Fixed-Time Synergetic Control for Manipulators

This paper addresses the trajectory tracking problem of robot manipulators by proposing a fixed-time synergetic control strategy. Synergetic control ensures exponential convergence of tracking errors while preserving continuous control inputs; however, its settling time remains dependent on the initial conditions, which limits its applicability in time-critical robotic tasks. To overcome this limitation, a novel fixed-time nonlinear macro-variable is introduced, and a corresponding synergetic control law is developed to guarantee convergence within a prescribed uniform time bound independent of initial states. Rigorous Lyapunov-based analysis is carried out to establish fixed-time stability of both the macro-variable and the closedloop tracking error dynamics, and explicit upper bounds on the convergence time are derived. The proposed approach preserves the smooth control characteristics of synergetic control while significantly improving transient performance. Numerical simulations conducted on a two-degree-of-freedom robotic manipulator demonstrate the effectiveness of the proposed controller and highlight its superior convergence speed compared to the classical synergetic control scheme.