Standing balance is modeled as an inverted pendulum: body mass m at height L above the ankle joint, which acts as a hinge. Left alone, gravity is an unstable torque that grows with tilt angle θ:
θ″ = (g/L)·sinθ − c·θ′ + acorr + anoise(stage)
θ is the lean angle from vertical, g/L is the destabilizing gravity term, cθ′ is ankle-muscle damping, acorr is the angular kick from your corrective push, and anoise is random postural sway that scales with the aging-stage slider (weaker proprioception and vestibular input mean noisier, less precise micro-corrections).
- Aging stage — scales both sway amplitude and the delay between your key press/click and when the correction actually lands, mirroring slower reaction time.
- Correction strength — the angular impulse each push delivers; too weak and sway wins, too strong and you overshoot the other way.
- Assistive sensors — path lighting reduces the noise term, and the fall-detection grid can apply one automatic braking impulse when the danger threshold is crossed, counted separately as a "sensor save" rather than a fall.
A fall is logged when |θ| passes roughly 25°. This is a simplified planar model for demonstration — real balance also involves hip/ankle strategies, stepping, and two-plane control.