Phase-Plane Based Model-Free Estimation of Steady-State Metabolic Cost

Abstract

The steady-state metabolic cost has been used to assess the performance of wearable robotic devices. Recently, real-time assessment of this metabolic cost has been employed in an objective function when optimizing robotic parameters for an individual user, thus personalizing the assistance to minimize human effort. However, the long estimation time needed for the model-based approach to metabolic cost estimation limits the optimization only to light-intensity activities. Here, we hypothesized that model-free, phase-plane estimation (PPE) would reduce the estimation time for the steady-state metabolic cost. First, we developed a phase-plane representation to classify the steady-state (where the change in metabolic rate is zero) and the transient metabolic dynamics. Second, we approximated the transient metabolic dynamics using a data-driven Gaussian mixture model and a real-time respiratory measure. We compared the performance of PPE with that of the model-based method by examining (1) walking performance assisted by a robotic prosthetic foot for individuals with and without Below Knee Amputation (BKA) and (2) squatting and running performance for individuals without BKA. PPE reduced the steady-state estimation time during walking for individuals with and without BKA by 31% and 40%, respectively. It also reduced estimation time by 56% and 24% for squatting and running conditions. These significant reductions in estimation time suggest that the data-driven PPE method can be used to rapidly estimate physical effort when personalizing the assistance from wearable robots. This expands the ability to conduct individual optimization for subjects engaged in physical intensive activities or for individuals with reduced physical strength.