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Efficient algorithms for geometric optimization
 ACM Comput. Surv
, 1998
"... We review the recent progress in the design of efficient algorithms for various problems in geometric optimization. We present several techniques used to attack these problems, such as parametric searching, geometric alternatives to parametric searching, pruneandsearch techniques for linear progra ..."
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Cited by 117 (12 self)
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We review the recent progress in the design of efficient algorithms for various problems in geometric optimization. We present several techniques used to attack these problems, such as parametric searching, geometric alternatives to parametric searching, pruneandsearch techniques for linear programming and related problems, and LPtype problems and their efficient solution. We then describe a variety of applications of these and other techniques to numerous problems in geometric optimization, including facility location, proximity problems, statistical estimators and metrology, placement and intersection of polygons and polyhedra, and ray shooting and other querytype problems.
The Exact Computation Paradigm
, 1994
"... We describe a paradigm for numerical computing, based on exact computation. This emerging paradigm has many advantages compared to the standard paradigm which is based on fixedprecision. We first survey the literature on multiprecision number packages, a prerequisite for exact computation. Next ..."
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Cited by 107 (12 self)
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We describe a paradigm for numerical computing, based on exact computation. This emerging paradigm has many advantages compared to the standard paradigm which is based on fixedprecision. We first survey the literature on multiprecision number packages, a prerequisite for exact computation. Next we survey some recent applications of this paradigm. Finally, we outline some basic theory and techniques in this paradigm. 1 This paper will appear as a chapter in the 2nd edition of Computing in Euclidean Geometry, edited by D.Z. Du and F.K. Hwang, published by World Scientific Press, 1994. 1 1 Two Numerical Computing Paradigms Computation has always been intimately associated with numbers: computability theory was early on formulated as a theory of computable numbers, the first computers have been number crunchers and the original massproduced computers were pocket calculators. Although one's first exposure to computers today is likely to be some nonnumerical application, numeri...
Assembly Sequencing with Toleranced Parts
, 1995
"... The goal of assembly sequencing is to plan a feasible series of operations to construct a product from its individual parts. Previous research has investigated assembly sequencing under the assumption that parts have nominal geometry. This paper considers the case where parts have toleranced geom ..."
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Cited by 31 (4 self)
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The goal of assembly sequencing is to plan a feasible series of operations to construct a product from its individual parts. Previous research has investigated assembly sequencing under the assumption that parts have nominal geometry. This paper considers the case where parts have toleranced geometry. Its main contribution is an efficient procedure that decides if a product admits an assembly sequence with infinite translations (i.e., translations that can be extended arbitrarily far along a fixed direction) that is feasible for all possible instances of the components within the specified tolerances. If the product admits one such sequence, the procedure can also generate it. For the cases where there exists no such assembly sequence, another procedure is proposed which generates assembly sequences that are feasible only for some values of the toleranced dimensions. If this procedure produces no such sequence, then no instance of the product is assemblable. These two proced...
Exact Computational Geometry and Tolerancing Metrology
, 1994
"... We describe the relevance of Computational Geometry to tolerancing metrology. We outline the basic issues and define the class of zone problems that is central in this area. In the context of the exact computation paradigm, these problems are prime candidates for "exact solution" since we ..."
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Cited by 25 (6 self)
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We describe the relevance of Computational Geometry to tolerancing metrology. We outline the basic issues and define the class of zone problems that is central in this area. In the context of the exact computation paradigm, these problems are prime candidates for "exact solution" since we show that they have boundeddepth. Metrologists in this field have mounted a quest for a reference software which will impose some certainty in a confusing market of metrology software. The use of exact computation in the reference software will solve many intractable difficulties associated with current approaches. In short, here is a practical area in which CG and exact computation can have a real impact. 1 Introduction Researchers in Computational Geometry (CG) have always been convinced that their subject is relevant to a variety of application areas. But CG'ers have often assumed that the application areas would come to CG to find answers to their questions. To what extent is this valid? I will d...
Kinematic Tolerance Analysis
 ComputerAided Design
, 1997
"... We present a general method for worstcase limit kinematic tolerance analysis: computing the range of variation in the kinematic function of a mechanism from its part tolerance specifications. The method covers fixed and multiple contact mechanisms with parametric or geometric part tolerances. We de ..."
