Robot Path Integration in Manufacturing Processes: Genetic Algorithm Versus Ant Colony Optimization

Tool path planning for automated manufacturing processes is a computationally complex task. This paper addresses the problem of tool path integration in the context of spray-forming processes. Tool paths for geometry-complicated parts are generated by partitioning them into individual freeform surfaces, generating the paths for each partition, and then, finally, interconnecting the paths from the different patches so as to minimize the overall path length. We model the problem as a variant of the rural postman problem (RPP), which we call open-RPP. In this paper, we present two different solutions to the open-RPP. The first solution is based on genetic algorithms and the second one is based on ant colony optimization. This paper presents and compares the results from both methods on sample data and on real-world automotive body parts. We conclude this paper with remarks about the effectiveness of our implementations and the pros and cons of each method.     

Functional webs for freeform architecture

Rationalization and construction‐aware design dominate the issue of realizability of freeform architecture. The former means the decomposition of an intended shape into parts which are sufficiently simple and efficient to manufacture; the latter refers to a design procedure which already incorporates rationalization. Recent contributions to this topic have been concerned mostly with small‐scale parts, for instance with planar faces of meshes. The present paper deals with another important aspect, namely long‐range parts and supporting structures. It turns out that from the pure geometry viewpoint this means studying families of curves which cover surfaces in certain well‐defined ways. Depending on the application one has in mind, different combinatorial arrangements of curves are required. We here restrict ourselves to so‐called hexagonal webs which correspond to a triangular or tri‐hex decomposition of a surface. The individual curve may have certain special properties, like being planar, being a geodesic, or being part of a circle. Each of these properties is motivated by manufacturability considerations and imposes constraints on the shape of the surface. We investigate the available degrees of freedom, show numerical methods of optimization, and demonstrate the effectivity of our approach and the variability of construction solutions derived from webs by means of actual architectural designs.?     

Tool path planning for compound surfaces in spray forming processes

Spray forming is an emerging manufacturing process. The automated tool planning for this process is a nontrivial problem, especially for geometry-complicated parts consisting of multiple freeform surfaces. Existing tool planning approaches are not able to deal with this kind of compound surface. This paper proposes a tool-path planning approach which optimizes the tool motion performance and the thickness uniformity. There are two steps in this approach. The first step partitions the part surface into flat patches based on the topology and normal directions. The second step determines the tool movement patterns and the sweeping directions for each flat patch. Based on the above two steps, optimal tool paths can be calculated. Experimental tests are carried out on automotive body parts and the results validate the proposed approach. Note to Practitioners-This paper was motivated by the problem of automatically planning tool paths for spray forming using Programmable Powdered Preforming Process (P4) technology. However, the proposed approach can be applied to other surface manufacturing applications such as spray painting, spray cleaning, rapid tooling, etc. Existing tool planning approaches are not able to handle complicated, multi-patch surfaces. This paper proposes a methodology to partition complicated surfaces into easy-to-handle patches and generate tool paths with optimized thickness uniformity and tool motion performance. We tested the approach using simulation on sample automotive body parts and proved its feasibility. However, this approach requires that the parts to be sprayed belong to the sheet-metal type so that the part geometry can be analyzed on a plane. In our future research, we will run physical tests on actual parts and investigate the deposition effects on the thickness uniformity.     

Generating subdivision surfaces from profile curves

The construction of freeform models has always been a challenging task. A popular approach is to edit a primitive object such that its projections conform to a set of given planar curves. This process is tedious and relies very much on the skill and experience of the designer in editing 3D shapes. This paper describes an intuitive approach for the modeling of freeform objects based on planar profile curves. A freeform surface defined by a set of orthogonal planar curves is created by blending a corresponding set of sweep surfaces. Each of the sweep surfaces is obtained by sweeping a planar curve about a computed axis. A Catmull-Clark subdivision surface interpolating a set of data points on the object surface is then constructed. Since the curve points lying on the computed axis of the sweep will become extraordinary vertices of the subdivision surface, a mesh refinement process is applied to adjust the mesh topology of the surface around the axis points. In order to maintain characteristic features of the surface defined with the planar curves, sharp features on the surface are located and are retained in the mesh refinement process. This provides an intuitive approach for constructing freeform objects with regular mesh topology using planar profile curves.     

Freeform Honeycomb Structures

Motivated by requirements of freeform architecture, and inspired by the geometry of hexagonal combs in beehives, this paper addresses torsion‐free structures aligned with hexagonal meshes. Since repetitive geometry is a very important contribution to the reduction of production costs, we study in detail “honeycomb structures”, which are defined as torsion‐free structures where the walls of cells meet at 120 degrees. Interestingly, the Gauss‐Bonnet theorem is useful in deriving information on the global distribution of node axes in such honeycombs. This paper discusses the computation and modeling of honeycomb structures as well as applications, e.g. for shading systems, or for quad meshing. We consider this paper as a contribution to the wider topic of freeform patterns, polyhedral or otherwise. Such patterns require new approaches on the technical level, e.g. in the treatment of smoothness, but they also extend our view of what constitutes aesthetic freeform geometry.     

