Evaluation of spatial straightness errors based on multi-target optimization

In order to realize accurate and fast evaluation for spatial straightness,its mathematical model and Successive Quadratic Programming(SQP) algorithm were investigated.Based on the condition of minimum zone method,a nonlinear programming model was established for spatial straightness error evaluation.This nonlinear model was further proved to be a multi-target optimization problem in essence,and could be transformed into a single-target optimization problem.A unified and efficient SQP algorithm was proposed to solve the model.As the nonlinear programming model is convex and SQP algorithm can retain such nonlinear information,the algorithm has very loose requirements for initial parameters and shows its stable,reliable and highly efficient in optimization.Several experiments of spatial straightness error evaluation were carried out,the results can meet the requirements for convex programming's global optimization very well,the precision is 10-3 mm and consumed time is about 0.4 s,which has proved the above mentioned conclusion.