Very fast collision detection for practical motion planning. I. The spatial representation

Martínez-Salvador, Begoña; Pobil, Ángel P. del; Pérez-Francisco, Miguel

doi:10.1109/robot.1998.677042

Cited by 6 publications

(5 citation statements)

References 10 publications

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“…We assume that we can compute a "small" bounding ball for the restriction of c(t) to any subinterval of I. Here, the words "ball" and "small" refer to the object-oriented Euclidean metric in R 12 , induced via a positive Borel measure µ in the space of the moving polygon (Section 2).…”

Section: Collision Detection Algorithmmentioning

confidence: 99%

“…Several authors suggest bounding volume shapes which are specifically tailored to the needs of collision detection. Typical examples are the generalized cylinders of [12] and the s-topes of [15]. Usually, they are derived from some ball covering.…”

Section: Introductionmentioning

confidence: 99%

“…There is a number of techniques for detecting collisions or computing the distance of moving objects by means of covering balls or hierarchies of covering balls [10,2,11,12,3,13,14]. We cover the moving objects by different bounding volumes (portions of balls and hyperboloids of one or two sheets).…”

Section: Introductionmentioning

confidence: 99%

“…, the vertex spheres not necessarily envelope the Listing 2 Intersection of fat moving polygon, determined by moving polygon and ball B R (g) ⊂ R12 , and fixed polygon.procedure INTERSECTION(P, F, g, R) moving polygon P, fixed polygon F, center g and radius R Require: Metric data of plane of P and edges of P has been pre-computed and is accessible from within this procedure. By the Cauchy interlacing theorem…”

mentioning

confidence: 99%

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Guaranteed collision detection with toleranced motions

Schröcker

Weber

2014

Computer Aided Geometric Design

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We present a method for guaranteed collision detection with toleranced motions. The basic idea is to consider the motion as a curve in the 12-dimensional space of affine displacements, endowed with an object-oriented Euclidean metric, and cover it with balls. The associated orbits of points, lines, planes and polygons have particularly simple shapes that lend themselves well to exact and fast collision queries. We present formulas for elementary collision tests with these orbit shapes and we suggest an algorithm, based on motion subdivision and computation of bounding balls, that can give a no-collision guarantee. It allows a robust and efficient implementation and parallelization. At hand of several examples we explore the asymptotic behavior of the algorithm and compare different implementation strategies.

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Section: Collision Detection Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Guaranteed collision detection with toleranced motions

Schröcker

Weber

2014

Computer Aided Geometric Design

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“…Sucesivamente va comprobando cada par de situaciones entre dos objetos, hasta encontrar la distancia mínima entre ellos. Martínez-Salvador y del Pobil [72] realizan una descomposición de los objetos en 3D mediante esferas. La simplicidad aportada por esta partición reduce el tiempo de computación en la detección de colisiones (Pérez y del Pobil [83]) y en el seguimiento de objetos en movimiento.…”

Section: Muestreo Del Espacio De Configuracionesunclassified

Planificación de movimientos en entornos dinámicos o inciertos mediante la coordinación de métodos aleatorios de búsqueda y funciones armónicas

Íñiguez Galbete

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En los métodos planificadores de trayectorias basados en funciones potenciales, la utilización de las funciones armónicas tiene la importante propiedad de no presentar mínimos locales. Sin embargo, la creación de planificadores basados en estas funciones armónicas se ha encontrado con serias dificultades, sobre todo cuando el número de grados de libertad es elevado. Por este motivo, esta tesis realiza inicialmente un estudio de las propiedades más relevantes de dichas funciones armónicas; destacando aquellas que han sido la causa de su reducida aplicación en la generación de trayectorias. Al mismo tiempo, el resultado de este estudio sirve de base para la proposición de métodos compensatorios que permitan reducir las propiedades negativas de las funciones armónicas, como funciones potenciales aplicables a la generación de movimientos en robótica. Después se considera los métodos numéricos de cálculo de las funciones armónicas, así como el coste computacional de los mismos. Con el objetivo de reducir el tiempo de cálculo, esta tesis propone una discretización jerárquica y un método eficiente de etiquetado de celdas. Por su parte, dicha discretización jerárquica, se va realizando progresivamente mediante muestreo aleatorio y descomposición de celdas, lo que genera un escenario parcialmente conocido que, sin embargo, permitirá en cierto número de casos encontrar la trayectoria buscada. Por lo tanto, esta propuesta reduce drásticamente el número de puntos de cálculo y, por consiguiente, el tiempo de computación. La tesis completa la propuesta de un planificador combinando las técnicas de muestreo con el cálculo de funciones armónicas mediante un método de exploración aleatorio conducido (PHM), aplicado a un espacio de configuraciones discretizado jerárquicamente sobre el que se va recalculando la función armónica. De esta forma la exploración se guía hacia zonas más prometedoras, intentando obtener la solución por fases. In methods based trajectories planners potential functions, the use of harmonic functions has the important property of not presenting local minima. However, the creation of planners based on these harmonic functions has met with serious difficulties, especially when the number of degrees of freedom is high. For this reason, this thesis makes an initial study of the properties most relevant of these harmonic functions, highlighting those that have been the cause of their limited application in the generation of trajectories. At the same time, the result of this study provides a basis for proposing compensatory methods to reduce the negative properties of harmonic functions as potential functions applicable to the generation of robotic movements. Then we consider numerical methods for calculating the harmonic functions and the computational cost of the same. In order to reduce computation time, this thesis proposes a hierarchical discretization and an efficient method of labeling cells. Meanwhile, this discretization hierarchical be made gradually by random sampling and decomposition of cells, generating a scene partially known, however, allow a number of cases in finding the trajectory sought. Therefore, this proposal drastically reduces the number of calculation points, and hence the computation time. The thesis, complete a proposed planner combining sampling techniques to the calculation of harmonic functions by a method of random exploration conducted (PHM), applied to a hierarchically discretized configuration space on which the harmonic function is recalculated. In this way the exploration is guided to more promising, trying to obtain the solution phases.

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Very fast collision detection for practical motion planning. II. The parallel algorithm

Pérez-Francisco

Pobil²,

Martínez-Salvador³

Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146)

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Very fast collision detection for practical motion planning. I. The spatial representation

Cited by 6 publications

References 10 publications

Guaranteed collision detection with toleranced motions

Guaranteed collision detection with toleranced motions

Planificación de movimientos en entornos dinámicos o inciertos mediante la coordinación de métodos aleatorios de búsqueda y funciones armónicas

Very fast collision detection for practical motion planning. II. The parallel algorithm

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