Robust Finite‐Time Control Using Fractional Synergetic Techniques for Robot Manipulators

ABSTRACT Synergetic control (SC) is recognized for its robustness and chattering‐free performance in robot‐manipulator applications requiring precise tracking. However, its effectiveness is constrained by sensitivity to model uncertainties; improper selection of macro‐variables, which can degrade transient response and robustness; and the lack of guaranteed finite‐time convergence when the system starts from a far initial position. Achieving accurate trajectory tracking within a finite time while ensuring smooth transients and robustness, therefore, remains a critical challenge, particularly under parameter uncertainties and external disturbances. To address these limitations, this study introduces a novel approach that integrates a finite‐time prescribed performance function (FTPPF) into synergetic macro‐variable design. The resulting finite‐time synergetic controller (FTSC) ensures error convergence within a prescribed time interval and reduces overshoot regardless of initial conditions. Fractional calculus (FC) is incorporated into the macro‐variable manifold to design the finite‐time fractional synergetic controller (FTFSC), providing a versatile framework that further enhances tracking accuracy and strengthens robustness against disturbances. Experimental validation on a 4‐DOF MICO robot compares the conventional synergetic controller with the proposed FTSC and FTFSC controllers. Results across diverse scenarios confirm that the proposed methods consistently achieve superior steady‐state and transient performance while significantly improving robustness and resilience to uncertainties and disturbances. Lyapunov‐based analysis demonstrates the asymptotic stability of the error dynamics.