Stability of Human Balance During Quiet Stance With Physiological and Exoskeleton Time Delays
Bibliographic record
Abstract
Human balance with exoskeleton assistance is studied using an inverted pendulum model, considering time delays in the muscle reflexes and the exoskeleton controller. The model includes two motors at the ankle joint whose maximum torques depend on the joint angle and angular velocity, reflecting the combined moment-generating capacity of all plantarflexor and dorsiflexor muscles. These “muscle-like” motors obey a proportional–derivative (PD) reflex control law where the angle and angular velocity of the ankle joint are subject to feedback delays. The stability of this system is analyzed using Galerkin projection to convert the governing neutral delay differential equation into a system of first-order ordinary differential equations (ODEs) and computing the eigenvalues of the ODE system. The stability analysis is then repeated with exoskeleton torques included at the ankle joint. The exoskeleton torques are assumed to obey a PD control law as well but with a unique state feedback delay. Stability charts reveal that the area of the stability region always increases as the exoskeleton delay decreases, but the area may decrease as the physiological delay decreases. The presented analytical framework enables investigation of the effect of control gains and time delays on the stability of a combined human–exoskeleton system.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".