Multi-Objective Bio-Inspired Optimization of a Passive Ankle Exoskeleton with a Geometry-Derived Moment Arm

Passive ankle exoskeleton models often assume a constant spring moment arm. Here spring rate, two attachment offsets and clutch threshold were optimized jointly with a geometry-derived moment arm. Data from 19 adults walking at 1.2 m s−1 drove a reduced plantarflexor model with fixed unassisted kinematics; force, travel and moment limits were checked on every stride. In the optimized geometry the moment arm fell 31% between engagement and peak dorsiflexion; a constant-lever approximation overestimated the device moment there by 71%. With active force and travel limits, the spring rate equalled their ratio and several attachment geometries were nearly equivalent (300–1500 N). At a 1000 N limit, the model predicted a 25.7% reduction in its priced plantarflexor energy (muscle-level, not whole-body), ranging from 15% to 40% across muscle-model variants and ±1%-of-cycle timing shifts (central 95% simulation interval 23.3–29.2% under one-frame timing errors). Among five bio-inspired optimizers, covariance matrix adaptation evolution strategy (CMA-ES) was the most reliable population-based method on the single-objective problem. Non-dominated sorting genetic algorithm II (NSGA-II) and S-metric selection evolutionary multi-objective algorithm (SMS-EMOA) approximated the benefit–force trade-off more completely than a budget-matched ε-constraint sweep, whereas constrained optimization by linear approximations (COBYLA) was better in the moment-limited region.