Auxiliary Robust Integral of the Sliding ModE (ARISE) Control Approaches for Rehabilitation of Neuromuscular Disorders

Abstract

In the United States alone, tens of millions of individuals are affected by neurological conditions (NCs), including but not limited to stroke, Parkinson’s disease (PD), multiple sclerosis (MS), cerebral palsy (CP), and spinal cord injury (SCI). As the global population continues to age, the incidence of these conditions is rising, with millions of new cases reported worldwide each year. NCs often lead to various physical impairments such as muscle weakness, paralysis, and a loss of voluntary limb control. These limitations can also contribute to secondary health issues like obesity, diabetes, and cardiovascular disease, largely due to reduced physical activity. As a result, individuals with NCs face significant challenges while performing everyday tasks, and their associated healthcare costs in the U.S. alone exceed $150 billion annually. Thus, there is a need to improve the quality of life for those with NCs. Many potential solutions have been introduced, but each are limited in someway. For example, functional electrical stimulation (FES), which bypasses typical neurological processes to activate an individual's muscles to provide active therapy, is one of the more capable solutions, but it results in the patient becoming fatigued quicker than normal. The focus of this thesis is on the improvement of FES-based therapies. More precisely, this thesis develops a novel robust and adaptive control structure for a combined FES and robotic system called a hybrid exoskeleton. Specifically, for the first time, a recently developed ARISE control approach is modified for a hybrid exoskeleton. Furthermore, the control law is augmented with neural networks (NNs) that learn uncertainties in the dynamic model.

The first half of this thesis proposes and develops an ARISE controller for a general, uncertain, and switched Euler-Lagrange (EL) dynamic model, which could model an exoskeleton alone (i.e., without FES). To demonstrate the generality of the proposed approach, a switched and uncertain control effectiveness matrix was assumed. In this half of the thesis, a SM term is injected through a filtered auxiliary error signal into the closed-loop dynamics (i.e., an ARISE controller is developed). The control law is designed in a way such that it has an integral of the SM term in it, which will help in reducing the chattering effect that is prevalent in SM controllers. Furthermore, an adaptive update law is defined to address the unknown terms in the control effectiveness matrix. In addition, through a Lyapunov-like stability analysis, a semi-global result with exponential trajectory tracking towards an ultimate bound is achieved, provided that certain conditions on the gains and initial values are satisfied. Moreover, the performance of the proposed controller was evaluated and compared against a traditional SM controller through simulations in Matlab/Simulink. Due to limitations in the available experimental tools, physical experiments were conducted on a non-switched dynamic system; a lower-limb exoskeleton platform. The comparative results are presented through a series of graphical analyses. The findings indicate that the proposed ARISE controller outperforms the SM controller in managing a both a switched and a continuous dynamic system. This superior performance remains consistent across varying dynamic parameters and external disturbances.

In the second half of this thesis, the ARISE controller is developed for a hybrid-exoskeleton. Particularly, hybrid exoskeletons have both motor and FES inputs, requiring the design of multiple controllers, and the control effectiveness that maps stimulation to torque output is unknown and nonlinear. Consequently, this work approximates the uncertain FES control effectiveness using a NN, increasing the optimality of the FES control design and slowing the onset of fatigue. Furthermore, another NN is designed to approximate additional uncertainties in the dynamic model and ARISE is used to compensate for unstructured and time-varying disturbances, yielding an improved trajectory tracking performance. Additionally, a Lyapunov-based stability analysis was conducted to ensure the stability and safety of the proposed control framework, establishing semi-global exponential trajectory tracking convergence within an ultimate bound. To demonstrate the proposed approach, this work considered a leg extension exercise. Subsequently, experiments were carried out by augmenting the exoskeleton used in the first part of the study with FES. The experiments included a total of two healthy subjects to evaluate the proposed control system's potential for an enhanced rehabilitation performance.