1. ‘Initial state’ coordinations reproduce the instant flexibility for human walking By: Esmaeil Davoodi Dr. Fariba Bahrami In the name of GOD May, 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. 2 Locomotor 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 Control Generation of stepping rhythm Posture control

3. 3 Walking Swing phase Swing phase The foot is off the ground The foot is off the ground Like a pendulum Like a pendulum Stance phase Stance phase The foot is on the ground The foot is on the ground Like an inverted pendulum Like an inverted pendulum Propulsive force: Propulsive force: Due to ankle joint torque Due to ankle joint torque

4. 4 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?

5. 5 Walking movement Walking movement cycle: Walking movement cycle: Central Pattern Generator (CPG) Walking Patterns Body Sensory feedbacks phase space Walking PatternLimit Cycle Attractors Robustness Stability

6. 6 Flexibility Stable walking: Stable walking: Active change of walking patterns according to changes of locomotion conditions. Active change of walking patterns according to changes of locomotion conditions. OR: Flexible change of limit cycle attractor OR: Flexible change of limit cycle attractor

7. 7 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 statesFlexibility

8. 8 Walking under extreme conditions Consider ankle torque cannot be fully generated Consider ankle torque cannot be fully generated Forward propulsive force: Forward propulsive force: Falling motion of the leg in the stance phase Falling motion of the leg in the stance phase The knee joint angle in the BSP ( Beginning of the Stance Phase ) Initial state Neutral state

9. 9 Torque level of the ankle joints & 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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11. 11 The neural system equations 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. 12 The body system equations 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 determined by environmental conditions Ankle joints torques

13. 13 Results (1) the ankle joint torque level of the left leg changes from normal level to zero

14. 14 Results (2) The ankle joint torque level of both legs changes from normal level to zero

15. 15 Results (3) Attractor changes of the system when the ankle joint torque level changes

16. 16 Conclusion This model was shown to implement flexible control of walking This 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.

17. 17 THANK YOU! ?