

Spinal Cat Walking on TreadmillGrillner and Zangger, 1984

Lamprey SwimmingMellen et al., 1995

Complete SCI Human Dimitrijevic et al., 1998


Lamprey with Spinal Transections

After Complete Transection of SCCohen et al., 1987

Dysfunctional Swimming after RegenerationCohen et al., 1999


Determining the Structure and PTC/PRC of the CPG

Neural Stimulators, Recording & Control Set-up

Complex Lamprey CPG ModelBoothe and Cohen, 2003

Schematic of Spinal Coordination Experiment

Simple Lamprey CPG ModelLasner et al., 1998


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(a) Integrate -and-Fire Neural Model(c) Biped with Passive Knees

(b) Control Loop with Sensory Feedback for One Limb (d) Hip/Knee Joint Angles and Foot -Falls for One Limb

External Perturbations

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Implementation of CPG Locomotory Controller


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)


Adaptive and Autonomous Control of Running Legs

Set the frequencyof strides

Set the center of the limb swing

Set the angular width of a stride


Sensory Adaptation Implementation


Basic neuron element: Integrate-and-fire

Hardware Implementation: Integrate-and-Fire Array

10 Neurons, 18 synapse/neuron

Neuron architecture

SynapseArray

Neu

rons


CPG based Running

Reality Check


CPG Controller with Sensory Feedback

Passive Knee joint

Driven Treadmill

Mechanical Harness


CPG based Running


Experiments


Experiment 1: Lesion Experiments

Sensory Feedback is Lesioned

Light ON: Sensory Feedback intact

Light OFF: Sensory Feedback Cut


Does 1.5 Mono-peds ~ One Bi-ped?


Serendipitous Gaits

‘Ballet Dancer’ ‘Strauss’


‘Other Gait…’

‘Night on the town’


Two Mono-peds -- One Bi-ped


Two Mono-peds to make One Bi-ped

Uncoupled: Right - Bad gaitLeft - Good gait

Coupled: Inhibition

Asymmetric Weights


Sensory Feedback Mediated Motor Neuron Spike Rate Adaptation (A1 Reflex)


How do we couple these oscillators: Spike Based Coupling

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Rate ofconvergence

Uncertainty Frequency range

Large pulses Fast Large Large

Small Slow Small Small

Multiple small Fast Small Large


Membrane Equation and Spike Coupling

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Phase update due to coupling

Direct Coupling

Spike Coupling


Geometry of Coupling …..Single Pulse coupling

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Via Analysis Collected Data on CPG Chip


Geometry of Coupling ….. 2 Spike Coupling

Measured Data

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Theoretical Prediction


Multiple Spike Coupling


Measured PTC and PRC for Lamprey SC

J. Vogelstein et al, 2004 (unpublished)


Basic neuron element: Integrate-and-fire

Hardware Implementation: Integrate-and-Fire Array

10 Neurons, 18 synapse/neuron

Neuron architecture

SynapseArray

Neu

rons


Coupling with Linear and Non-Linear Synapses

• Uncoupled neurons

• Excitatory linear or nonlinear synaptic current inputs

• Discharging currents


Coupling with Linear and Non-Linear Synapses

Membrane potential


Firing Rates

Firing rates versus current inputs for linear and nonlinear synapses


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


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


Entrainment

• Phase delay function of weight:

– Strong weight --> small delay

– Weak weight --> large delay

• ~ 0 - 180° attainable

• Finer tuning possible for lower phase delays


Emulation of waveforms required for biped locomotion

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


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


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.jhu.edu/http://www.iguana-robotics.comhttp://www.life.umd.edu/biology/cohenlab/http://www.ine-web.org

coupled spiking oscillators constructed with integrate-and-fire neural networks

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