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In this paper, a decentralized adaptive fuzzy control has been developed for two cooperating robotic manipulators moving an object with impedance interaction. The contact forces are described using gradients of nonlinear potentials; then, the deformations of the contact surface can be obtained by an impedance approach. The cooperating manipulators are considered as a combination of subsystems, and the decentralized local dynamics coupled with physical interactions among the subsystems are developed. To compensate for the effect of dynamics uncertainties and external disturbances, decentralized fuzzy control combining parameter adaptations and disturbance observers is constructed. It guarantees the motion trajectories and impedance forces of the constrained object converging to the desired manifolds. It is theoretically established that the disturbance observers compensate for unparameterizable uncertainties, while the adaptive fuzzy mechanism compensates for the fast-changing components of the uncertainties that go beyond the disturbance observers. Moreover, unknown nonlinear dynamics such as the inertia matrix, Coriolis/centripetal matrix, and frictions, as well as interconnections with nonlinear bounds, can be accommodated through online learning. The experiments on two real robots have been carried out to verify the effectiveness of the proposed theoretical results.
Li et al. (Wed,) studied this question.