Overall stiffness derivation and enhancement algorithm of a flying cable-driven parallel robot

Flying cable-driven parallel robots (CDPRs) are a special subclass of cable-driven robots that offer mobility in air compared with the traditional CDPRs. These flying CDPRs possess weaker stiffness due to their high maneuverability and cable’s unilaterality, which may result in fluctuations around a desired nominal moving platform pose. The focus of this study is on the derivation of the overall stiffness and enhancement method of stiffness with regard to the weakest degree of freedom. The overall stiffness is divided into two parts, namely, active and passive stiffnesses. The line geometry theory is introduced to derive the explicit expression of the active stiffness, which is a 3D Hessian matrix. Results showed that the rotational stiffness around the z-axis k_zz is the weakest stiffness based on the overall stiffness matrix expression. Furthermore, we summarize the stiffness distribution of the flying CDPR in the entire workspace. Specifically, we present a stiffness-oriented cable tension distribution algorithm to achieve the best feasible stiffness considering the enhancement of k_zz and tensions’ limit, which is only applicable for the flying CDPR with redundant actuation. Simulation results demonstrate that the proposed algorithm can remarkably enhance stiffness.