Switched Adaptive Integral Concurrent Learning for Powered FES-Cycling

摘要

Functional electrical stimulation (FES) and motorized cycles have the potential to recover lost function and mobility in people with neurological disorders. However, the human-robot system is uncertain, nonlinear, and time-varying, posing technical challenges to customizing the interaction across participants. In this paper, a closed-loop switching adaptive controller is designed to achieve cadence tracking using a powered FES-cycling system. The adaptive design copes with the parametric uncertainty of the cycle-rider dynamics and the unknown switching muscle control effectiveness by computing estimates of the uncertain parameters. A saturated state-feedback controller activates the quadriceps muscle groups, whereas an integral concurrent learning technique activates the electrical motor and leverages input-output data to estimate the parametric uncertainty and achieve cadence tracking. A switching Lyapunov-based stability analysis is developed in two phases. The initial phase ensures bounded tracking and estimation when a learning condition has not been attained; in the second phase, global exponential tracking and estimation convergence is ensured, given an online-verified finite excitation condition is satisfied. The developed controller was tested during three FES-cycling trials with different cadence trajectories and learning conditions in eight able-bodied individuals and three participants with neurological conditions (NCs) during ten-minute and five-minute experiments, respectively. The system achieves an average RMS cadence tracking error of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.49\pm0.42$</tex-math> </inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.66\pm0.36$</tex-math> </inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.69\pm0.58$</tex-math> </inline-formula> revolutions per minute (RPM) with the able-bodied participants, while an average RMS cadence tracking error of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3.15\pm0.97$</tex-math> </inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.60\pm0.17$</tex-math> </inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3.47\pm1.43$</tex-math> </inline-formula> RPM for the participants with NCs in three cycling trials. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —FES-Cycling is a rehabilitation strategy recommended to recover muscle capacity and improve cardiovascular function in people with neurological disorders. Although significant progress has been made on the closed-loop control of FES-cycling systems, a critical need exists to develop adaptive strategies to comply with the nonlinear, time-varying muscle responses to FES, cope with the uncertain parameters of the cycle-rider system, and improve tracking performance. This paper develops a decoupled control design for muscles and motor. The FES controller is tuned using minimal parameters to yield bounded muscle responses with a tunable saturation limit. The electric motor control is designed using an adaptive-based method that estimates the uncertain parameters in the cycle-rider system and strategically exploits the muscle input to improve tracking performance. Results from cycling trials in able-bodied individuals and participants with neurological conditions demonstrate the feasibility of the adaptive control design to tracking different t