Cooperative multiple elastic‐joint arms control using the (p, q)‐analogue of Bernstein operators as the uncertainty approximator

Abstract

AbstractThis paper presents the position‐force tracking control problem of cooperative multiple elastic‐joint robotic arms, encountering model nonlinearities, unknown perturbations, and dynamic uncertainties. To this mean, an adaptive function approximation technique (FAT) is proposed, authorizing the reference trajectory to be tracked by the object. This potential originates from the universal approximation feature of the FAT‐based methodologies. The (p, q)‐analogue of the Bernstein operators is utilized for this purpose. Since the systems' parameters are not precisely known, adaptive laws are employed for adjusting the uncertainty coefficients. The Lyapunov stability theorem assures that all signals in the error space remain uniformly ultimately bounded (UUB). In the end, two elastic‐joint arms carrying a rigid object are utilized for validation of the theoretical outcomes. The suggested strategy is also compared to the Chebyshev neural network (CNN). The results show the benefit of the existing method, managing the system even in the presence of disturbances and uncertainties with lower tuning parameters compared with CNN.