Evolutionary Computation for Optimal LQR Weighting Matrices for Lower Limb Exoskeleton Feedback Control

The present work discusses optimal feedback control of a lower limb exoskeleton by determining optimal Linear Quadratic Regulator (LQR) weighting matrices. A simplified model of human gait having four degrees of freedom is developed to describe the dynamics of the Single Support Phase (SSP) of the gait cycle. The system is linearized about the reference trajectory to apply an optimal controller. It is observed that the choice of weight matrices are important to controller performance. Instead of conventional diagonal weight matrices, the more complex symmetric weight matrix is used in the study. An optimization problem is formulated to find the optimal weighting matrix by minimizing tracking error of joint angles. Non-dominated sorting genetic algorithm (NSGA)-II is then used to obtain the solution of a multi-objective constrained optimization problem.