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Results for “Convex polyhedra”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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8 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Collision detection for spacecraft proximity operations

A new collision detection algorithm has been developed for use when two spacecraft are operating in the same vicinity. The two spacecraft are modeled as unions of convex polyhedra, where the resulting polyhedron many be either convex or nonconvex. The relative motion of the two spacecraft is assumed to be such that one vehicle is moving with constant linear and angular velocity with respect to the other. Contacts between the vertices, faces, and edges of the polyhedra representing the two spacecraft are shown to occur when the value of one or more of a set of functions is zero. The collision detection algorithm is then formulated as a search for the zeros (roots) of these functions. Special properties of the functions for the assumed relative trajectory are exploited to expedite the zero search. The new algorithm is the first algorithm that can solve the collision detection problem exactly for relative motion with constant angular velocity. This is a significant improvement over models of rotational motion used in previous collision detection algorithms.

Vaughan, Robin M.↗
NASA NTRS1987

Collision detection for spacecraft proximity operations

Collision Detection for Spacecraft Proximity Operations This thesis describes the development of a new collision detection algorithm to be used when two spacecraft are operating in the same vicinity. The two spacecraft are modelled as unions of convex polyhedra, where the polyhedron resulting from the union may be either convex or nonconvex. The relative motion of the two spacecraft is assumed to be such that one vehicle is moving with constant linear and angular velocity with respect to the other. The algorithm determines if a collision is possible and, if so, predicts the time when the collision will take place. The theoretical basis for the new collision detection algorithm is the C-function formulation of the configuration space approach recently introduced by researchers in robotics. Three different types of C-functions are defined that model the contacts between the vertices, edges, and faces of the polyhedra representing the two spacecraft. These C-functions are used to formulate three "collision" conditions. The first of these conditions limits the points representing potential collisions to the zeros of the C-functions. The new algorithm is fundamentally a search for the smallest zero of any C-function that satisfies the second and third collision conditions. The C-functions are shown to be transcendental functions of time for the assumed trajectory of the moving spacecraft. The zeros of these functions cannot be expressed in dosed form. Therefore, numerical search procedures are developed to find aLl of the zeros of a C-function in specified bounded intervals of time. These bounded intervals of time are found by examining the second and third collision conditions. The capabilities of the new algorithm are demonstrated for several example cases. These include examples of collisions determined by zeros of each of the three different types of C-functions. In addition to predicting the time of first contact of the polyhedra, the algorithm identifies the features of the two polyhedra that are touching at this time. The new collision detection algorithm is the first such algorithm that is capable of solving the collision detection problem exactly for the case where the moving object has constant linear and angular velocities. This is a significant improvement on previous collision detection algorithms described in the literature. In particular, the ability to handle constant angular velocity represents a more realistic type of rotational motion than those which have been used in other algorithms.

Robin M Vaughan↗
NASA NTRS2010

A Review of Discrete Element Method (DEM) Particle Shapes and Size Distributions for Lunar Soil

As part of ongoing efforts to develop models of lunar soil mechanics, this report reviews two topics that are important to discrete element method (DEM) modeling the behavior of soils (such as lunar soils): (1) methods of modeling particle shapes and (2) analytical representations of particle size distribution. The choice of particle shape complexity is driven primarily by opposing tradeoffs with total number of particles, computer memory, and total simulation computer processing time. The choice is also dependent on available DEM software capabilities. For example, PFC2D/PFC3D and EDEM support clustering of spheres; MIMES incorporates superquadric particle shapes; and BLOKS3D provides polyhedra shapes. Most commercial and custom DEM software supports some type of complex particle shape beyond the standard sphere. Convex polyhedra, clusters of spheres and single parametric particle shapes such as the ellipsoid, polyellipsoid, and superquadric, are all motivated by the desire to introduce asymmetry into the particle shape, as well as edges and corners, in order to better simulate actual granular particle shapes and behavior. An empirical particle size distribution (PSD) formula is shown to fit desert sand data from Bagnold. Particle size data of JSC-1a obtained from a fine particle analyzer at the NASA Kennedy Space Center is also fitted to a similar empirical PSD function.

Lane, John E.↗
NASA NTRS1973

Textural features for image classification

Description of some easily computable textural features based on gray-tone spatial dependances, and illustration of their application in category-identification tasks of three different kinds of image data - namely, photomicrographs of five kinds of sandstones, 1:20,000 panchromatic aerial photographs of eight land-use categories, and ERTS multispectral imagery containing several land-use categories. Two kinds of decision rules are used - one for which the decision regions are convex polyhedra (a piecewise-linear decision rule), and one for which the decision regions are rectangular parallelpipeds (a min-max decision rule). In each experiment the data set was divided into two parts, a training set and a test set. Test set identification accuracy is 89% for the photomicrographs, 82% for the aerial photographic imagery, and 83% for the satellite imagery. These results indicate that the easily computable textural features probably have a general applicability for a wide variety of image-classification applications.

Haralick, R. M.↗
NASA NTRS1992

Distance estimation and collision prediction for on-line robotic motion planning

An efficient method for computing the minimum distance and predicting collisions between moving objects is presented. This problem is incorporated into the framework of an in-line motion-planning algorithm to satisfy collision avoidance between a robot and moving objects modeled as convex polyhedra. In the beginning, the deterministic problem where the information about the objects is assumed to be certain is examined. L(1) or L(infinity) norms are used to represent distance and the problem becomes a linear programming problem. The stochastic problem is formulated where the uncertainty is induced by sensing and the unknown dynamics of the moving obstacles. Two problems are considered: First, filtering of the distance between the robot and the moving object at the present time. Second, prediction of the minimum distance in the future in order to predict the collision time.

Kyriakopoulos, K. J.↗
NASA NTRS1991

Distance estimation and collision prediction for on-line robotic motion planning

An efficient method for computing the minimum distance and predicting collisions between moving objects is presented. This problem has been incorporated in the framework of an in-line motion planning algorithm to satisfy collision avoidance between a robot and moving objects modeled as convex polyhedra. In the beginning the deterministic problem, where the information about the objects is assumed to be certain is examined. If instead of the Euclidean norm, L(sub 1) or L(sub infinity) norms are used to represent distance, the problem becomes a linear programming problem. The stochastic problem is formulated, where the uncertainty is induced by sensing and the unknown dynamics of the moving obstacles. Two problems are considered: (1) filtering of the minimum distance between the robot and the moving object, at the present time; and (2) prediction of the minimum distance in the future, in order to predict possible collisions with the moving obstacles and estimate the collision time.

Kyriakopoulos, K. J.↗
NASA NTRS1993

Surface acquisition through virtual milling

Surface acquisition deals with the reconstruction of three dimensional objects from a set of data points. The most straightforward techniques require human intervention, a time consuming proposition. It is desirable to develop a fully automated alternative. Such a method is proposed in this paper. It makes use of surface measurements obtained from a 3-D laser digitizer - an instrument which provides the (x,y,z) coordinates of surface data points from various viewpoints. These points are assembled into several partial surfaces using a visibility constraint and a 2-D triangulation technique. Reconstruction of the final object requires merging these partial surfaces. This is accomplished through a procedure that emulates milling, a standard machining operation. From a geometrical standpoint the problem reduces to constructing the intersection of two or more non-convex polyhedra.

Marshal L Merriam↗