Why inverse simulations overestimate optimal ankle exoskeleton assistance: the role of bi-articular coordination and joint stiffness.
Israel Luis, Elena M Gutierrez-Farewik, Maarten Afschrift
Simulations overestimate the best ankle exoskeleton setting because they ignore two things: the gastrocnemius must stay partly active to flex the knee, and silencing the soleus (which provides most ankle stiffness) makes the joint too floppy.
Current models don't account for either.
Key findings
1The gastrocnemius's dual role at the ankle and knee is the primary reason submaximal assistance is optimal: it must remain active to satisfy the knee flexion moment at every assistance level, and beyond the optimum, the combined exoskeleton-plus-gastrocnemius moment exceeds the required ankle moment, triggering compensatory tibialis anterior and biceps femoris short head activation that raises overall muscle activity and metabolic cost.
2Changes in muscle force-generating capacity (the force-length-velocity relationship) do not explain the submaximal optimum; the force-length-velocity multiplier in the plantarflexors actually increased slightly with higher assistance, so this mechanism was ruled out.
3Increasing exoskeleton assistance reduced ankle joint stiffness by up to approximately 55% compared with unassisted walking, driven primarily by the loss of soleus stiffness (which dropped 65% at about 70% assistance), a consequence that standard effort-minimizing cost functions do not penalize.
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What it does not show
Inverse simulation held joint kinematics and kinetics fixed at unassisted values, so no gait adaptation was permitted; real users change their walking pattern when an exoskeleton is added, and the authors acknowledge this is a confound. All simulations were driven by data from 8 healthy adults (mean age 39); the findings may not generalize to older adults, people with neurological impairment, or those with altered muscle architecture. The stiffness values are a lower bound: the model does not include antagonist co-contraction, reflex-mediated stiffness, or time-history-dependent muscle behavior, all of which increase real joint impedance. The cost function minimized only the sum of squared muscle activations; no term penalized loss of joint stiffness or stability, which the authors identify as the key structural omission. No experimental data exist on how ankle joint stiffness actually changes across exoskeleton assistance levels, so the stiffness findings are purely model-derived and unvalidated against measurement. The metabolic energy model and the specific muscle model (gait2392) are one choice among many; the authors note that a previous study using a different moment-time profile and metabolic model reached the same qualitative conclusions, but quantitative values would differ.
Declared interests
Funded by the Royal Institute of Technology. The authors state that a large language model (Claude, Anthropic) was used for grammar and language editing only, and that all scientific content, analyses, and interpretations are exclusively from the authors. No industry sponsor, no competing financial interests, and no author involvement in exoskeleton design or manufacturing are declared.
The easy way to misread this
Do not read the simulated optimal assistance levels (about 60% for activations, about 80% for metabolic power) as the clinically optimal exoskeleton setting. The entire point of the paper is that these simulated values overestimate the experimentally observed optimum (roughly 0.6–0.8 Nm/kg versus 1.1–1.2 Nm/kg predicted), and the overestimation is attributed to the model's failure to penalize the loss of ankle joint stiffness. The numbers are a property of the simulation, not a prescription for the clinic.
Summarised by AI from the full paper, without a clinician reviewing it. Check it against the source before it changes what you do. Read it on PubMed →