Designing Quad‐dominant Meshes with Planar Faces

We study the combined problem of approximating a surface by a quad mesh (or quad‐dominant mesh) which on the one hand has planar faces, and which on the other hand is aesthetically pleasing and has evenly spaced vertices. This work is motivated by applications in freeform architecture and leads to a discussion of fields of conjugate directions in surfaces, their singularities and indices, their optimization and their interactive modeling. The actual meshing is performed by means of a level set method which is capable of handling combinatorial singularities, and which can deal with planarity, smoothness, and spacing issues.     

重建自由曲面的神经网络算法

利用神经网络方法解决退向工程设计中的自由贡面重建问题，在ＢａｃｋＰｒｏｐａｇａｔｉｏｎ算法的基础上，吸取了模拟退火的算法优点，神经网络的学习采用按概率随机随机接受一个不成功训练值的方法，使学习跳出局部最优解，最终收敛于全局最优解，试验证明，用这种方法解决自由曲面的重建问题，可以达到良好的效果，优于以往文献提出的方法。     

面向层析测量反求工程的自由曲面轮廓集分割技术

轮廓集的分割分为粗略分割和精化两个阶段．粗略分割是指从其他层上抽取和种子轮廓最相似的轮廓，提出了基于轮廓串匹配的优化方法；在精化阶段，提出了基于转角映射的特征连接点辨识技术，用来调整粗略分割轮廓段的两端点．实例表明，文中算法解决了自由曲面轮廓集精确分割的问题，为进一步实现三维特征参数识别和CAD模型重构打下了基础．     

Volumetric feature recognition for machining components with freeform surfaces

This paper describes a procedure for the extraction of features of a part containing a combination of 2.5D features and freeform surfaces. This work invokes a previous algorithm that was designed to recognize machining features from 2.5D parts destined to be machined on a 3-axis milling machine. The essence of that algorithm was a volume decomposition based on a recursive descent into the part, yielding a feature graph that captured both the geometry and the spatial relationships of the features. This work augments the previous algorithm with the ability to handle a limited class of components having freeform surfaces. Freeform features are defined similar to the 2.5D features as comprising a planar contour, but substituting a bottom freeform surface for the depth. Covering faces, defined as projection of the freeform surface on the faces of the bounding box of the surface, are used as equivalent planar faces for performing the recursive descent. Inter-feature open edges are used to signal the relationship between the freeform feature and other neighboring features. Examples of molds and components that were machined using the proposed algorithms are also presented.     

Efficient offset trimming for deformable planar curves using a dynamic hierarchy of bounding circular arcs

We present an efficient algorithm for computing a family of trimmed offsets for planar freeform curves under deformation. The algorithm is based on a dynamic bounding volume hierarchy (BVH) for the untrimmed offsets of a given planar curve, which can be generated efficiently using a hierarchy of recursive bisections of the given curve. The proposed algorithm is effective for deformable planar curves. At each time frame, we segment the input curve into monotone spiral pieces (Barton and Elber, 2011), which is the only pre-processing needed for the dynamic BVH construction. To speed up the on-line generation of dynamic BVH, we employ the bounding circular arcs (BCA) of Meek and Walton (1995) that can be computed very efficiently using the position and tangent information at the endpoints of each monotone spiral curve segment. Using several experimental results, we demonstrate the performance improvement of our algorithm over the previous biarc-based algorithm of Kim et al. (2012).     

Optimal Spline Approximation via ℓ0‐Minimization

Splines are part of the standard toolbox for the approximation of functions and curves in ?^d. Still, the problem of finding the spline that best approximates an input function or curve is ill‐posed, since in general this yields a “spline” with an infinite number of segments. The problem can be regularized by adding a penalty term for the number of spline segments. We show how this idea can be formulated as an ?₀‐regularized quadratic problem. This gives us a notion of optimal approximating splines that depend on one parameter, which weights the approximation error against the number of segments. We detail this concept for different types of splines including B‐splines and composite Bézier curves. Based on the latest development in the field of sparse approximation, we devise a solver for the resulting minimization problems and show applications to spline approximation of planar and space curves and to spline conversion of motion capture data.     

