An Adaptive Neuro-Fuzzy Fractional-Order PID Controller for Energy-Efficient Tracking of a 2-DOF Hip–Knee Lower-Limb Exoskeleton

For safe and efficient human–robot interaction, lower-limb exoskeletons used for assistance and rehabilitation need to be precisely and energy-efficiently controlled. By creating an adaptive neuro-fuzzy fractional-order PID (ANFIS-FOPID) controller, this project seeks to improve tracking accuracy, robustness, and energy efficiency in a two-degree-of-freedom hip–knee exoskeleton. The Euler–Lagrange formulation is used to derive a nonlinear dynamic model, and a Lyapunov-based stability analysis is used to show that the closed-loop system remains uniformly ultimately bounded under disturbances and parameter uncertainties. The suggested controller performs noticeably better than traditional PID and fixed-parameter FOPID controllers, according to numerical simulations conducted under both normal and perturbed conditions. The ANFIS FOPID achieves root mean square errors below 0.028 rad and lowers the integral absolute errors at the hip and knee joints to 0.1454 and 0.1480, as opposed to 0.3496–0.3712 for PID controllers. Under ±10% parameter uncertainty, the total control-energy proxy drops from 2870.0 (PID) to 936.25, a 67.4% decrease, and stays at 1587.93. Statistically significant variations in energy consumption are confirmed by one-way ANOVA (p < 10−176). Large effect sizes are found (η2 = 0.237–0.314). These results demonstrate the superior tracking performance, robustness, and energy efficiency of the ANFIS-FOPID controller. The results set a quantitative standard for future experimental validation and hardware-in-the-loop implementation, despite being based on high-fidelity simulations.