Trajectory Tracking of Delta Parallel Robot via Adaptive Backstepping Fractional-Order Non-Singular Sliding Mode Control

The utilization of the Delta parallel robot in high-speed and high-precision applications has been extensive, with motion stability being a critical performance measure. To address the inherent inaccuracies of the model and minimize the impact of external disturbances on motion stability, we propose an adaptive backstepping fractional-order non-singular terminal sliding mode control (ABF-NTSMC). Initially, by employing a backstepping algorithm, we select the virtual control for subsystems as the state variable function in joint space while incorporating a calculus operator to enhance fractional-order sliding mode control (SMC). Subsequently, we describe factors such as model uncertainty and external disturbance using a lumped uncertainty function and estimate its upper bound through an adaptive control law. Ultimately, we demonstrate system stability for our proposed control approach and provide an analysis of finite convergence time. The effectiveness of this presented scheme is demonstrated through simulation and experimental research.