Trajectory tracking of Stanford robot manipulator by fractional-order sliding mode control

In this work, a fractional integral sliding-mode control scheme based on the Caputo- Fabrizio derivative and the Atangana-Baleanu integral of the Stanford robot for trajectory tracking tasks is developed and presented. The coupled system is composed of the robot manipulator and the induction motors that drive its joints. The mathematical model of the system is obtained by the Euler-Lagrange method and generalized to an arbitrary or-der via the Caputo-Fabrizio derivative. The actuators are controlled by fractional PI con-trollers based on the Atangana-Baleanu integral, while a fractional integral sliding mode control law is also developed for trajectory tracking control. In this context, a fractional version of the sliding surface via the Caputo-Fabrizio derivative is introduced to improve the performance of the control system. In addition, to attenuate the chattering effects, a fractional integral term, based on the Atangana-Baleanu integral, is introduced on the slid-ing surface further improving system performance with less power consumption. The con-ventional integral sliding mode control and an optimal super-twisting sliding mode con-trol are also introduced for comparison with the proposed control strategy. The control schemes were tuned using the Cuckoo method. External disturbances are also considered in the system dynamics, as well as different end-effector reference trajectories, which were designed to carry out manufacturing tasks. Simulation results confirm the superiority of our control scheme for trajectory-tracking applications over its conventional version and the optimal super-twisting sliding mode control, even with external disturbances and tra-jectory changes. To show the robustness of the proposed control scheme under different operating conditions, all the numerical simulations were performed considering the same orders and gains. Finally, our control law introduces the fractional derivative and integral of Caputo-Fabrizio and Atangana-Baleanu respectively, which have not been used enough in the modeling and control of robotic systems. Therefore, it is interesting to analyze the contributions and advantages that arise when using them.(c) 2023 Elsevier Inc. All rights reserved.