On the Dynamic and Control for a Three Degree-of-Freedom Robotic Arm Used for Rehabilitation Purposes in Medicine

Abstract

Abstract The usage of “robotic arms” for passive rehabilitation of post-stroke patients has been gaining relevance, considering how it can assist medical personal to carry out their tasks properly. However, when it comes to controlling these kinds of devices, it normally must deal with non-linearities issues resulting from the mathematical model of robotic arms, which is the case for three degrees of freedom (3DoF) articulated arm. Besides, uncertainties and constraints must be considered, as well as proper reduction of error signals, to assist real patients. For the given case of study, two control strategies were developed and implemented: PID and Sliding Mode Control with LQG. For both cases, the nonlinear mathematical model was developed and implemented as the system to be controlled. The PID controller was developed as a performance reference and comparison, and the Sliding Mode Controller with Extended Kalman Filter (LQG) design was proposed to increase robustness and stability on tracking trajectories to the rehabilitation of patients. The mathematical model of the 3DOF robotic arm was derived from the Euler-Lagrange formulation which is based on energy equations. For both control strategies, the system was implemented in Matlab© and Simulink© environments. While both show good performance in terms of settling time, SMC delivers the best results in terms of energy costs, noise rejection, and uncertainties, which can be easily set up with a combination of LQG control strategies. Since weight compensation was considered for the plant “robotic arm” design, the control could be applied for a real robot prototype, and it is scalable in terms of physical parameters and the required compensation forces.