Lyapunov-guided adaptive tuning of lupaş q-bernstein polynomial coefficients for precision object handling in multi-robot electrical manipulators

This paper presents an adaptive output feedback tracking controller for cooperative multiple electrically driven robotic arms. The main innovation lies in employing the Lupaş q-analogue of the Bernstein polynomials as an uncertainty approximator whose coefficients are updated through Lyapunov-based learning laws, marking the first engineering application of this operator within an adaptive control framework. Unlike conventional adaptive, neural, or fuzzy-based schemes, the proposed method is regressor-free, relies solely on joint-position measurements, and avoids the intricate tuning procedures and computational burden typically associated with neuro-fuzzy approximators. A rigorous Lyapunov analysis ensures that all position and force tracking errors remain uniformly ultimately bounded. The controller is implemented on a dual-arm cooperative manipulation setup and quantitatively compared with two state-of-the-art approximation techniques. The simulation results confirm the proposed method’s superior precision, robustness, and real-time efficiency in the presence of model uncertainties and external disturbances.