Topic

# Position (vector)

About: Position (vector) is a research topic. Over the lifetime, 31241 publications have been published within this topic receiving 277115 citations.

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TL;DR: In this article, the authors developed a form of theory which appears to be appropriate to measurements of position on a sphere and demonstrated the simultaneous distribution of the amplitude and direction of the vector sum of a number of random unit vectors of given precision.

Abstract: Any topological framework requires the development of a theory of errors of characteristic and appropriate mathematical form. The paper develops a form of theory which appears to be appropriate to measurements of position on a sphere. The primary problems of estimation as applied to the true direction, and the precision of observations, are discussed in the subcases which arise. The simultaneous distribution of the amplitude and direction of the vector sum of a number of random unit vectors of given precision, is demonstrated. From this is derived the test of significance appropriate to a worker whose knowledge of precision lies entirely in the internal evidence of the sample. This is the analogue of ‘Student’s’ test in the Gaussian theory of errors. The general formulae obtained are illustrated using measurements of the direction of remanent magnetization in the directly and inversely magnetized lava flows obtained in Iceland by Mr J. Hospers.

5,482 citations

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TL;DR: A new conceptually simple approach to controlling compliant motions of a robot manipulator that combines force and torque information with positional data to satisfy simultaneous position and force trajectory constraints specified in a convenient task related coordinate system is presented.

Abstract: A new conceptually simple approach to controlling compliant motions of a robot manipulator is presented. The 'hybrid' technique described combines force and torque information with positional data to satisfy simultaneous position and force trajectory constraints specified in a convenient task related coordinate system. Analysis, simulation, and experiments are used to evaluate the controller's ability to execute trajectories using feedback from a force sensing wrist and from position sensors found in the manipulator joints. The results show that the method achieves stable, accurate control of force and position trajectories for a variety of test conditions.

2,991 citations

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TL;DR: The level set method is couple to a wide variety of problems involving external physics, such as compressible and incompressible flow, Stefan problems, kinetic crystal growth, epitaxial growth of thin films, vortex-dominated flows, and extensions to multiphase motion.

Abstract: The level set method was devised by S. Osher and J. A. Sethian (1988, J. Comput. Phys.79, 12–49) as a simple and versatile method for computing and analyzing the motion of an interface Γ in two or three dimensions. Γ bounds a (possibly multiply connected) region Ω. The goal is to compute and analyze the subsequent motion of Γ under a velocity field v. This velocity can depend on position, time, the geometry of the interface, and the external physics. The interface is captured for later time as the zero level set of a smooth (at least Lipschitz continuous) function ϕ (x, t); i.e., Γ(t)={x|ϕ(x, t)=0}. ϕ is positive inside Ω, negative outside Ω, and is zero on Γ(t). Topological merging and breaking are well defined and easily performed. In this review article we discuss recent variants and extensions, including the motion of curves in three dimensions, the dynamic surface extension method, fast methods for steady state problems, diffusion generated motion, and the variational level set approach. We also give a user's guide to the level set dictionary and technology and couple the method to a wide variety of problems involving external physics, such as compressible and incompressible (possibly reacting) flow, Stefan problems, kinetic crystal growth, epitaxial growth of thin films, vortex-dominated flows, and extensions to multiphase motion. We conclude with a discussion of applications to computer vision and image processing.

2,174 citations

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TL;DR: In this article, the authors propose an approach based on characterizing the position and orientation of an object as a single point in a configuration space, in which each coordinate represents a degree of freedom in the position or orientation of the object.

Abstract: This paper presents algorithms for computing constraints on the position of an object due to the presence of ther objects. This problem arises in applications that require choosing how to arrange or how to move objects without collisions. The approach presented here is based on characterizing the position and orientation of an object as a single point in a configuration space, in which each coordinate represents a degree of freedom in the position or orientation of the object. The configurations forbidden to this object, due to the presence of other objects, can then be characterized as regions in the configuration space, called configuration space obstacles. The paper presents algorithms for computing these configuration space obstacles when the objects are polygons or polyhedra.

1,996 citations

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01 Dec 1980TL;DR: In this article, a method of actively controlling the apparent stiffness of a manipulator end effecter is presented, which allows the programmer to specify the three transnational and three rotational stiffness properties of a frame located arbitrarily in hand coordinates.

Abstract: A method of actively controlling the apparent stiffness of a manipulator end effecter is presented. The approach allows the programmer to specify the three transnational and three rotational stiffness of a frame located arbitrarily in hand coordinates. Control of the nominal position of the hand then permits simultaneous position and force control. Stiffness may be changed under program control to match varying task requirements. A rapid servo algorithm is made possible by transformation of the problem into joint space at run time. Applications examples are given.

1,212 citations