Research On Optimal Matching Technology For Digital Manufacturing And Inspection

Optimal matching technology for free-form objects attracts considerable attention as an important topic in digital manufacturing and inspection. Many attempts have been made to solve the problem from various points of view. But, the research on the key technologies of optimal matching is in theoretics phase yet. In this paper, the foundational theoretics and approaches for free-form surface matching are expounded comprehensively from the aspect of calculating closest point, initial transformation estimate, matching precision, global optimization and constrained matching, etc. in order to achieve the optimal matching between free-form objects.Firstly, a novel algorithm to calculate closest point, based on recursive quadtree decomposition, is presented, which combines with the robust arithmetic for multivariate Bernstein-form polynomials and Bezier surface segmentation algorithm. This algorithm transforms the abstract algebraic operation of finding the closet point to a straightforward intersection problem between surface and parametric plane, avoids disadvantage of iterative method that requires a good initial point. The result demonstrates that the proposed algorithm is practical and efficient.Secondly, the problems on initial transformation estimate, matching precision and global optimization is farther discussed. By means of the minimum bounding box and differential character of free-form surface, two rough localization algorithms are proposed, which can give a better initial estimate that approaches to the optimal body transformation and optimize the search space for the follow-up iterative matching algorithm. A maximum distance criterion, based on the directed Hausdorff distance, is adopted to refine the transformation between objects by reducing the effect of data noise and partial surface distortion. On basis of these, an improved iterative algorithm is used in the exact adjustment to ensure the global optimization.In addition, taking the free-form blanks with offset surface for example, the constrained matching is discussed. Starting with the constrained optimization method, an algorithm for the even distribution of the machining allowance is developed. Using the Rockafellar multiplier method, the constrained optimization problem is transformed to unconstrained optimization that is then solved by the alternating variable method. The result shows that the proposed algorithm is efficient.Finally, a method for pruning plane point is proposed, which improves the efficiency of the matching algorithm based on curvature. Given some simulative experiments for multi-view data fusion in reverse engineering, workpiece localization in NC machining and free-form surface inspection. Experiment results show the validity and accuracy of the proposed algorithms in this paper.