Fractional Order Lyapunov based Indirect Adaptive Backstepping Control Design for DELTA Robot

This paper presents a novel Fractional Order Lyapunov-based Indirect Adaptive Backstepping Control strategy for the precise trajectory tracking of a DELTA robot. The proposed approach integrates fractional calculus with Lyapunov stability theory to enhance the robustness and adaptability of the controller in the presence of system uncertainties and external disturbances. Unlike conventional backstepping controllers, the indirect adaptive mechanism estimates unknown system parameters online, improving control performance without requiring precise dynamic modeling. In robotic systems, accurately capturing the inherent viscoelasticity, actuator dynamics, and noninteger-order behaviors requires fractional-order modeling, which provides a more realistic and flexible representation of system dynamics. The necessity of fractional calculus in robotics motivates the design of the proposed controller, ensuring better adaptability and robustness. The effectiveness of the control strategy is validated through simulation results, demonstrating its feasibility and improved performance in robotic applications.