Parallel Contour Path Planning for Complicated Cavity Part Fabrication using Voronoi-based Distance Map

To generate parallel contour path for direct production of complicated cavity component, a novel path planning based on Voronoi-based distance map is presented in this paper. Firstly, the grid representation of polygonal slice is produced by hierarchical rasterization using graphics hardware acceleration and divided into Voronoi cells of contour by an exact EDT (Euclidean distance transformation). Then, each VCI (Voronoi cell of inner contour) is further subdivided into CLRI (closed loop region of inner contour) and OLRI (open loop region of inner contour). Closed paths for each CLRI and the block merging VCO (Voronoi cell of outer contour) and all OLRIs are generated by local and global isoline extraction, respectively. The final path ordered in circumferential and radial directions is obtained by sorting and connecting all individual paths. In comparison with conventional methods such as pair-wise intersection and Voronoi diagram, the proposed algorithm is numerically robust, can avoid null path and self-intersection because of the application of distance map and discrete Voronoi diagram. It is especially used for FGM (Functionally Graded Material) design and fabrication.Mechanical Engineerin

Path Planning for Mobile Robot Navigation using Voronoi Diagram and Fast Marching

For navigation in complex environments, a robot need s to reach a compromise between the need for having efficient and optimized trajectories and t he need for reacting to unexpected events. This paper presents a new sensor-based Path Planner w hich results in a fast local or global motion planning able to incorporate the new obstacle information. In the first step the safest areas in the environment are extracted by means of a Vorono i Diagram. In the second step the Fast Marching Method is applied to the Voronoi extracted a reas in order to obtain the path. The method combines map-based and sensor-based planning o perations to provide a reliable motion plan, while it operates at the sensor frequency. The m ain characteristics are speed and reliability, since the map dimensions are reduced to an almost uni dimensional map and this map represents the safest areas in the environment for moving the robot. In addition, the Voronoi Diagram can be calculated in open areas, and with all kind of shaped obstacles, which allows to apply the proposed planning method in complex environments wher e other methods of planning based on Voronoi do not work.This work has been supported by the CAM Project S2009/DPI-1559/ROBOCITY2030 I

Finding the Maximum Subset with Bounded Convex Curvature

We describe an algorithm for solving an important geometric problem arising in computer-aided manufacturing. When machining a pocket in a solid piece of material such as steel using a rough tool in a milling machine, sharp convex corners of the pocket cannot be done properly, but have to be left for finer tools that are more expensive to use. We want to determine a tool path that maximizes the use of the rough tool. Mathematically, this boils down to the following problem. Given a simply-connected set of points P in the plane such that the boundary of P is a curvilinear polygon consisting of n line segments and circular arcs of arbitrary radii, compute the maximum subset Q of P consisting of simply-connected sets where the boundary of each set is a curve with bounded convex curvature. A closed curve has bounded convex curvature if, when traversed in counterclockwise direction, it turns to the left with curvature at most 1. There is no bound on the curvature where it turns to the right. The difference in the requirement to left- and right-curvature is a natural consequence of different conditions when machining convex and concave areas of the pocket. We devise an algorithm to compute the unique maximum such set Q. The algorithm runs in O(n log n) time and uses O(n) space. For the correctness of our algorithm, we prove a new generalization of the Pestov-Ionin Theorem. This is needed to show that the output Q of our algorithm is indeed maximum in the sense that if Q\u27 is any subset of P with a boundary of bounded convex curvature, then Q\u27 is a subset of Q

Effect of Area-Filling Path on the Residual Stresses Developed During Weld-Deposition Based Additive Manufacturing

There is an increasing interest in the industry for using Additive Manufacturing techniques not just for prototyping but for actual applications too. For this to happen, various constraints in commercialization of the metallic components made by using additive manufacturing have to be overcome. Management of thermally induced residual stresses during the deposition of metal is one of the major challenges that need to be addressed. With the help of numerical and experimental methods, this paper studies effect of area filling paths on the residual stresses developed during weld-deposition. Finite element analysis is done using ANSYS Mechanical APDL for different area filling paths. The temperature gradient and the thermally induced residual stress produced during material deposition are predicted using finite element analysis. The obtained results were validated with the help of experiments. A GMAW welding system was attached to the CNC to create the desired area filling pattern. The residual stresses were measured using a XRD system. The process parameters used in the finite element study and experiments were based on initial trials carried out to determine the operatable range of parameters. Three area-filling patterns viz., zig-zag, contour (outside-in) and contour (inside-out) were analyzed; maximum residual stress concentration was found to occur in the case of contour (outside-in)

