Feedback control of heart rate during robotics-assisted end-effector-based stair climbing

Abstract

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.

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

“…For both oxygen uptake and heart rate dynamics identification, a first-order linear time-invariant (LTI) system was used, with parameters k, the steady-state gain, and τ , the time constant. Other studies have shown that this simple model can be sufficient for accurate feedback control ofVO 2 (Schindelholz & Hunt, 2015) as well as HR Hunt, Fankhauser, & Saengsuwan, 2015;Riedo & Hunt, 2016). The model is expressed in continuous (P c ) and discrete (P d ) time as…”

“…The measured plant outputVO 2 is fed back as a controller input, enabling the controller to continuously calculate P target based on the control error betweenVO 2 target andVO 2 . The control design method developed in Riedo & Hunt (2016) for HR control was also applied here for control ofVO 2 . This control approach applies three important constraints for the effective feedback controller transfer function integrator (inclusion of (1 − z −1 ) in R(z −1 )), low-pass characteristics (inclusion of z −1 in S(z −1 ), i.e.…”

“…A previous study, conducted using an end-effector gait rehabilitation robot (G-EO Evolution system, Reha Technology AG, Switzerland), implemented and tested a feedback system for control of heart rate (HR) (Riedo & Hunt, 2016). However, a more comprehensive physiological assessment consists of measurement of both heart rate and the rate of oxygen uptake (denotedVO 2 and referred to in the sequel simply as 'oxygen uptake').…”

“…The feedback structure employed here for control of oxygen uptake is based on a method previously proposed for HR control (Riedo & Hunt, 2016). The principal challenge for HR control was to deal appropriately with broad-spectrum heart rate variability, whereas for control of oxygen uptake it is the breath-by-breath variability ofVO 2 which is important.…”

“…The principal challenge for HR control was to deal appropriately with broad-spectrum heart rate variability, whereas for control of oxygen uptake it is the breath-by-breath variability ofVO 2 which is important. The purposely low-pass characteristics of the control approach developed in Riedo and Hunt (2016) therefore promised to be suitable for this new application also. A further contribution of the present work is a comparison of HR andVO 2 dynamics, because HR can conveniently be measured simultaneously withVO 2 : based on previous studies using other exercise modalities (Bearden & Moffatt, 2001;Zhang et al, 2014), it was hypothesized that the time constant of the heart rate response would be higher than that for oxygen uptake.…”