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‘‘Initial state’ coordinations Initial state’ coordinations reproduce the instant flexibility reproduce the instant flexibility
for human walkingfor human walking
By: Esmaeil DavoodiBy: Esmaeil Davoodi
Dr. 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.
2
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
3
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/)()()()( 0
14
1
3
iuuf
tufy
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
12
The body system The body system equationsequations
otherwise
zforzg
otherwise
zforzzf
xxPxxPugT
xxPxxPugT
TfT
TfT
m
rur
lul
brbr
blbl
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lmbspl
1
00)(
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)()()((
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265265114
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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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ConclusionConclusion This model was shown to implement flexible control of This model was shown to implement flexible control of
walkingwalking
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.