‘‘Initial state’ coordinations Initial state’ coordinations reproduce the instant flexibility reproduce the instant flexibility

for human walkingfor human walking

By: Esmaeil DavoodiBy: Esmaeil DavoodiDr. Fariba BahramiDr. Fariba Bahrami

In the name of GOD

May, 2007May, 2007

Reference: A. Ohegane, et.al, “'Initial state' coordinations reproduce the instant flexibility for human walking,” Biol. Cybern, vol. 93, no. 6, pp. 426-435, 2005.

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Locomotor ControlLocomotor Control

An important feature of human locomotor control is the instant adaptability to unpredictable changes.

goal: Understanding the mechanisms of

this flexible control system

Locomotor ControlLocomotor ControlGeneration of stepping rhythm

Posture control

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WalkingWalking Swing phaseSwing phase

The foot is off the groundThe foot is off the ground Like a pendulumLike a pendulum

Stance phaseStance phase The foot is on the groundThe foot is on the ground Like an inverted pendulumLike an inverted pendulum

Propulsive force:Propulsive force: Due to ankle joint torqueDue to ankle joint torque

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Flexible control It has been shown that torque level of ankle

joint is the highest among all leg joints Thus: restrictions of ankle joint torque level

penalize walking performance

Human: FLEXIBLE CONTROL !!!

Question: How is flexible control established?

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Walking movementWalking movement Walking movement cycle:Walking movement cycle:

Central Pattern Generator (CPG)

Walking Patterns Body

Sensory feedbacks

phase spaceWalking Pattern Limit Cycle Attractors

Robustness Stability

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Flexibility Flexibility Stable walking:Stable walking:

Active change of walking patterns Active change of walking patterns according to changes of locomotion according to changes of locomotion conditions.conditions.

OR: Flexible change of limit cycle OR: Flexible change of limit cycle attractorattractor

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Neutral states & Flexibility

Neutral states latent in dynamical systems play a key role in changes of the system behavior

In the neighborhood of the neutral state, a little difference in the way the system approaches the neutral state can induce the system to converge to quite different behaviors

Presence of neural states Flexibility

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Walking under extreme Walking under extreme conditionsconditions

Consider ankle Consider ankle torque cannot be torque cannot be fully generatedfully generated

Forward propulsive Forward propulsive force:force: Falling motion of the Falling motion of the

leg in the stance leg in the stance phasephase

0

The knee joint angle in the BSP (Beginning of the Stance Phase) Initial state

Neutral state

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Torque level of the ankle Torque level of the ankle joints &joints &

Neutral state Neutral state When the torque level of the ankle joints changes,

the neutral state φ0 also shifts the larger the torque level, the closer φ0

When the torque level is sufficiently high, the neutral state is latent

But when the torque level becomes too low, the neutral state becomes more obvious in the BSP

That is, because of the perturbation, the neutral state not only shifts but also surfaces in a certain phase (Beginning of the Stance Phase ) of the dynamics of the walking

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The neural system The neural system equationsequations

14,...,1),,0max()())((

)()()('

))((3/)()()()( 014

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iuuftufy

tbvatutv

txFuywtutvtutu

ii

iiii

ij iijiiiii

Potential of the i’th neuron

Responsible for the accommodation and refractoriness

Connecting weight

Time constant of inner state

Time constant of the accommodation and refractory

Output of the i’th neuron

Sensory feedback from the body

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The body system The body system equationsequations

otherwisezfor

zg

otherwise

zforzzf

xxPxxPugT

xxPxxPugT

TfT

TfT

m

rur

lul

brbr

blbl

rmbspr

lmbspl

100

)(

)(

)()(

)()()((

)()()((

)(

)(

265265114

243243113

Torques generated in the knee joints

Equilibrium angles in the knee joints

A constant which expresses the normal level of ankle joint torque

A parameter which is determinedby environmental conditions

Ankle joints torques

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ResultResultss(1)(1)

the ankle joint torque level of the left leg changes from normal level to zero

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ResultsResults(2)(2)

The ankle joint torque level of both legs changes from normal level to zero

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ResultResultss(3)(3)

Attractor changes of the system when the ankle joint torque level changes

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ConclusionConclusion This model was shown to implement flexible control of walkingThis model was shown to implement flexible control of walking

The strategy for the flexible control of the two coupled dynamics can be described as follows the system state in the phase when the neutral state can surface should

be regarded as the initial state which determines the dynamics of the system

the initial state should be renewed in different conditions

This initial state will be one of the constraints of the walking system.

The constraint will be generated as a function of the neutral state.

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THANK YOU!

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