Sensorimotor Integration in How is locomotion controlled? Lampreys - PDF document

Locomotion in Animals Sensorimotor Integration in • How is locomotion controlled? Lampreys and Robots: CPG • Could be a clock – sending out periodic Principles signals Avis H. Cohen M. Anthony Lewis • Could be mechanical – depending on the University of Maryland Iguana Robotics mechanics and pendulum action of the limbs Adaptive Motion of Animals and Adaptive Motion of Animals and Machines Machines Locomotion in Animals Locomotion: Biological Control In all organisms locomotion is a function of several types of • Can’t be a clock – not adaptive enough signals: * – Feedforward signals from a central pattern generator (CPG) – Initiation and guidance from the organisms’ brain • Can’t be purely passive or purely * – Sensory inputs signaling the position of the body in the world mechanical – what about uphill? What – Proper integration of control signals with mechanics of the about fish? organism ALL ARE NECESSARY FOR ADAPTIVE LOCOMOTION Adaptive Motion of Animals and Adaptive Motion of Animals and Machines Machines Nature of the CPG Central Pattern Generator • What does the CPG look like? • Vertebrate CPG – Studies in the simple vertebrate, the lamprey – Locomotion is a simple series of traveling waves of • How does it work? muscle contractions which travel down the spinal cord with no limbs or paired fins to move. – The neural feedforward signals can be seen in the isolated spinal cord – with no brain or sensory feedback present. Adaptive Motion of Animals and Adaptive Motion of Animals and Machines Machines 1

Structure Of Neural wave the CPG • Cut the spinal cord into pieces > Isolated spinal cord • Each piece goes at Activity travels along its own frequency spinal cord – head end to tail end – to • Pieces as short as 3 produce traveling segments can burst wave of movement periodically Adaptive Motion of Animals and Adaptive Motion of Animals and Machines Machines CPG Structure Nature of Oscillators • Each oscillator consists of one or more segments • CPG is distributed – not a single source of signals controlling the chain of segments. • Each oscillator has its own preferred frequency • CPG is a chain of coupled oscillators. • When coupled, they all go at a single frequency – composite frequency is a combination frequency, not that of any single oscillator • The oscillators are stable to perturbations Adaptive Motion of Animals and Adaptive Motion of Animals and Machines Machines Basic Model for Two Oscillators Basic Structure of CPG From Cohen, Holmes and Rand, 1982. Later generalized by Kopell and Ermentrout to any periodic H • Chain of coupled non-linear oscillators function. • Coupled up and down the chain by bidirectional coupling – long and short connections Adaptive Motion of Animals and Adaptive Motion of Animals and Machines Machines 2

Assumptions New Evidence • Each segmental oscillator is a simple limit cycle oscillator (stable non-linear oscillator) – maybe true, but not important • Does the CPG behave like a chain of relative-phase coupled oscillators? • The oscillator can be described by a single parameter - the phase angle around the limit cycle – not true, but hard to fix • How does a chain of relative-phase coupled oscillators behave? • The coupling function is a relatively weak periodic function - input doesn't perturb the oscillator far off its limit cycle – false! • How does a chain of non-relative phase coupled oscillators behave? • The coupling is a function of the phase difference between the pairs of oscillators – show here – false! • How does the real CPG behave? • The coupling is nearest neighbor – false, and being fixed, but hard • A new model presented for comparison Adaptive Motion of Animals and Adaptive Motion of Animals and Machines Machines Testing the Assumption of Coupling Dominance Relative Phase Coupling • Begin with a stochastic model for a chain of coupled oscillators with coupling weakened in the middle – generate simulated data for both a • Kopell and Ermentrout: The lamprey spinal cord should relative phase and a non-relative phase model. exhibit “coupling dominance” • Use the simulated data to estimate the parameters in a model of two • Definition: If a chain of coupled oscillators contains only coupled oscillators. short distance connections, and if frequency differences are small, then the phase lags between oscillators depend on • Compare the strengths and directions of coupling between relative the properties of either the ascending or the descending coupling – BUT NOT BOTH phase and non-relative models • Compare results from simulations to experimental data • Either the ascending or the descending will dominate Adaptive Motion of Animals and Adaptive Motion of Animals and Machines Machines Model for Estimating Parameters Non-relative Phase Coupling • The non-relative phase model: The coupling is on for part of the cycle and off for part of the cycle. On and off of coupling depend on the absolute phase of the presynaptic oscillators. When the coupling is on, it depends on the relative phase between the oscillators. Adaptive Motion of Animals and Adaptive Motion of Animals and Machines Machines 3