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Cited by 23 (3 self)
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We present a general method for worstcase limit kinematic tolerance analysis: computing the range of variation in the kinematic function of a mechanism from its part tolerance specifications. The method covers fixed and multiple contact mechanisms with parametric or geometric part tolerances. We develop a new model of kinematic variation, called kinematic tolerance space, that generalizes the configuration space representation of nominal kinematic function. Kinematic tolerance space captures quantitative and qualitative variations in kinematic function due to variations in part shape and part configuration. We derive properties of kinematic tolerance space that express the relationship between the nominal kinematics of mechanisms and their kinematic variations. Using these properties, we develop a practical kinematic tolerance space computation algorithm for planar pairs with two degrees of freedom. 1
Robotic Manipulation for Parts Transfer and Orienting: Mechanics, Planning, and Shape Uncertainty
, 1996
"... Robots can modify their environmentby manipulating objects. To fully exploit this ability, it is important to determine the manipulation capabilities of a given robot. Such characterization in terms of the physics and geometry of the task has important implications for manufacturing applications, wh ..."
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Cited by 17 (6 self)
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Robots can modify their environmentby manipulating objects. To fully exploit this ability, it is important to determine the manipulation capabilities of a given robot. Such characterization in terms of the physics and geometry of the task has important implications for manufacturing applications, where simpler hardware leads to cheaper and more reliable systems. This thesis develops techniques for robots to transfer parts from a known position and orientation to a goal position and orientation, and to orient parts by bringing them from an unknown initial orientation to a goal orientation. This parts feeding process is an important aspect of flexible assembly. Designing automatic planners that capture the task mechanics and geometry leads to flexible parts transfer and orienting systems. The implemented parts feeding systems use simple effectors that allow manipulation of a broad class of parts, and simple sensors that are robust and inexpensive. The main research issues are to identify a ...
Orienting Toleranced Polygonal Parts
, 2000
"... Parts manufactured to tolerances have variations in shape. Most previous work in robotic manipulation assumes that parts do not have shape variations. Orienting devices such as bowl feeders often fail due to variations in part shape. We study the effects of uncertainty in part shape on orienting to ..."
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Cited by 8 (0 self)
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Parts manufactured to tolerances have variations in shape. Most previous work in robotic manipulation assumes that parts do not have shape variations. Orienting devices such as bowl feeders often fail due to variations in part shape. We study the effects of uncertainty in part shape on orienting to develop systems that can orient toleranced polygonal parts. We present a tolerance model in which the part center of mass and vertices lie in circular uncertainty zones around their nominal positions. The variations in part shape are characterized by the tolerance model and the part’s nominal shape. We describe the nondeterminism that arises due to part shape uncertainty for a conveyorbased orienting system and show that sensorbased and sensorless orienting plans can exist for toleranced polygonal parts. We present implemented planners that generate orienting plans for the entire variational class of part shapes
Parts Orienting with Shape Uncertainty
 In IEEE International Conference on Robotics and Automation
, 1997
"... Parts manufactured to tolerances have shape variations. Most work in robotic manipulation assumes that part shape does not vary. Orienting devices such as bowl feeders frequently fail due to variations in part shape. In this paper we develop techniques to orient parts with shape uncertainty. We pres ..."
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Cited by 8 (6 self)
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Parts manufactured to tolerances have shape variations. Most work in robotic manipulation assumes that part shape does not vary. Orienting devices such as bowl feeders frequently fail due to variations in part shape. In this paper we develop techniques to orient parts with shape uncertainty. We present a shape uncertainty model and describe the nondeterminism in parts orienting that arises from shape uncertainty. We characterize a class of parts that can be reliably oriented with sensorbased and sensorless orienting plans under shape uncertainty. We present implemented planners that generate orienting plans for the entire variational class of part shapes given a nominal part shape and shape uncertainty bounds. We describe experiments to demonstrate generated plans and outline issues for future work. 1 Introduction Parts manufactured to tolerances have variations in shape. However most work in robotic manipulation assumes the part shape is known exactly and that parts have no shape v...
Design for Tolerance of ElectroMechanical Assemblies: An Integrated Approach
 IEEE Trans. Robotics and Automation
, 1999
"... ..."
Shape Tolerance for Robot Gripper Jaws
"... In [19] we specified robot grippers that can orient and grasp parts with an arrangement of trapezoidal jaw modules. Since jaw modules may be imprecisely machined, we define a parametric tolerance class such that part alignment is guaranteed for all jaw geometry in the class. This tolerance class is ..."
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Cited by 2 (2 self)
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In [19] we specified robot grippers that can orient and grasp parts with an arrangement of trapezoidal jaw modules. Since jaw modules may be imprecisely machined, we define a parametric tolerance class such that part alignment is guaranteed for all jaw geometry in the class. This tolerance class is derived based on analysis of toppling, motion trajectory, and formclosure. Given maximal jaw geometry from the previous algorithm, we describe an O(n 3 ) algorithm to compute the parametric tolerance class based on maximal and minimal jaw specifications. We have implemented the algorithm and report results from physical experiments. 1.