Computational Sensory Motor Systems Lab Johns Hopkins University 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

Computational Sensory Motor Systems Lab Johns 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 Descending signals

Computational Sensory Motor Systems Lab Johns Hopkins University Applications: Biomorphic Robots (IS Robotics, Inc.)(Star Wars, Lucas Films)

Computational Sensory Motor Systems Lab Johns 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 Lab Johns Hopkins University Applications: Physical Augmentation Neural prosthesis for spinal cord patients Cleveland FES Center, Case-Western Reserve U.

Computational Sensory Motor Systems Lab Johns Hopkins University CPG Control Locomotion Across Species Spinal Cat Walking on Treadmill Grillner and Zangger, 1984 Lamprey Swimming Mellen et al., 1995 Complete SCI Human Dimitrijevic et al., 1998

Computational Sensory Motor Systems Lab Johns Hopkins University Lamprey with Spinal Transections After Complete Transection of SC Cohen et al., 1987 Dysfunctional Swimming after Regeneration Cohen et al., 1999

Computational Sensory Motor Systems Lab Johns Hopkins University Determining the Structure and PTC/PRC of the CPG Neural Stimulators, Recording & Control Set-up Complex Lamprey CPG Model Boothe and Cohen, 2003 Schematic of Spinal Coordination Experiment Simple Lamprey CPG Model Lasner et al., 1998

Computational Sensory Motor Systems Lab Johns Hopkins University Implementation of CPG Locomotory Controller

Computational Sensory Motor Systems Lab Johns 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 Lab Johns Hopkins University 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

Computational Sensory Motor Systems Lab Johns Hopkins University Sensory Adaptation Implementation

Computational Sensory Motor Systems Lab Johns Hopkins University Basic neuron element: Integrate-and-fire Hardware Implementation: Integrate-and-Fire Array 10 Neurons, 18 synapse/neuron Neuron architecture Synapse Array Neurons

Computational Sensory Motor Systems Lab Johns Hopkins University CPG based Running Reality Check

Computational Sensory Motor Systems Lab Johns Hopkins University CPG Controller with Sensory Feedback Passive Knee joint Driven Treadmill Mechanical Harness

Computational Sensory Motor Systems Lab Johns Hopkins University CPG based Running

Computational Sensory Motor Systems Lab Johns Hopkins University Experiments

Computational Sensory Motor Systems Lab Johns Hopkins University Experiment 1: Lesion Experiments Sensory Feedback is Lesioned Light ON: Sensory Feedback intact Light OFF: Sensory Feedback Cut

Computational Sensory Motor Systems Lab Johns Hopkins University Does 1.5 Mono-peds ~ One Bi-ped?

Computational Sensory Motor Systems Lab Johns Hopkins University Serendipitous Gaits ‘Ballet Dancer’‘Strauss’

Computational Sensory Motor Systems Lab Johns Hopkins University ‘Other Gait…’ ‘Night on the town’

Computational Sensory Motor Systems Lab Johns Hopkins University Two Mono-peds -- One Bi-ped

Computational Sensory Motor Systems Lab Johns Hopkins University Two Mono-peds to make One Bi-ped Uncoupled: Right - Bad gait Left - Good gait Coupled: Inhibition Asymmetric Weights

Computational Sensory Motor Systems Lab Johns Hopkins University Sensory Feedback Mediated Motor Neuron Spike Rate Adaptation (A1 Reflex)

Computational Sensory Motor Systems Lab Johns Hopkins University How do we couple these oscillators: Spike Based Coupling

Computational Sensory Motor Systems Lab Johns Hopkins University Membrane Equation and Spike Coupling Membrane equations Weight of Impulse  Phase update due to coupling Direct Coupling Spike Coupling

Computational Sensory Motor Systems Lab Johns Hopkins University Geometry of Coupling …..Single Pulse coupling Via AnalysisCollected Data on CPG Chip

Computational Sensory Motor Systems Lab Johns Hopkins University Geometry of Coupling ….. 2 Spike Coupling Measured DataTheoretical Prediction

Computational Sensory Motor Systems Lab Johns Hopkins University Multiple Spike Coupling

Computational Sensory Motor Systems Lab Johns Hopkins University Measured PTC and PRC for Lamprey SC J. Vogelstein et al, 2004 (unpublished)

Computational Sensory Motor Systems Lab Johns Hopkins University Measured PTC and PRC for Lamprey SC J. Vogelstein et al, 2004 (unpublished)

Computational Sensory Motor Systems Lab Johns Hopkins University Basic neuron element: Integrate-and-fire Hardware Implementation: Integrate-and-Fire Array 10 Neurons, 18 synapse/neuron Neuron architecture Synapse Array Neurons

Computational Sensory Motor Systems Lab Johns Hopkins University Coupling with Linear and Non-Linear Synapses Uncoupled neurons Excitatory linear or nonlinear synaptic current inputs Discharging currents

Computational Sensory Motor Systems Lab Johns Hopkins University Coupling with Linear and Non-Linear Synapses Membrane potential

Computational Sensory Motor Systems Lab Johns Hopkins University Firing Rates Firing rates versus current inputs for linear and nonlinear synapses

Computational Sensory Motor Systems Lab Johns 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 Lab Johns 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 Lab Johns Hopkins University Entrainment Phase delay function of weight: –Strong weight --> small delay –Weak weight --> large delay ~ ° attainable Finer tuning possible for lower phase delays

Computational Sensory Motor Systems Lab Johns Hopkins University Emulation of waveforms required for biped locomotion Using described technique, waveforms for different robotic limbs can be created

Computational Sensory Motor Systems Lab Johns Hopkins University Emulation of waveforms required for biped locomotion Using described technique, waveforms for different robotic limbs can be created

Computational Sensory Motor Systems Lab Johns 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 Lab Johns 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 , Feb URLs: