An Optimized Type 2 Fuzzy Control with Time Delay Estimation for Gait Trajectory Tracking in Lower-Limb Exoskeleton Robot

Abstract This study proposed a novel nonlinear approach based on time delay estimation (TDE) integrated with optimized type 2 fuzzy logic control (T2FLC) to enhance the trajectory tracking of uncertain lower-limb exoskeleton (LLEX) robots with external disturbances. The TDE was first established based on an ultra-local model (ULM) and an intelligent proportional, integral, derivative (iPID) controller. Furthermore, the particle swarm optimization algorithm (PSO) was used to optimize the T2FLC structure. The proposed method (T2FLC-TDE) demonstrated superior accuracy in tracking human gait trajectories, with fast convergence time, for both the hip and knee joints, compared with the traditional PID and time delay-based type 1 fuzzy control (T1FLC-TDE) approaches. The root mean square (RMS) values for tracking errors achieved by the T2FLC-TDE were 0.0011 for the hip joint and 0.0106 for the knee joint. The integral time absolute error (ITAE) showed small error results of 0.0021 and 0.0011 for the hip and knee joints, respectively. The findings confirmed the efficacy and robustness of the proposed method in tracking human gait trajectories with small tracking errors and fast convergence time, even in the presence of external disturbance.