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11.09.2009 - BIRS: Noise, Time Delay and Balance Control

John Milton
  • Inattention appears to "help" balance
  • Mechanical time-scales matter
  • Stick-balancing appears to be tune to the edge of boundary
    • Don't balance it upright, balance slightly off-center
    • Random walk with an optimal search
      • Non-predictive solution (Maybe stochastic?)
    • Continuous control is too expensive
    • Suggest a discontinuous "act-and-wait"
  • Passive control
    • Better off if you wait to cntrol until stability boundary reached
  • Increased activation delay corresponds to better performance
  • Energy vs Co-energy (How do these correspond to all of the stability studies?)
Bob Peterka
  • Observable behavior
    • Kinematics
    • Ground reaction forces
    • EMG response
    • Muscle images
    • ...neural recordings...
  • Experimental and modeling approaches
    • Musculoskeletal dynamics
    • Sensor dynamics
    • Controller
      • Internal models
        • Head vs Trunk (Thomas Mergner)
          • Perception is not perfect
      • Predictors
  • Experiments
    • Used a pseudo-random turning sequence to rotational perturbations
    • Gain and phase of response to rotational perturbations
      • Gain drops off at high frequency
      • Phase leads at low frequency and lags at high frequency
    • Four modes of control
      • Active control
      • Integrative control
      • Fast-acting control
      • Load control
    • Delayed proprioceptive feedback
    • Positive force feedback (force control)
    • Sensory integration feedback (weighted sensory information)
    • Rapid response control (springs and dampers)
Valero-Cuevas
Toro Okihara
  • Stochastic resonance - does the shaking make things better?
    • Perhaps the shaking helps?
  • Non-locality
    • Need to look at components interacting instead of each individual component
Ami Radunskaya
  • Delay differential equations
    • \dot{x} = \sin ( x(t-\tau) )
    • Euler's method can be "exact" as long as the step-size directly divides the delay-length
    • dde23 - look-up in matlab
    • What about initial requirements on Laplace equations?
  • m\ddot{x}(t) +b \dot{x}(t) + q \dot{x}(t-\tau) + k x(t)
    • b^2 = 4 mk is critically stable in standard spring-mass-damper
    • b>q the system is stable in this delayed equation
    • To find boundary of stability put in solutions of the form
      • z(t) = e^{\lambda t}
      • Characteristic Polynomial
        • \lambda^2+b\lambda+q\lambdae^{-\lambda\tau}+k = 0
        • Lambda cannot have imaginary solutions with Re>0
        • If lambda is purely imaginary:
          • \tau = \frac{1}{\omega}\arctan \left( \frac{\omega^2-k}{\omega b} \right)
Lena Ting
  • Postural control
    • prepatory response (immediate / feedforward)
    • short-latency (stretch reflexes) 40 ms
    • long-latency (automatic postural response) 100 ms
    • decision (steps) 200 ms
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