Modeling and Control Synthesis of Robotic Digits for Movement Coordination In an Anthropomorphic and Impaired Hand

Abstract

The human hand is an intricate structure capable of realizing complex Activities of Daily Living using an effective combination of mechanisms, sensing, actuation and control functions. This thesis presents the road towards the mathematical realization and control of an impaired human hand model. The research focuses on formulating a mathematical model of the musculoskeletal system with robust control theoretical frameworks to regulate the voluntary flexion/extension motion of fngers in the presence of time delay due to actuation force, noisy joint sensors, and perturbations. Maintaining the movement coordination of the robotic fngers with the central nervous system (CNS) and natural digits is crucial for robust performance in a partially impaired anthropomorphic hand. A bond graph model of 21 Degrees of Freedom comprising a biomechanical system with four natural and one robotic digit for optimal trajectory through force regulation is formulated. A mathematical framework in the human palm reference frame using physiological, kinematics, and viscoelastic dynamics to explore the biomechanics of movement coordination is constructed. Physiologically optimal controllers better represent CNS decision-making processes with proper neural inputs and proprioceptor feedback. An optimal Linear Quadratic Regulator and robust Linear Quadratic Gaussian Integral controller developed from physiological cost factors simulating the CNS are evaluated using a modeling–simulation paradigm. Physiological models include multiple zero eigenvalues, representing a signifcantly redundant system. A fngertip trajectory tracking H∞ control paradigm by reducing model order is created. The minimal state space realization method enabled pole-zero cancellation of the transfer function, facilitating a reduced order state feedback controller and minimizing computing complexity by eliminating uncontrollable and unobservable states. In a wellposed biomechanical model control problem, it is computationally challenging to establish control techniques that are robust to disturbances and uncertainties while maintaining physiological characteristics. Actuation force time delay, parametric uncertainty, exogenous disturbances, and sensory noise are incorporated to establish a realistic biomechanical model. A mixed µ-synthesis controller is developed considering the real parametric uncertainty. The motion of the robotic fnger when perturbed from an initial equilibrium position is considered. The controller regulates the mechanical fnger movement using joint feedback force and stabilizes at the desired equilibrium position by tracking the joint angular position profle. The suggested LQR, LQG Integral Control, H∞, and the novel mixed µ-synthesis controller schemes are robust to noise and disturbances and deliver the required performance within physiological bounds. The model is simulated in MATLAB/Simulink to facilitate user programming, calculation, and visualization. Developing a biologically inspired neurophysiological controller with robust performance has many applications, including assistive rehabilitation devices, hand movement disorder diagnosis and mobility restoration in patients with pathological and neural disorders (e.g., hemiparetic patients), robotic manipulators, task-specifc applications in sports biomechanics, and ergonomics.