오프셋 곡선 및 곡면의 자가 교차 검출 및 제거

학위논문(박사)--서울대학교 대학원 :공과대학 컴퓨터공학부,2020. 2. 김명수.Offset curves and surfaces have many applications in computer-aided design and manufacturing, but the self-intersections and redundancies must be trimmed away for their practical use. We present a new method for offset curve and surface trimming that detects the self-intersections and eliminates the redundant parts of an offset curve and surface that are closer than the offset distance to the original curve and surface. We first propose an offset trimming method based on constructing geometric constraint equations. We formulate the constraint equations of the self-intersections of an offset curve and surface in the parameter domain of the original curve and surface. Numerical computations based on the regularity and intrinsic properties of the given input curve and surface is carried out to compute the solution of the constraint equations. The method deals with numerical instability around near-singular regions of an offset surface by using osculating tori that can be constructed in a highly stable way, i.e., by offsetting the osculating torii of the given input regular surface. We reveal the branching structure and the terminal points from the complete self-intersection curves of the offset surface. From the observation that the trimming method based on the multivariate equation solving is computationally expensive, we also propose an acceleration technique to trim an offset curve and surface. The alternative method constructs a bounding volume hierarchy specially designed to enclose the offset curve and surface and detects the self-collision of the bounding volumes instead. In the case of an offset surface, the thickness of the bounding volumes is indirectly determined based on the maximum deviations of the positions and the normals between the given input surface patches and their osculating tori. For further acceleration, the bounding volumes are pruned as much as possible during self-collision detection using various geometric constraints imposed on the offset surface. We demonstrate the effectiveness of the new trimming method using several non-trivial test examples of offset trimming. Lastly, we investigate the problem of computing the Voronoi diagram of a freeform surface using the offset trimming technique for surfaces. By trimming the offset surface with a gradually changing offset radius, we compute the boundary of the Voronoi cells that appear in the concave side of the given input surface. In particular, we interpret the singular and branching points of the self-intersection curves of the trimmed offset surfaces in terms of the boundary elements of the Voronoi diagram.오프셋 곡선 및 곡면은 computer-aided design (CAD)와 computer-aided manufacturing (CAM)에서 널리 이용되는 연산들 중 하나이다. 하지만 실용적인 활용을 위해서는 오프셋 곡선 및 곡면에서 생기는 자가 교차를 찾고 이를 기준으로 오프셋 곡선 및 곡면에서 원래의 곡선 및 곡면에 가까운 불필요한 영역을 제거하여야한다. 본 논문에서는 오프셋 곡선 및 곡면에서 생기는 자가 교차를 계산하고, 오프셋 곡선 및 곡면에서 생기는 불필요한 영역을 제거하는 알고리즘을 제안한다. 본 논문은 우선 오프셋 곡선 및 곡면의 자가 교차점들과 그 교차점들이 기인한 원래 곡선 및 곡면의 점들이 이루는 평면 이등변 삼각형 관계로부터 오프셋 곡선 및 곡면의 자가 교차점의 제약 조건을 만족시키는 방정식들을 세운다. 이 제약식들은 원래 곡선 및 곡면의 변수 공간에서 표현되며, 이 방정식들의 해는 다변수 방정식의 해를 구하는 solver를 이용하여 구한다. 오프셋 곡면의 경우, 원래 곡면의 주곡률 중 하나가 오프셋 반지름의 역수와 같을 때 오프셋 곡면의 법선이 정의가 되지 않는 특이점이 생기는데, 오프셋 곡면의 자가 교차 곡선이 이 부근을 지날 때는 자가 교차 곡선의 계산이 불안정해진다. 따라서 자가 교차 곡선이 오프셋 곡면의 특이점 부근을 지날 때는 오프셋 곡면을 접촉 토러스로 치환하여 더 안정된 방법으로 자가 교차 곡선을 구한다. 계산된 오프셋 곡면의 자가 교차 곡선으로부터 교차 곡선의 $xyz$-공간에서의 말단 점, 가지 구조 등을 밝힌다. 본 논문은 또한 바운딩 볼륨 기반의 오프셋 곡선 및 곡면의 자가 교차 곡선 검출을 가속화하는 방법을 제시한다. 바운딩 볼륨은 기저 곡선 및 곡면을 단순한 기하로 감싸고 기하 연산을 수행함으로써 가속화에 기여한다. 오프셋 곡면의 자가 교차 곡선을 구하기 위하여, 본 논문은 오프셋 곡면의 바운딩 볼륨 구조를 기저 곡면의 바운딩 볼륨과 기저 곡면의 법선 곡면의 바운딩 볼륨의 구조로부터 계산하며 이때 각 바운딩 볼륨의 두께를 계산한다. 또한, 바운딩 볼륨 중에서 실제 오프셋 곡선 및 곡면의 자가 교차에 기여하지 않는 부분을 깊은 재귀 전에 찾아서 제거하는 여러 조건들을 나열한다. 한편, 자가 교차가 제거된 오프셋 곡선 및 곡면은 기저 곡선 및 곡면의 보로노이 구조와 깊은 관련이 있는 것이 알려져 있다. 본 논문에서는 자유 곡면의 연속된 오프셋 곡면들로부터 자유 곡면의 보로노이 구조를 유추하는 방법을 제시한다. 특히, 오프셋 곡면의 자가 교차 곡선 상에서 나타나는 가지 점이나 말단 점과 같은 특이점들이 자유 곡면의 보로노이 구조에서 어떻게 해석되는지 제시한다.1. Introduction 1 1.1 Background and Motivation 1 1.2 Research Objectives and Approach 7 1.3 Contributions and Thesis Organization 11 2. Preliminaries 14 2.1 Curve and Surface Representation 14 2.1.1 Bezier Representation 14 2.1.2 B-spline Representation 17 2.2 Differential Geometry of Curves and Surfaces 19 2.2.1 Differential Geometry of Curves 19 2.2.2 Differential Geometry of Surfaces 21 3. Previous Work 23 3.1 Offset Curves 24 3.2 Offset Surfaces 27 3.3 Offset Curves on Surfaces 29 4. Trimming Offset Curve Self-intersections 32 4.1 Experimental Results 35 5. Trimming Offset Surface Self-intersections 38 5.1 Constraint Equations for Offset Self-Intersections 38 5.1.1 Coplanarity Constraint 39 5.1.2 Equi-angle Constraint 40 5.2 Removing Trivial Solutions 40 5.3 Removing Normal Flips 41 5.4 Multivariate Solver for Constraints 43 5.A Derivation of f(u,v) 46 5.B Relationship between f(u,v) and Curvatures 47 5.3 Trimming Offset Surfaces 50 5.4 Experimental Results 53 5.5 Summary 57 6. Acceleration of trimming offset curves and surfaces 62 6.1 Motivation 62 6.2 Basic Approach 67 6.3 Trimming an Offset Curve using the BVH 70 6.4 Trimming an Offset Surface using the BVH 75 6.4.1 Offset Surface BVH 75 6.4.2 Finding Self-intersections in Offset Surface Using BVH 87 6.4.3 Tracing Self-intersection Curves 98 6.5 Experimental Results 100 6.6 Summary 106 7. Application of Trimming Offset Surfaces: 3D Voronoi Diagram 107 7.1 Background 107 7.2 Approach 110 7.3 Experimental Results 112 7.4 Summary 114 8. Conclusion 119 Bibliography iDocto

