Abstract: 3D matching is the basis for machining allowance distribution and profile error evaluation of complex surface, but existing methods are hard to guarantee stable matching accuracy, due to inherent measurement defects such as uneven point distribution, uneven density and local point missing. This paper proposes a novel 3D matching method of mathematical modeling and parameter calculation based on the variance minimization principle. It can linearly calculate the motion variables during each iteration, and appear quadratic convergence. The equivalent condition between the variance minimization matching and the TDM matching is derived, and the quantitative representations of both matching parameter error and point position error are analyzed. In addition, the effectiveness of the proposed method is demonstrated by the experiments of visual localization in robot grinding, allowance distribution in propeller machining and profile analysis in crankshaft inspection. It shows that the variance minimization has the advantage of overcoming the wrong squared distance minimization with respect to the high-density points or noisy points.

Key words: 3D matching, complex surface, normal/moment flow, variance minimization