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An open-closed-loop iterative learning method for multiple flexible manipulator systems with repeatable motion tasks was proposed to achieve the consensus tracking of a specified desired reference trajectory. The open-closed-loop iterative learning control scheme was used to reduce the effects of model error and disturbances, as the boundedness of both the tracking error and the control input can be simultaneously guaranteed. In addition, when combined with a novel rotational joint with a continuously adjustable stiffness, the open-closed-loop iterative learning method enhances the adaptability to meet the strict requirements of the next generation of robots with the physical human–robot interaction and highly dynamic motion. The convergence conditions of the approach were obtained by the theoretical analysis. The simulation results show that this control algorithm has a good tracking accuracy and a fast convergence rate when used in the high-precision trajectory control for robots.

Design of Open-Closed-Loop Iterative Learning Control With Variable Stiffness for Multiple Flexible Manipulator Robot Systems