Closed-form error space calculation for parallel/hybrid manipulators considering joint clearance, input uncertainty, and manufacturing imperfection

Abstract

This study proposes a generalized approach to error space calculation for parallel/hybrid manipulators resulting from joint clearance, input uncertainty, and manufacturing imperfection. First, the local pose deviation caused by each error is parameterized using exponential coordinates, and the distribution is defined as a Gaussian on the motion group. Second, the linear relationship between the local pose error caused by the disturbance of the passive joint and that by other error sources is derived based on the Baker–Campbell–Hausdorff formula. Third, closed-form formulas are developed for error propagation on independent and non-independent group elements, thereby determining the covariance and mean of the pose error distribution of the end-effector. Fourth, the error space and maximum deviation along/about each axis are extracted from the covariance matrix and mean at the designated confidence level. Finally, four numerical cases are presented to demonstrate the effectiveness and advantages of the proposed method. The experimental evidence indicates that the proposed method can be applied to planar and spatial parallel/hybrid manipulators and has a significantly high computation speed.