Semidefinite programming for Chebyshev fitting of spatial straight line with applications to cutter location planning and tolerance evaluation

This paper presents a novel model for fitting of spatial straight line based on Chebyshev norm. The problem is firstly formulated as a minimax problem, and then reformulated as a semidefinite programming (SDP) problem, which could be solved by many interior-point algorithms. The application of the proposed approach to two problems arising from manufacturing engineering, i.e. planning of the initial location of cylindrical cutter for flank milling and evaluation of the spatial straightness error, is discussed. Examples and numerical simulations illustrate the efficiency of the novel model.