Post on 16-Dec-2015
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
Computational Sensory Motor Systems LabJohns Hopkins University
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
Computational Sensory Motor Systems LabJohns Hopkins University
Applications: Biomorphic Robots
(IS Robotics, Inc.) (Star Wars, Lucas Films)
Computational Sensory Motor Systems LabJohns Hopkins University
Applications: Physical Augmentation
• Neural prosthesis for spinal cord patients• Artificial limbs for amputees• Exoskeletons for enhanced load carrying, running and
jumping
Computational Sensory Motor Systems LabJohns Hopkins University
Applications: Physical Augmentation
• Neural prosthesis for spinal cord patients
Cleveland FES Center, Case-Western Reserve U.
Computational Sensory Motor Systems LabJohns Hopkins University
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
Computational Sensory Motor Systems LabJohns Hopkins University
Lamprey with Spinal Transections
After Complete Transection of SCCohen et al., 1987
Dysfunctional Swimming after RegenerationCohen et al., 1999
Computational Sensory Motor Systems LabJohns Hopkins University
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
Computational Sensory Motor Systems LabJohns Hopkins University
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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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(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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(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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(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
Implementation of CPG Locomotory Controller
Computational Sensory Motor Systems LabJohns Hopkins University
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)
Computational Sensory Motor Systems LabJohns Hopkins University
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
Computational Sensory Motor Systems LabJohns Hopkins University
Sensory Adaptation Implementation
Computational Sensory Motor Systems LabJohns Hopkins University
Basic neuron element: Integrate-and-fire
Hardware Implementation: Integrate-and-Fire Array
10 Neurons, 18 synapse/neuron
Neuron architecture
SynapseArray
Neu
rons
Computational Sensory Motor Systems LabJohns Hopkins University
CPG based Running
Reality Check
Computational Sensory Motor Systems LabJohns Hopkins University
CPG Controller with Sensory Feedback
Passive Knee joint
Driven Treadmill
Mechanical Harness
Computational Sensory Motor Systems LabJohns Hopkins University
CPG based Running
Computational Sensory Motor Systems LabJohns Hopkins University
Experiments
Computational Sensory Motor Systems LabJohns Hopkins University
Experiment 1: Lesion Experiments
Sensory Feedback is Lesioned
Light ON: Sensory Feedback intact
Light OFF: Sensory Feedback Cut
Computational Sensory Motor Systems LabJohns Hopkins University
Does 1.5 Mono-peds ~ One Bi-ped?
Computational Sensory Motor Systems LabJohns Hopkins University
Serendipitous Gaits
‘Ballet Dancer’ ‘Strauss’
Computational Sensory Motor Systems LabJohns Hopkins University
‘Other Gait…’
‘Night on the town’
Computational Sensory Motor Systems LabJohns Hopkins University
Two Mono-peds -- One Bi-ped
Computational Sensory Motor Systems LabJohns Hopkins University
Two Mono-peds to make One Bi-ped
Uncoupled: Right - Bad gaitLeft - Good gait
Coupled: Inhibition
Asymmetric Weights
Computational Sensory Motor Systems LabJohns Hopkins University
Sensory Feedback Mediated Motor Neuron Spike Rate Adaptation (A1 Reflex)
Computational Sensory Motor Systems LabJohns Hopkins University
How do we couple these oscillators: Spike Based Coupling
0 0.2 0.4 0.6 0.8 10
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Del_theta = 0.00, # spikes rho/C = 3.00Del_theta = 0.04, # spikes rho/C =
0 0.2 0.4 0.6 0.8 10
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Del_theta = 0.00, # spikes rho/C = 3.00Del_theta = 0.04, # spikes rho/C =
Rate ofconvergence
Uncertainty Frequency range
Large pulses Fast Large Large
Small Slow Small Small
Multiple small Fast Small Large
Computational Sensory Motor Systems LabJohns Hopkins University
Membrane Equation and Spike Coupling
spon
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Membrane equations
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Weight of Impulse
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Phase update due to coupling
Direct Coupling
Spike Coupling
Computational Sensory Motor Systems LabJohns Hopkins University
Geometry of Coupling …..Single Pulse coupling
0
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0.002
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0.005
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0 0.002 0.004 0.006 0.008
Series2
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Via Analysis Collected Data on CPG Chip
Computational Sensory Motor Systems LabJohns Hopkins University
Geometry of Coupling ….. 2 Spike Coupling
Measured Data
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Theoretical Prediction
Computational Sensory Motor Systems LabJohns Hopkins University
Multiple Spike Coupling
Computational Sensory Motor Systems LabJohns Hopkins University
Measured PTC and PRC for Lamprey SC
J. Vogelstein et al, 2004 (unpublished)
Computational Sensory Motor Systems LabJohns Hopkins University
Measured PTC and PRC for Lamprey SC
J. Vogelstein et al, 2004 (unpublished)
Computational Sensory Motor Systems LabJohns Hopkins University
Basic neuron element: Integrate-and-fire
Hardware Implementation: Integrate-and-Fire Array
10 Neurons, 18 synapse/neuron
Neuron architecture
SynapseArray
Neu
rons
Computational Sensory Motor Systems LabJohns Hopkins University
Coupling with Linear and Non-Linear Synapses
• Uncoupled neurons
• Excitatory linear or nonlinear synaptic current inputs
• Discharging currents
Computational Sensory Motor Systems LabJohns Hopkins University
Coupling with Linear and Non-Linear Synapses
Membrane potential
Computational Sensory Motor Systems LabJohns Hopkins University
Firing Rates
Firing rates versus current inputs for linear and nonlinear synapses
Computational Sensory Motor Systems LabJohns Hopkins University
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
Computational Sensory Motor Systems LabJohns Hopkins University
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
Computational Sensory Motor Systems LabJohns Hopkins University
Entrainment
• Phase delay function of weight:
– Strong weight --> small delay
– Weak weight --> large delay
• ~ 0 - 180° attainable
• Finer tuning possible for lower phase delays
Computational Sensory Motor Systems LabJohns Hopkins University
Emulation of waveforms required for biped locomotion
Using described technique, waveforms for different robotic limbs can be created
Computational Sensory Motor Systems LabJohns Hopkins University
Emulation of waveforms required for biped locomotion
Using described technique, waveforms for different robotic limbs can be created
Computational Sensory Motor Systems LabJohns Hopkins University
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
Computational Sensory Motor Systems LabJohns Hopkins University
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