End-effector robots for gait training have potential for cardiovascular fitness therapy. We developed and tested a heart rate (HR) controller for end-effector robots, operated in stair-climbing mode. The structure has an inner loop for volitional control of exercise work rate and an automatic outer loop to compute target work rate and control HR. Feedback design focused on disturbances caused by HR variability, by shaping the input-sensitivity function to give low-pass loop characteristics. Using five able-bodied subjects, command response tests revealed consistent, accurate and stable performance for all subjects with root-mean-square (RMS) HR tracking error 3.85 ± 0.66 bpm (mean ± SD) and average control signal power 1.62 ± 0.13 W 2. Disturbances in cadence were successfully rejected with RMS HR tracking error 5.78 ± 0.63 bpm and average control signal power 0.40 ± 0.12 W 2. Feasibility of the HR control strategy for end-effector robots was proven. The controller showed consistent behaviour for all command response and disturbance rejection tasks. Robustness was proven since the single LTI controller used a nominal model which was not specific to any of the five subjects. Physiological HR variability is the principal feedback design issue for HR control, while parametric/structural plant uncertainty is secondary.
A heart rate (HR) feedback control system for end-effector gait rehabilitation robots was previously developed and successfully tested, but oxygen uptake (VO 2 ) is thought to better characterize physiological exercise intensity. The aim of the present study was to identify and compareVO 2 and HR dynamics, and to develop and test aVO 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 ofVO 2 (RMSEV O 2 ), average control signal power (P P ) and RMS error of volitionally controlled power (RMSE P ). The nominal first-order linear model forVO 2 had time constant τ = 52.4 s and steady-state gain k = 0.0174 (l/min)/W. The mean time constant τ = 67.3 s for HR was significantly higher than forVO 2 , where τ = 53.4 (p = 0.048). Command responses for a targetVO 2 profile gave consistent and accurate tracking with RMSEV O 2 = 0.198 ± 0.070 l/min, P P = 2.15 ± 0.70 W 2 and RMSE P = 39.2 ± 15.4 W (mean ± SD). Disturbance rejection performance was also found to be satisfactory. The results of the controller tests confirm the feasibility of the pro-posedVO 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 ofVO 2 . ARTICLE HISTORY
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