Extremum Seeking Control of a Robotic Ankle-Foot Orthosis Targeting the Soleus Muscle Activation during Walking

Stroke survivors experience muscle weakness and low weight-bearing capacity that impair their walking. The activation of the plantarflexor muscles is diminished following a stroke, which degrades propulsion and balance. Powered exoskeletons can improve gait capacity and restore impaired muscle activity. However, a technical barrier exists to generate systematic control methods to predictably and safely perturb the paretic leg using a wearable device to characterize the plantarflexors' muscle output for gait training. In this paper, a closed-loop robust controller is designed to impose an ankle joint rotation (i.e., a kinematic perturbation) in the mid-late stance phase to target the soleus muscle using a powered cable-driven ankle-foot orthosis. The goal is to generate soleus muscle activity increments throughout a gait experiment by applying ankle perturbations. This ability to modulate plantarflexor activity can be used in future conditioning studies to improve push-off and propulsion during walking. However, the optimal perturbation magnitude for each participant is unknown. Hence, online adaptation of the ankle perturbation is well-motivated to modulate the soleus response measured using surface electromyography (EMG). An extremum seeking controller (ESC) is implemented in real-time to compute the ankle perturbation magnitude (i.e., dorsiflexion angle) exploiting the soleus EMG response from the previous perturbed step to maximize the soleus response in the next perturbed step. A Lyapunov-based stability analysis is used to guarantee exponential kinematic tracking of the ankle perturbation objective.