A stochastic Hammerstein model for control of oxygen uptake during robotics-assisted gait

Robotics-assisted gait devices have been introduced as part of rehabilitation therapy for people with neurological impairment. The scope of application has recently been expanded to encompass cardiopulmonary training and assessment, but the response of oxygen uptake to progressively increasing work rate while walking with robotics assistance can be strongly nonlinear. This hampers efforts to estimate cardiopulmonary performance parameters. We hypothesized that a linear increase in oxygen uptake can be achieved by employing feedback control. We aimed to develop a nonlinear stochastic model of oxygen uptake response to work rate during robotics-assisted gait, and to employ this model to design and test feedback strategies for control of oxygen uptake during incremental exercise testing. A new model structure was developed consisting of a Hammerstein component, i.e. a static nonlinear gain combined with a linear time-invariant transfer function, and a stochastic approximation of regularized breath-by-breath fluctuations in oxygen uptake. Simulation results using the model and a range of control design parameters confirmed the ability of feedback to achieve a linear increase in work rate in the face of strong plant nonlinearity. This new approach could be applied during incremental exercise tests and may lead to improved understanding and estimates of the sub-maximal gas exchange threshold and peak cardiorespiratory performance parameters