Learning variable impedance control is a powerful method to improve the performance of force control. However, current methods typically require too many interactions to achieve good performance. Data-inefficiency has limited these methods to learn force-sensitive tasks in real systems. In order to improve the sampling efficiency and decrease the required interactions during the learning process, this paper develops a data-efficient learning variable impedance control method that enables the industrial robots automatically learn to control the contact force in the unstructured environment. To this end, a Gaussian process model is learned as a faithful proxy of the system, which is then used to predict long-term state evolution for internal simulation, allowing for efficient strategy updates. The effects of model bias are reduced effectively by incorporating model uncertainty into long-term planning. Then the impedance profiles are regulated online according to the learned humanlike impedance strategy. In this way, the flexibility and adaptivity of the system could be enhanced. Both simulated and experimental tests have been performed on an industrial manipulator to verify the performance of the proposed method.

Calibration is necessary for dual manipulator to complete operational tasks. This paper proposes an effective robot-robot and hand-eye calibration method based on virtual constraints. Firstly, a rotational error model and a translational error model are established based on the relationships between the transformation matrices of the dual manipulator calibration system. Then a poses-alignment method is designed to make the poses of the two robots satisfy the constructed virtual constraints. At the aligned positions, the joint angles of the two robots are saved and used to calculate the values of the variables in the error models. Finally, the robot-robot and hand-eye rotational errors are estimated by an iterative algorithm. These errors are then used to calculate translational errors based on the SVD (singular value decomposition) method. To show the feasibility and effectiveness of the proposed method, experiments of robot-robot and hand-eye calibration for dual manipulators are performed. The experiment results demonstrate that the accuracy of the dual manipulator system is improved greatly.