Is there a trade-off between economy and task goal variability in transfemoral amputee gait?

Energy cost minimization has been widely accepted to regulate gait. Optimization principles have been frequently used to explain how individuals adapt their gait pattern. However, there have been rare attempts to account for the role of variability in this optimization process. Motor redundancy can enable individuals to perform tasks reliably while achieving energy optimization. However, we do not know how the non-goal-equivalent and goal-equivalent variability is regulated. In this study, we investigated how unilateral transfemoral amputees regulate step and stride variability based on the task to achieve energy economy. Nine individuals with unilateral transfemoral amputation walked on a treadmill at speeds of 0.6, 0.8, 1.0, 1.2 and 1.4 m/s using their prescribed passive prostheses. We calculated the step-to-step and stride-to-stride variability and applied goal equivalent manifold (GEM) based control to decompose goal-equivalent and non-goal-equivalent manifold. To quantify the energy economy, the energy recovery rate (R) was calculated based on potential energy and kinetic energy. Comparisons were made between GEM variabilities and commonly used standard deviation measurements. A linear regression model was used to investigate the trade-off between R and GEM variabilities. Our analysis shows greater variability along the goal-equivalent manifold compared to the non-goal-equivalent manifold (p