Increasing the viscosity of elastic joints can significantly improve the performance of elastic joint robots during physical human–robot interactions. However, current approaches for injecting viscous elements require an additional damper to be added in parallel with the elastic elements. In this paper, we propose a new concept called virtual viscous element injection (VVI), which enables a robot to exhibit viscoelasticity without altering its mechanical structure. VVI relies only on motor-side dynamics reshaping and state feedback. Interestingly, the VVI method allows high-resolution joint torque measurements in elastic joint robots, unlike in physical viscoelastic joint robots, which measure joint torque using higher-order derivatives of the positions. Furthermore, the VVI method is proved to preserve the passivity of robot dynamics, which provides numerous possibilities for the applications of combined passivity-based controllers. Specifically, we first emphasize the impedance control method using VVI. The results demonstrate that the VVI-DF method, which combines the direct feedback (DF) method with VVI, addresses the issue of excessive acceleration feedback in the controller. This provides looser constraints for achieving a high-gain torque loop in impedance control. Moreover, this paper also provides examples of the application of VVI combined with passivity-based position and torque controllers. Experiments and simulations demonstrate the effectiveness of the proposed methods. The proposed method can be extended to various robots, such as exoskeletons, and collaborative robots.

In this article, the stiffness mapping of compliant robotic systems is generalized to the special Euclidean group SE(3). A geometric framework is proposed to unify the existing stiffness models. We analyze the symmetry and exactness relationship between joint and Cartesian stiffness matrices in this framework. To verify the theoretical results, motions of different types of manipulators, including serial and parallel ones, are tested in simulations. Based on the conservative property of the stiffness matrix, an impedance control strategy to achieve variable stiffness is proposed. In addition, a feasible stiffness identification method is developed using the skew-symmetric structure of the stiffness matrix.