Backstepping Control of a Motorized Ankle Orthosis Targeting the Soleus Muscle During Walking*

Abstract

The gait patterns of stroke survivors become slow and metabolically inefficient as a result of muscle weakness and low weight-bearing capacity. Exoskeletons and assistive robots can improve gait kinematics and energetics. However, the use of these powered devices may cause a reliance on the device itself that results in limited lasting improvement of the paretic leg function. Specifically, there exists a need to strengthen and train the response of weak ankle muscles, such as the soleus muscle, in stroke survivors. Impaired activation of the soleus muscle induces unnatural gait kinematics and reduced propulsion. The mechanical modulation of the soleus muscle can improve its loading response and enhance gait performance after a stroke. This paper develops a closed-loop feedback controller to manipulate the ankle joint dynamics to mechanically control the soleus muscle response using a motorized ankle orthosis. The control method is inspired by backstepping control techniques and developed to connect the ankle joint angular velocity and the soleus muscle response during the stance phase of walking. The tracking objective is quantified using an integral-like muscle error between the desired soleus response and the actual muscle response, which is measurable using surface electromyography (EMG). The closed-loop electric motor controller is designed to apply ankle perturbations exploiting the backstepping error and an adaptive control term to cope with uncertain parameters that satisfy the linear-in-the-parameters property. A switching signal is developed using heel and toe ground reaction forces to strategically perturb the ankle and target the soleus muscle loading response in real-time during the mid-late stance phase of walking. A Lyapunov-based stability analysis is used to guarantee a globally uniformly ultimately bounded (GUUB) tracking result.