Robust adaptive impedance control of coordinated electrically driven robots: An engineering application for the (p,q)-analogue of Bernstein-Stancu operators

Function approximation techniques have emerged as influential mathematical tools for designing compliant motion controllers capable of managing objects using multiple electrical manipulators without the need for exact models. However, their effectiveness often relies on having access to velocity signals, which may not always be practical in real-world situations. This paper introduces an observer-based robust adaptive impedance control strategy that employs the (p,q)-analogue of Bernstein-Stancu operators as uncertainty estimators to tackle uncertainties 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 in the controlled system are uniformly ultimately bounded (UUB). The suggested controller 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.