Time-Delay Control-Based Fractional-Order Sliding Mode for Trajectory Tracking of a Delta Robot: Real-Time Application

Abstract

In this article, a time delay control-based fractional-order sliding mode (TDCFOS) approach is proposed for the trajectory tracking of a parallel Delta robot. The complex, nonlinear, and unknown dynamics of the robot are estimated using the time-delay estimation (TDE) method, which provides a model-free control structure and avoids the need for precise dynamic modeling. The use of a fractional-order sliding mode increases the flexibility of the controller and improves the tracking error when compared with conventional integer-order schemes, particularly under chal-lenging conditions, such as increased operating speed. The stability of the closed-loop system is rigorously established through a Lyapunov-based analysis, ensuring reliable and robust performance under uncertainties and external perturbations. Experimental validations conducted on a Delta robot confirm that the proposed TDCFOS approach outperforms the traditional time-delay-based integer-order sliding mode controller (TDCIOS) in terms of tracking performance. Across two experimental scenarios involving all three robot joints, the proposed controller achieves reductions in root mean square error (RMSE) of 49% and 50.5%, and maximum absolute error (MAE) of 38% and 45.5%, respectively, com-pared with the TDCIOS controller.