Fourier series-based control of exoskeleton legs for adaptive rehabilitation with parameter variations

Latterly, a variety of researches have been concentrated on developing and utilizing leg exoskeletons to serve and assure recuperation for people with mobility challenges. Commonly, both linear and nonlinear techniques are applied to adhere to the intended trajectory. Alternatively, this work has advocated a new analytical approach to guide and refine patient movement using Fou-rier series function. The hip and knee joint angles are described by a combination of sine and cosine functions, each joint is described by 8 coefficients, leading to a total of 16 coefficients. The coefficients are computed to ensure the boundary conditions at the start, midpoint, and end of the run time. Next, the hip and knee torques are obtained using the proposed Fourier series function to steer the leg's movement, guaranteeing it tracks the predefined references trajectories. The leg's dynamic model is tested using Monte Carlo method under broad set of operational conditions. The knee joint displayed a maximum velocity of (1.92 rad/s) and a frequency of about 1.86 Hz while the hip joint recorded a maximum velocity of (0.82 rad/s) and a frequency of about (0.93 Hz). In addition, the observed maximum torque at the hip joint was determined as (89 N·m) while at the knee joint it was (39 N·m). These results illustrated that the proposed approach effectively directs the patient readily, reliably, and with high stability despite a broad range of patients features.