Intersecting a freeform surface with a general swept surface

We present efficient and robust algorithms for intersecting a rational parametric freeform surface with a general swept surface. A swept surface is given as a one-parameter family of cross-sectional curves. By computing the intersection between a freeform surface and each cross-sectional curve in the family, we can solve the intersection problem. We propose two approaches, which are closely related to each other. The first approach detects certain critical points on the intersection curve, and then connects them in a correct topology. The second approach converts the intersection problem to that of finding the zero-set of polynomial equations in the parameter space. We first present these algorithms for the special case of intersecting a freeform surface with a ruled surface or a ringed surface. We then consider the intersection with a general swept surface, where each cross-sectional curve may be defined as a rational parametric curve or as an implicit algebraic curve.     

由整体到局部的平面曲线部分匹配算法

在基于曲线匹配的检索系统中,提高曲线的匹配速度和精度具有重要的意义.提出一种平面曲线的部分匹配算法,该算法分为整体搜索和局部匹配2个阶段.首先整体搜索确定候选的匹配区域,然后在局部进行精确匹配和验证.对于特征点较少的曲线,根据曲率极值点将曲线划分为多条曲线段,采用局部线性搜索法实现曲线的部分匹配.实验结果说明了算法的有效性.     

Sweep曲面自相交的快速检测和消除

借鉴offset曲线去除自相交的方法提出了一种去除sweep曲面自相交的方法.首先根据sweep曲面上的点到脊线的距离来判断是否产生自相交;然后确定自相交候选区间集,并去除自相交点集.该方法可以推广到一般曲面与sweep曲面的求交,也可以推广到sweep曲面的offset操作中.在北京大学自主开发的几何造型系统PUM2.0中,通过大量的实例验证了该方法的稳定性和有效性.     

采用捕鱼策略的优化方法

引入一种采用渔夫捕鱼策略的新的优化方法。该优化方法主要采用移动搜索、收缩搜索和加速搜索三种搜索技术。设初始时在搜索域中随机分布有若干个点,每个点看作一个“渔夫”,每个“渔夫”通过移动、收缩和加速三种搜索方式在搜索空间中独立开展寻优活动,以搜寻全局的最优解或最优点。测试结果表明,该算法具有较好的全局搜索能力,因而该优化方法是有效的和可行的。     

Integration of design and manufacturing for structural shape optimization

This paper presents an integrated design and manufacturing approach that supports shape optimization of structural components. The approach starts from a primitive concept stage, where boundary and loading conditions of the structural component are given to the designer. Topology optimization is conducted for an initial structural layout. The discretized structural layout is smoothed using parametric B-Spline surfaces. The B-Spline surfaces are imported into a CAD system to construct parametric solid models for shape optimization. Virtual manufacturing (VM) techniques are employed to ensure that the optimized shape can be manufactured at a reasonable cost. The solid freeform fabrication (SFF) system fabricates physical prototypes of the structure for design verification. Finally, a computer numerical control (CNC) machine is employed to fabricate functional parts as well as mold or die for mass production of the structural component. The main contribution of the paper is incorporating manufacturing into the design process, where manufacturing cost is considered for design. In addition, the overall design process starts from a primitive stage and ends with functional parts. A 3D tracked vehicle roadarm is employed throughout this paper to illustrate the overall design process and various techniques involved.     

Design, fabrication and measurement of ultra-precision micro-structured freeform surfaces

Due to the geometry complexity and high precision requirement, there still possess a lot of challenges in the design, manufacturing and measurement of ultra-precision micro-structured freeform surfaces (e.g. microlens array) with submicrometer form accuracy and surface finish in nanometer range. Successful manufacturing of ultra-precision micro-structured freeform surface not only relies on the high precision of machine tools, but also largely depends on comprehensive consideration of advanced optics design, modelling and optimization of the machining process, freeform surface measurement and characterization.This paper presents the theoretical basis for the establishment of an integrated platform for design, fabrication, and measurement of ultra-precision micro-structured freeform surfaces. The platform mainly consists of four key modules, which are Optics Design Module, Data Exchange Module, Machining Process Simulation and Optimization Module and Freeform Measurement and Evaluation Module. A series of experiments have been conducted to evaluate the performance of the platform and its capability is realized through a trial implementation in design, fabricating and measurement of a microlens array. The results predicted by the system are found to agree well with the experimental results. These show that the proposed integrated platform not only helps to shorten the cycle time for the development of microlens array components but also provides an important means for optimization of the surface quality in ultra-precision machining of micro-structured surfaces. With this successful development of the system, optimal machining parameters, the best cutting strategy, and optimization of the surface quality of the ultra-precision freeform surfaces can be obtained without the need for conducting time-consuming and expensive cutting tests.     

The Convex Hull of Freeform Surfaces

We present an algorithm for computing the convex hull of freeform rational surfaces. The convex hull problem is reformulated as one of finding the zero-sets of polynomial equations; using these zero-sets we characterize developable surface patches and planar patches that belong to the boundary of the convex hull.