Output error bound prediction of parallel manipulators based on the level set method

This paper presents an approach for predicting the exact output error bound of parallel manipulators based on the level set method. In the proposed approach, the error model of parallel manipulators is formulated as a constraint optimization problem, which is solved by means of searching techniques used in the level set method. The exact output error bound can be captured by tracking the time-evolution of the output error interface in the workspace. Taking advantage of the inverse error mapping from the workspace to the joint space, the calculation model can be derived in a closed form and solved in a straightforward manner. Using the proposed method, the entire output error bound, rather than the maximal output error, can be obtained, which gives an intuitive geometric insight of the accuracy performance of parallel manipulators. Additionally, the proposed method can be applied to both planar and spatial parallel manipulators, even when they are suffering from forward singularities. In the end, a numerical example is provided to demonstrate the effectiveness and efficiency of the proposed approach.