Graphical abstract

A biologically-inspired actuation system, including muscles, spinal reflexes, and vestibular feedback, may be capable of achieving more natural gait mechanics in powered prostheses or exoskeletons. In this study, we developed a Virtual Muscle Reflex (VMR) system to control ankle torque and tuned it using data from human responses to anteroposterior mechanical perturbations at three walking speeds. The system consists of three Hill-Type muscles, simulated in real time, and uses feedback from ground reaction force and from stretch sensors on the virtual muscle fibers. Controller gains, muscle properties, and reflex/vestibular time delays were optimized using Covariance Matrix Adaptation (CMA) to minimize the difference between the VMR torque output and the torque measured from the experiment. We repeated the procedure using a conventional finite-state impedance controller. For both controllers, the coefficient of determination ( R 2 ) and root-mean-square error (RMSE) was calculated as a function of time within the gait cycle. The VMR had lower RMSE than the impedance controller in 70%, and in 60% of the trials, the R 2 of the VMR controller was higher than for the impedance controller. We concluded that the VMR system can better reproduce the human responses to perturbations than the impedance controller.