Chain Model Used to Generate Coupling Estimates from Model Simulated Data with Relative Phase Coupling • Total coupling strength • Model: 12 oscillators, two groups of 6 connected via kept constant strong nearest neighbor coupling except in the middle α a = 2 α d = constant • Coupling: α a = ascending α d = descending • Weakened coupling varied from 0.0 to 1.0 • The estimated ascending • Weakened coupling in the middle = α dw/aw fraction is predominantly ascending for values above near 0. • This is how a model with coupling dominance behaves Adaptive Motion of Animals and Adaptive Motion of Animals and Machines Machines Coupling Estimates: Model with Coupling Estimates from Model Non-Relative Phase Coupling with Relative Phase Coupling • Total coupling is kept constant • Total coupling strength is α a = 2 α d = constant kept constant • Ascending fraction of the • Weakened coupling is coupling – γ is varied varied from 0.0 to 1.0 continuously from 0.0 to 1.0 • The estimated ascending • Estimated values jump from fraction varies continuously descending to ascending with the values put in the • Weakened connections are model kept constant • Thus a model with coupling dominance will always reflect that dominance Adaptive Motion of Animals and Adaptive Motion of Animals and Machines Machines Experimental Data Conclusions about CPGs Behavior of • Oscillators are limit cycle oscillators. experimental data: • Coupled bidirectionally with strong ascending and Estimates have descending coupling. (Data not shown) continuous values as we • Coupling is strong with both long and short change components. (Data not shown) conditions Like non-relative phase coupling • Coupled spinal oscillators do not behave like relative phase coupled oscillators. Unlike relative phase coupling Adaptive Motion of Animals and Adaptive Motion of Animals and Machines Machines 4

CPGs: Made Adaptive by Sensory Sensors and Feedback Feedback • There is no clock – oscillators can and • Each organism has sensors to provide input MUST be adaptable. to trigger new cycles of the CPG, and to alter the frequency of the oscillators. • CPG must be able to accommodate to the • In limbed animals, they are joint and muscle environment of the organism. receptors. • In lamprey, they are stretch receptors in the • Sensory feedback provides necessary input spinal cord itself. for accommodation. Adaptive Motion of Animals and Adaptive Motion of Animals and Machines Machines Sensory Feedback to Trigger Slowly Decaying Excitation Cycles After bending Stretch stops, the receptors cycles slowly can relax back to entrain baseline. the rhythm of the spinal cord Adaptive Motion of Animals and Adaptive Motion of Animals and Machines Machines Slowly Decaying Excitation Bending slower than baseline • Stretch receptors can entrain rhythm – Drive does trigger cycles to generate adaptive not always frequency ease • Bending adds a positive drive to the system rhythm during and for a short time after the bending back to ends baseline – • But: drive is not as an engineer would do it overshoots – examples: Adaptive Motion of Animals and Adaptive Motion of Animals and Machines Machines 5

Bending slower than baseline Bending at close frequency Even at close Drive can frequency, overpower drive appears receptors and makes trying to entrainment entrain harder and causes abrupt overshoot Adaptive Motion of Animals and Adaptive Motion of Animals and Machines Machines Sensory Feedback and Robotic Collaborators Locomotion • Physiology: Guan Li & Nicholas Mellen • Mathematics: Tim Kiemel • New Robotics Work: Tony Lewis Ralph Etienne-Cummings Mitra Hartmann Adaptive Motion of Animals and Adaptive Motion of Animals and Machines Machines 6