FRACTIONAL MODELING AND DESIGN ON CONTROL SYSTEM OF 2-DOF LOWER-LIMB EXOSKELETON ROBOT MODEL

In recent years, exoskeletons have become more popular due to technological advances in robotics and the acceptance of humans to interact with robotic systems. Exoskeletons have multiple applications, including medicine and the military. The first is usually focused on rehabilitation tasks, for example, in patients who have suffered cerebrovascular strokes, and whose motor skills in some parts of the body are affected. In this context, the motivation for proposing a fractional-order control scheme for an exoskeleton is that it can be applied in functional therapies for this type of patient, helping to recover motor skills. Rehabilitation tasks are associated with a precise and robust control system. In this work, a fractional-order sliding mode control system inspired by the Caputo–Fabrizio derivative and the Riemann–Liouville integral of a 2-degrees-of-freedom lower-limb exoskeleton for trajectory tracking tasks is designed and developed in this paper. Induction motors power the joints, so the coupled system consists of the mechanism, the hip and knee joints, and their actuators. The system’s mathematical model is obtained using the Euler–Lagrange approach and generalized to an arbitrary order via the Caputo–Fabrizio derivative. The actuators are driven by fractional-order PI control laws based on the Riemann–Liouville integral, whereas a fractional integral sliding mode control is also designed for trajectory tracking. In this sense, the Caputo–Fabrizio derivative is introduced into the sliding surface to improve the controller performance. Similarly, an integral action is incorporated, inspired by the Riemann–Liouville integral, to cope with the chattering effects generated by the switching term. Additionally, to cope with external disturbances and parametric uncertainties a neural network inspired by the Caputo–Fabrizio derivative is introduced, further improving the performance of the control scheme. The considered fractional operators add degrees of freedom that can be tuned for better reference trajectory tracking with a smaller error. The conventional version of the proposed controller is also implemented for comparison purposes between both controllers. The gains and orders on the two controllers are tuned using the Cuckoo search algorithm. Simulation results verified the superiority and robustness of our control system in terms of the root mean square error operating under different scenarios such as joint friction, external disturbances, and various reference trajectories. A control combining an integral sliding mode approach, PI controllers, and a neural network, where the Caputo derivative and the Riemann–Liouville integral are introduced, has not been reported yet.