Optimal Linear Quadratic Gaussian Torque Controller (LQG) for Upper Limb Rehabilitation

With the increasing numbers of degrees of freedom (DOF), modeling and control of the upper-limb robotic devices become significantly challenging. Model uncertainties, parameter inaccuracies, and incompletely known frictional effects also become inevitable, leading to the need for robust controller design. This paper presents the design of an optimal Linear Quadratic Gaussian torque controller (LQG) with integral action for upper limb rehabilitation robot under the independent joint control paradigm. The controller is motivated to ensure optimal robust torque control, to avoid modelling uncertainties, and to simplify control design process. The proposed method is demonstrated through a simulation study and implemented experimentally on two active joints of a 5-DOF robot prototype. The LQG closed-loop control system responses to both step and input/output disturbance inputs demonstrated superior performance of the controller to the traditional PID controller. The elbow flexion/extension and shoulder abduction/adduction experiments involving healthy subjects verified that the controller is able to deliver better performance within 0.0047Nm and 0.0068 Nm RMS torque tracking errors for shoulder and elbow respectively.