Results 1  10
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164
Randomized Kinodynamic Motion Planning with Moving Obstacles
, 2000
"... We present a randomized motion planner for robots that must avoid moving obstacles and achieve a specified goal under kinematic and dynamic constraints. The planner samples the robot's statetime space by picking control inputs at random and integrating the equations of motion. The result is a roa ..."
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Cited by 190 (12 self)
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We present a randomized motion planner for robots that must avoid moving obstacles and achieve a specified goal under kinematic and dynamic constraints. The planner samples the robot's statetime space by picking control inputs at random and integrating the equations of motion. The result is a roadmap of sampled statetime points, called milestones, connected by short admissible trajectories. The planner does not precompute the roadmap as traditional probabilistic roadmap planners do; instead, for each planning query, it generates a new roadmap to find a trajectory between an initial and a goal statetime point. We prove in this paper that the probability that the planner fails to find such a trajectory when one exists quickly goes to 0, as the number of milestones grows. The planner has been implemented and tested successfully in both simulated and real environments. In the latter case, a vision module estimates obstacle motions just before planning starts; the planner is then allocated a small, fixed amount of time to compute a trajectory. If a change in the obstacle motion is detected while the robot executes the planned trajectory, the planner recomputes a trajectory on the fly. 1
Collision Detection Between Geometric Models: A Survey
 In Proc. of IMA Conference on Mathematics of Surfaces
, 1998
"... In this paper, we survey the state of the art in collision detection between general geometric models. The set of models include polygonal objects, spline or algebraic surfaces, CSG models, and deformable bodies. We present a number of techniques and systems available for contact determination. We a ..."
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Cited by 184 (15 self)
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In this paper, we survey the state of the art in collision detection between general geometric models. The set of models include polygonal objects, spline or algebraic surfaces, CSG models, and deformable bodies. We present a number of techniques and systems available for contact determination. We also describe several Nbody algorithms to reduce the number of pairwise intersection tests. 1 Introduction The goal of collision detection (also known as interference detection or contact determination) is to automatically report a geometric contact when it is about to occur or has actually occurred. The geometric models may be polygonal objects, splines, or algebraic surfaces. The problem is encountered in computeraided design and machining (CAD/CAM), robotics and automation, manufacturing, computer graphics, animation and computer simulated environments. Collision detection enables simulationbased design, tolerance verification, engineering analysis, assembly and disassembly, motion pla...
Efficient Collision Detection of Complex Deformable Models using AABB Trees
 J. Graphics Tools
, 1998
"... We present a scheme for exact collision detection between complex models undergoing rigid motion and deformation. The scheme relies on a hierarchical model representation using axisaligned bounding boxes (AABBs). In recent work, AABB trees have been shown to be slower than oriented bounding box ..."
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Cited by 170 (1 self)
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We present a scheme for exact collision detection between complex models undergoing rigid motion and deformation. The scheme relies on a hierarchical model representation using axisaligned bounding boxes (AABBs). In recent work, AABB trees have been shown to be slower than oriented bounding box (OBB) trees. In this paper, we describe a way to speed up overlap tests between AABBs, such that for collision detection of rigid models, the difference in performance between the two representations is greatly reduced. Furthermore, we show how to quickly update an AABB tree as a model is deformed. We thus find AABB trees to be the method of choice for collision detection of complex models undergoing deformation. In fact, because they are not much slower to test, are faster to build, and use less storage than OBB trees, AABB trees might be a reasonable choice for rigid models as well. Keywords: computer animation, collision detection, hierarchical data structures, deformable model...
A survey of visibility for walkthrough applications
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER
, 2003
"... Visibility algorithms for walkthrough and related applications have grown into a significant area, spurred by the growth in the complexity of models and the need for highly interactive ways of navigating them. In this survey, we review the fundamental issues in visibility and conduct an overview of ..."
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Cited by 145 (8 self)
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Visibility algorithms for walkthrough and related applications have grown into a significant area, spurred by the growth in the complexity of models and the need for highly interactive ways of navigating them. In this survey, we review the fundamental issues in visibility and conduct an overview of the visibility culling techniques developed in the last decade. The taxonomy we use distinguishes between pointbased and fromregion methods. Pointbased methods are further subdivided into object and imageprecision techniques, while fromregion approaches can take advantage of the cellandportal structure of architectural environments or handle generic scenes.
Optimized Spatial Hashing for Collision Detection of Deformable Objects
, 2003
"... We propose a new approach to collision and self collision detection of dynamically deforming objects that consist of tetrahedrons. Tetrahedral meshes are commonly used to represent volumetric deformable models and the presented algorithm is integrated in a physicallybased environment, which can ..."
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Cited by 110 (32 self)
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We propose a new approach to collision and self collision detection of dynamically deforming objects that consist of tetrahedrons. Tetrahedral meshes are commonly used to represent volumetric deformable models and the presented algorithm is integrated in a physicallybased environment, which can be used in game engines and surgical simulators. The proposed algorithm employs a hash function for compressing a potentially infinite regular spatial grid. Although the hash function does not always provide a unique mapping of grid cells, it can be generated very efficiently and does not require complex data structures, such as octrees or BSPs. We have investigated and optimized the parameters of the collision detection algorithm, such as hash function, hash table size and spatial cell size. The algorithm can detect collisions and self collisions in environments of up to 20k tetrahedrons in realtime. Although the algorithm works with tetrahedral meshes, it can be easily adapted to other object primitives, such as triangles.
