Lyapunov-based adaptive adjustment of (p,q)-Analogue Meyer-König and Zeller operator coefficients with applications to compliant motion control in collaborative robotic arms

This paper introduces an observer-based robust adaptive compliant motion control strategy that employs (p,q)-analogue of Meyer-König and Zeller operators as estimators to tackle uncertainties, external disturbances, and friction force in collaborative multiple electrical manipulators. This approach leverages visual task-space information and doesn't depend on velocity feedback, enhancing cost-effectiveness and applicability in practical robotic systems. The lumped uncertainty is first modeled by this operator. The adaptation laws, derived from stability analysis, are then employed to tune its coefficients, which are not presented in the previous literature. By applying the Lyapunov lemma, the paper ensures that error signals within the controlled system are uniformly ultimately bounded (UUB). The suggested strategy is evaluated in a system featuring two arms managing a rigid load. Simulation results showcase the effectiveness and versatility of the proposed approach. The outcomes are also compared with two advanced approximation techniques to demonstrate the precision and effectiveness of the suggested controller design.