Available wrench set robustness under hybrid joint-space control to uncertain wrench for a cable-driven parallel robot

For a overconstrained cable-driven parallel robot (CDPR), the number of cables is more than the number of the moving platform degrees of freedom. Therefore, a hybrid joint-space control method is used, where as many cables as the moving platform degrees of freedom are kinematically controlled, and the redundant ones are tension controlled. However, the selection of which cables to tension control is not straightforward. This work aims at evaluating the maximum value of the resistance to the wrench deviation, while tension-controlling a chosen cable set, by computing a performance index called available wrench set robustness (AWSR). In this case, the wrench deviation refers to the difference between the actual wrench and the nominal model wrench, which is related to the wrench uncertainties influenced by elements such as varying mass, shifted centre of mass and environmental disturbances. Firstly, owing to the inhomogeneous wrench deviation, a normalization method was proposed. Based on this, geometrically, the AWSR is defined as the minimum distance from the nominal wrench to the hyperplane boundary of available wrench set. As an application example of a planar CDPR with four cables and a spatial CDPR with eight cables, a comparison with previous methods illustrated that the proposed method significantly increased the range of wrench deviation, and this avoids situations where the configuration is not feasible using the traditional method. Therefore, the proposed method is more suitable for uncertain wrenches.