Feedback control of oxygen uptake during robotics-assisted end-effector-based stair climbing

A heart rate (HR) feedback control system for end-effector gait rehabilitation robots was previously developed and successfully tested, but oxygen uptake ( $ \dot {{\rm V}}{\rm O}_2 $ ) is thought to better characterize physiological exercise intensity. The aim of the present study was to identify and compare $ \dot {{\rm V}}{\rm O}_2 $ and HR dynamics, and to develop and test a $ \dot {{\rm V}}{\rm O}_2 $ controller for an end-effector robot operated in stair climbing mode. Six able-bodied subjects were recruited for controller testing. Command response, disturbance rejection and robustness were assessed by means of three quantitative outcome measures: root-mean-square (RMS) error of $ \dot {{\rm V}}{\rm O}_2 $ ( $ {\rm RMSE}_{\dot{\rm V}O_2} $ ), average control signal power ( $ P_{\Delta P} $ ) and RMS error of volitionally controlled power ( $ {\rm RMSE}_P $ ). The nominal first-order linear model for $ \dot {{\rm V}}{\rm O}_2 $ had time constant $ \tau =52.4 $ s and steady-state gain k=0.0174 (l/min)/W. The mean time constant $ \tau = 67.3 $ s for HR was significantly higher than for $ \dot {{\rm V}}{\rm O}_2 $ , where $ \tau = 53.4 $ (p=0.048). Command responses for a target $ \dot {{\rm V}}{\rm O}_2 $ profile gave consistent and accurate tracking with $ {\rm RMSE}_{\dot{\rm V}O_2} = 0.198 \pm 0.070 $ l/min, $ P_{\Delta P} = 2.15 \pm 0.70 $ W2 and $ {\rm RMSE}_P = 39.2 \pm 15.4 $ W ( $ {\rm mean} \pm {\rm SD} $ ). Disturbance rejection performance was also found to be satisfactory. The results of the controller tests confirm the feasibility of the proposed $ \dot {{\rm V}}{\rm O}_2 $ feedback control strategy. Robustness was verified as the single LTI controller was specific to only one of the subjects and no difference in outcome values was apparent across all subjects. Subject-specific variability in breath-by-breath respiratory noise is the main challenge in feedback control of $ \dot {{\rm V}}{\rm O}_2 $ .