Accurate and fast proximity queries between polyhedra using convex surface decomposition
, 2001
"... The need to perform fast and accurate proximity queries arises frequently in physicallybased modeling, simulation, animation, realtime interaction within a virtual environment, and game dynamics. The set of proximity queries include intersection detection, tolerance verification, exact and approxi ..."
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Cited by 97 (14 self)
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The need to perform fast and accurate proximity queries arises frequently in physicallybased modeling, simulation, animation, realtime interaction within a virtual environment, and game dynamics. The set of proximity queries include intersection detection, tolerance verification, exact and approximate minimum distance computation, and (disjoint) contact determination. Specialized data structures and algorithms have often been designed to perform each type of query separately. We present a unified approach to perform any of these queries seamlessly for general, rigid polyhedral objects with boundary representations which are orientable 2manifolds. The proposed method involves a hierarchical data structure built upon a surface decomposition of the models. Furthermore, the incremental query algorithm takes advantage of coherence between successive frames. It has been applied to complex benchmarks and compares very favorably with earlier algorithms and systems. 1.
Fast proximity queries with swept sphere volumes
, 1999
"... We present novel algorithms for fast proximity queries using swept sphere volumes. The set of proximity queries includes collision detection and both exact and approximate separation distance computation. We introduce a new family of bounding volumes that correspond to a core primitive shape grown ..."
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Cited by 94 (19 self)
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We present novel algorithms for fast proximity queries using swept sphere volumes. The set of proximity queries includes collision detection and both exact and approximate separation distance computation. We introduce a new family of bounding volumes that correspond to a core primitive shape grown outward by some offset. The set of core primitive shapes includes a point, line, and rectangle. This family of bounding volumes provides varying tightness of t to the underlying geometry. Furthermore, we describe efficient and accurate algorithms to perform different queries using these bounding volumes. We present a novel analysis of proximity queries that highlights the relationship between collision detection and distance computation. We also present traversal techniques for accelerating distance queries. These algorithms have been used to perform proximity queries for applications including virtual prototyping, dynamic simulation, and motion planning on complex models. As compared to earlier algorithms based on bounding volume hierarchies for separation distance and approximate distance computation, our algorithms have
3D Collision Detection: A Survey
 Computers and Graphics
, 2000
"... Many applications in Computer Graphics require fast and robust 3D collision detection algorithms. These algorithms can be grouped into four approaches: spacetime volume intersection, swept volume interference, multiple interference detection and trajectory parameterization. While some approaches ar ..."
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Cited by 84 (3 self)
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Many applications in Computer Graphics require fast and robust 3D collision detection algorithms. These algorithms can be grouped into four approaches: spacetime volume intersection, swept volume interference, multiple interference detection and trajectory parameterization. While some approaches are linked to a particular object representation scheme (e.g., spacetime volume intersection is particularly suited to a CSG representation), others do not. The multiple interference detection approach has been the most widely used under a variety of sampling strategies, reducing the collision detection problem to multiple calls to static interference tests. In most cases, these tests boil down to detecting intersections between simple geometric entities, such as spheres, boxes aligned with the coordinate axes, or polygons and segments. The computational cost of a collision detection algorithm depends not only on the complexity of the basic interference test used, but also on the ...
Efficiently Approximating the MinimumVolume Bounding Box of a Point Set in Three Dimensions
 In Proc. 10th ACMSIAM Sympos. Discrete Algorithms
, 2001
"... We present an efficient O(n + 1/ε^4.5)time algorithm for computing a (1 + 1/ε)approximation of the minimumvolume bounding box of n points in R³. We also present a simpler algorithm (for the same purpose) whose running time is O(n log n+n/ε³). We give some experim ..."
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Cited by 77 (12 self)
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We present an efficient O(n + 1/ε^4.5)time algorithm for computing a (1 + 1/ε)approximation of the minimumvolume bounding box of n points in R³. We also present a simpler algorithm (for the same purpose) whose running time is O(n log n+n/ε³). We give some experimental results with implementations of various variants of the second algorithm. The implementation of the algorithm described in this paper is available online [Har00].
Collision and Proximity Queries
, 2003
"... In a geometric context, a collision or proximity query reports information about the relative configuration or placement of two objects. Some of the common examples of such queries include checking whether two objects overlap in space, or whether their boundaries intersect, or computing the minimum ..."
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Cited by 74 (15 self)
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In a geometric context, a collision or proximity query reports information about the relative configuration or placement of two objects. Some of the common examples of such queries include checking whether two objects overlap in space, or whether their boundaries intersect, or computing the minimum Euclidean separation distance between their boundaries. Hundreds of papers have been published on di#erent aspects of these queries in computational geometry and related areas such as robotics, computer graphics, virtual environments, and computeraided design. These queries arise in di#erent applications including robot motion planning, dynamic simulation, haptic rendering, virtual prototyping, interactive walkthroughs, computer gaming, and molecular modeling. For example, a largescale virtual environment, e.g., a walkthrough, creates a model of the environment with virtual objects. Such an environment is used to give the user a sense of presence in a synthetic world and it s