Predictor feedback models for stick balancing with delay mismatch and sensory dead zones

Area of Science:

• Human motor control
• Biophysics
• Robotics and control theory

Background:

• Human stick balancing involves complex feedback mechanisms to maintain stability.
• Sensory perception (position, velocity) and reaction time delays are critical factors.
• Existing models often simplify or omit the impact of sensory dead zones and predictor imperfections.

Purpose of the Study:

• To investigate human stick balancing using a control model incorporating delayed state feedback and mismatched predictor feedback.
• To mathematically model the system using delay-differential equations with event-driven switching.
• To determine the impact of sensory dead zones and predictor delay mismatch on balancing performance and identify critical thresholds.

Main Methods:

• Developed a mathematical model based on delay-differential equations with event-driven switching.
• Introduced a 'delay mismatch' parameter to quantify predictor imperfection.
• Numerically determined the maximum admissible switching delay (critical delay) using a practical stabilizability concept.
• Validated the model against 44 human stick balancing trials.

Main Results:

• Perfect prediction in balancing is not possible due to sensory dead zones and inherent delays.
• The critical delay was compared to a realistic human reaction time (230 ms).
• Numerical simulations yielded plausible human perception parameters: position threshold ~1°, velocity threshold 4.24–9.35°/s, and delay mismatch 100–150 ms.

Conclusions:

• The mismatched predictor feedback model accurately simulates human stick balancing.
• Sensory dead zones and predictor delay mismatch are significant limitations in human postural control.
• Identified critical thresholds provide insights into the human sensorimotor system's capabilities and limitations.