WPMAVM: Weighted plus-and-minus allowance variance minimization algorithm for solving matching distortion

Point cloud matching is widely used in the calibration and measurement of complex curved surfaces, and the matching accuracy affects both the subsequently machined surface quality and measurement results. In the actual application, the existing iterative closest point (ICP) algorithm is prone to matching distortion when the measurement point clouds have inherent defects such as unclosed shape, uneven density and Gaussian noise. Despite this problem can be solved by the variance-minimization matching (VMM) algorithm, but the point clouds match distortedly both for ICP and VMM particularly when the workpieces behave with complex and unknown allowance distribution. For examples, the car bodywork is characterized by remarkable flexibility with local deformation, resulting in abnormal allowance, while the machined engine blade shows over- and less-cutting induced minus and abnormal allowances in high and low curvature areas, respectively. In this paper, a weighted plus-and-minus allowance variance minimization (WPMAVM) algorithm is proposed to overcome these problems. Specifically, the plus-and-minus allowance in the objective function of VMM algorithm is subdivided into the sum of plus-and-minus allowance variance minimization to suppress the distortion caused by the plus-and-minus allowance. The weighted term w, defined as the distance function from the point to the weighted plus-and-minus mean, is introduced to suppress the distortion caused by the abnormal allowance. The simulation and experimental comparisons on three typical workpieces show that the proposed algorithm has better robustness to minus allowance and abnormal point clouds compared to the existing ICP and VMM algorithms.