In this work, we propose a framework to address the autonomous impedance regulation problem of robots in a class of constrained manipulation tasks. In this framework, a human arm endpoint stiffness model is used to extract the task stiffness geometry along the constrained trajectory, which is then encoded offline and reproduced online by a Gaussian Mixture Model (GMM) and the Gaussian Mixture Regression (GMR), respectively. Furthermore, the full Cartesian impedance of the robot is formulated through an optimal control problem, i.e., the Linear-Quadratic Regulator (LQR), in which the task stiffness geometry (extracted from human demonstrations) is considered as the time-varying weighting matrix Q. The optimal impedance is eventually realised by the robot through a task geometry consistent Cartesian impedance controller. A tank-based passivity observer is implemented to give evidence on the stability of the system during online impedance variations. To evaluate the performance of the framework, a comparative experiment with three different impedance settings (i.e., the proposed framework, the framework without LQR and the framework without GMM/GMR) for Franka Emika Panda to perform a door opening task was conducted. The results reveal that our framework outperforms the other two, in terms of tracking error and the interaction forces.

Ball screws play a significant role in maintaining transmission accuracy and stability. Accurate prediction of the remaining useful life (RUL) for the ball screw can provide reliable decision-making information for predictive maintenance. However, the RUL prediction of ball screws with the precision indicator under time-varying operating conditions (OCs) is rarely involved. Moreover, obtaining data for the whole life cycle of each OC is impractical due to time and expenditure constraints. To address the aforementioned issues, this article proposes a hybrid approach for RUL prediction under time-varying OCs. First, a time-varying stochastic model considering the precision indicator is established. Then, the data-driven algorithm is proposed to estimate the unknown parameters with limited data. Finally, the effectiveness of the proposed method in prognostics is experimentally validated through the designed platform and compared with the commonly used methods.

To highlight the key factors which influence the dynamic performance of the harmonic drive, a refined harmonic drive model considering nonlinear stiffness, kinematic error, and friction of the critical components is established. A dedicated experimental apparatus based on double motor twisting is constructed to measure the characteristics of harmonic drive, and the attribute parameters of the proposed model are identified. A series of experiments on the dynamic transmission error at different driving velocities are carried out to verify the proposed model. Based on the proposed model, the influence of different component stiffness on the velocity step response of the harmonic drive is analyzed. The results show that the influence of the component stiffness on the system dynamic response is more significant at high driving velocity, the increase of the stiffness of each component will decrease the dynamic transmission accuracy of harmonic drive, and the bearing radial stiffness is the most sensitive parameter to system’s dynamic response among all the stiffness factors.