Robust adaptive control of cooperative multiple manipulators based on the Stancu–Chlodowsky universal approximator

Abstract

In this paper, the position-force tracking issue of an object moved by cooperative manipulators with model nonlinearities, dynamic uncertainties, and when there are unknown perturbations is investigated. For this purpose, a hybrid adaptive scheme for force–position control using the function approximation technique (FAT) is proposed, which allows the object to follow the desired path. The universal approximation feature of FAT-based approaches makes them ideal candidates for estimating different functions. In this research, the Stancu–Chlodowsky polynomials are utilized to approximate disturbances and uncertain dynamic terms. Since the system parameters may not be exactly known, adaptive rules for dealing with uncertainties are proposed. Through Lyapunov theorems, it is shown that using the proposed FAT-based adaptive method, all error signals related to position and force tracking remain limited. This means that the cooperative manipulators are able to move the object efficiently in the desired trajectory while keeping the internal force limited. Finally, the theoretical accomplishments are demonstrated by using the designed structure to control a cooperative robotic system with two manipulators moving an object. The proposed methodology is also compared to those of a strong state-of-the-art approximator, the Chebyshev Neural Network (CNN). The outcomes show that the proposed adaptive FAT-based approach is effective in operating the system even when there are perturbations and uncertainties.