Efficient mobile robot path planning by Voronoi-based heuristic

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Enhanced online programming for industrial robots

The use of robots and automation levels in the industrial sector is expected to grow, and is driven by the on-going need for lower costs and enhanced productivity. The manufacturing industry continues to seek ways of realizing enhanced production, and the programming of articulated production robots has been identified as a major area for improvement. However, realizing this automation level increase requires capable programming and control technologies. Many industries employ offline-programming which operates within a manually controlled and specific work environment. This is especially true within the high-volume automotive industry, particularly in high-speed assembly and component handling. For small-batch manufacturing and small to medium-sized enterprises, online programming continues to play an important role, but the complexity of programming remains a major obstacle for automation using industrial robots. Scenarios that rely on manual data input based on real world obstructions require that entire production systems cease for significant time periods while data is being manipulated, leading to financial losses. The application of simulation tools generate discrete portions of the total robot trajectories, while requiring manual inputs to link paths associated with different activities. Human input is also required to correct inaccuracies and errors resulting from unknowns and falsehoods in the environment. This study developed a new supported online robot programming approach, which is implemented as a robot control program. By applying online and offline programming in addition to appropriate manual robot control techniques, disadvantages such as manual pre-processing times and production downtimes have been either reduced or completely eliminated. The industrial requirements were evaluated considering modern manufacturing aspects. A cell-based Voronoi generation algorithm within a probabilistic world model has been introduced, together with a trajectory planner and an appropriate human machine interface. The robot programs so achieved are comparable to manually programmed robot programs and the results for a Mitsubishi RV-2AJ five-axis industrial robot are presented. Automated workspace analysis techniques and trajectory smoothing are used to accomplish this. The new robot control program considers the working production environment as a single and complete workspace. Non-productive time is required, but unlike previously reported approaches, this is achieved automatically and in a timely manner. As such, the actual cell-learning time is minimal