Showing papers on "Configuration space published in 1988"

Wave packets in minisuperspace.

Abstract: Wave packets in minisuperspace of quantum gravity are explicitly constructed for a Friedmann model containing either a massless or a massive homogeneous scalar field. Unparametrized tubelike standing waves corresponding to classically returning paths in configuration space can be constructed if a ``final condition'' with respect to the scale factor a is assumed to hold. Sensible wave packets are only obtained for certain discrete values of the mass and only in regions not too close to the classical turning point. Therefore it is meaningless in minisuperspace of quantum gravity to extend classical paths through this region to a recollapsing phase. This suggests that we introduce higher degrees of freedom which can produce classical paths by continuous measurement.

The density manifold and configuration space quantization

Abstract: On developpe la structure geometrique differentielle d'une variete de Frechet de densites. Ceci fournit un cadre geometrique a la quantification reliee a la mecanique stochastique de Nelson. On etudie les structures riemanniennes et symplectiques de la variete densite et on deduit l'equation de Schrodinger a partir d'un principe variationnel

Subtask performance by redundancy resolution for redundant robot manipulators

Abstract: The problem of selecting joint space trajectories for redundant manipulators is considered. Solutions which allow secondary tasks to be performed by the arm simultaneously with end-effector motions may be selected in a number of ways. An algorithm to accomplish this, by means of conditions on a scalar function of the joint variables, is introduced and analyzed. Problems inherent in schemes involving constraints in configuration space are considered. >

From kinematics to shape: an approach to innovative design

Abstract: We address the problem of designing the shape of solid objects to satisfy a given set of functional specifications. In particular, we show how to design elementary components of mechanical devices (kinematic pairs) from a description of their desired behavior and a set of constraints. This is done using a backtracking algorithm that modifies (or creates) object shapes by adding and deleting line and arc segments to the objects' contours. These modifications are guided by the configuration space description of the desired behavior. The algorithm is extended to handle both qualitative and causal descriptions of desired behaviors. This work is based on the theory of shape and kinematics developed in [Joskowicz, 1988].

Trajectory planning in robotic continuous-path applications

Abstract: Trajectory planning of robot motions for continuous-path operations is formulated in configuration space, resorting to the intrinsic properties of the path traced by point of the end effector. It is shown that, by referring the orientation of the end effector to a unique orthogonal frame defined at every point of the aforementioned path, a systematic procedure for trajectory planning in configuration space is derived. The computations required to determine the angular velocity and angular acceleration of the path frame reduce to computing the Darboux vector of the path and its time derivative. >

Generation of configuration space obstacles: the case of a moving sphere

Abstract: Algebraic algorithms are presented for generating the boundary of configuration space obstacles arising from the motion of a sphere among obstacles. The boundaries of the obstacles are given by patches of algebraic surfaces. Algorithms are given for both implicit and parametric surface patches. Both convex and nonconvex obstacles are considered. In the case of convex obstacles, the topology of convolution faces is the same as the adjacency graph of faces, edges, and vertices of the obstacle. Further, there are no redundancies in the convolution faces. Redundancies on the convolution can occur in the case of nonconvex obstacles. It is possible to detect these redundancies from the the intersections and self-intersections of convolution faces. Simple solids are also considered. >

Method and apparatus for path planning

Abstract: A method and apparatus for path planning are presented. Path planning involves propagating cost waves in a configuration space representation of a task space. A space variant metric and budding are used for cost wave propagation. The disclosed method and apparatus are readily adaptable to robots with n degrees of freedom.

First integrals that are polynomial in momenta for a mechanical system on a two-dimensional torus

Abstract: In a large collection of examples of completely integrable Hamiltonian systems, the first integrals are polynomial in momenta, lhtegrals that are linear in momenta correspond to one-parameter groups of symmetries of a dynamical system [i]. In the case of separation of variables, in the Hamilton-Jacobi equation integrals naturally arise that are quadratic in momenta. The problem of the existence of linear and quadratic integrals for a natural mechanical system with two degrees of freedom on the plane was considered in [2]. In [3], linear and quadratic integrals on the two-dimensional sphere are investigated. In addition, it has been proved that for natural mechanical systems with a two-dimensional compact configuration space of genus greater than one, integrals that are analytic in momenta are lacking [4].

Strings with zero tension

Abstract: We describe bosonic strings by using a kind of Lagrangian compatible with the zero tension limit. The work is developed on an extended configuration space and the quantization is carried out with details.

The exponential of the two-dimensional massless scalar field as an infrared Jaffe field

Abstract: The definition of the Wick exponential of the massless scalar field in two dimensions as an operator-valued distribution is discussed in the Krein space realization of the field. It is shown that the exponential Wick power series converges strongly on a suitably dense domain, provided that it is smeared with test functions which satisfy some growth conditions in configuration space. Such conditions are similar to the high energy bounds previously introduced by Jaffe for the definition of strictly localizable fields. In this case it is found that the Wick exponential is strictly localizable in momentum space.

Inequivalent quantizations and fundamentally perfect spaces.

Abstract: We investigate the problem of inequivalent quantizations of a physical system with multiply connected configuration space X. For scalar quantum theory on X we show that state vectors must be single-valued if and only if the first homology group H/sub 1/(X) is trivial, or equivalently the fundamental group ..pi../sub 1/(X) is perfect. The theta-structure of quantum gauge and gravitational theories is discussed in light of this result.

Collision avoidance using a free space enumeration method based on grid expansion

Abstract: This paper describes a general and simple method for planning collision-free paths of manipulators. Many algorithms have been proposed for the collision avoidance problem, but no general and simple method has been developed which can be applied to any type of manipulator. The method based on the configuration space approach seems promising, but the configuration space is a multi-dimensional space and the amount of data concerning free space is enormous. However, most of these data are not used to plan a single motion of a manipulator. The free space concerned in planning a motion can be determined independently of the kinematic characteristics of the manipulator by a method based on grid expansion. The algorithm is as follows. First, collisions are detected during a linear movement in the configuration space and a set of collision-free configurations is calculated. Then the collision checking operations are propagated to neighbouring configurations. This process is continued until the wavefront from the i...

Origin and Infinity Manifolds for Mechanical Systems with Homogeneous Potentials

Abstract: We study manifolds describing the behavior of motions close to the origin and at infinity of configuration space, for mechanical systems with homogeneous potentials. We find an inversion between these behaviors when the sign of the degree of homogeneity is changed. In some cases, the blow up equations can be written in canonical form, by first reducing to a contact structure. A motivation for the use of blow-up techniques is given, and some examples are studied in detail.

Planning robot motions in the Sharp system

Abstract: Automating the programming of assembly robots necessitates to develop methods for planning robot motions. In this paper we describe the geometric models and the reasoning techniques we have implemented as part of the SHARP system (SHARP is an automatic robot programming system currently under development at the LIFIA laboratory). We first present which modelling facilities are required for constructing a suitable representation of the robot world. Then, we show how this representation has been used for implementing two classes of reasoning functions: functions aimed at computing collision free trajectories for the robot and its payload, and functions allowing to automatically generate contact based motions under uncertainty constraints (i.e motions involved in grasping and in part-mating operations). Our method for solving the first motion planning problem operates in the configuration space. It is based on two types of techniques aimed at computing the valid ranges of values associated with some selected motion directions, and at constructing and searching a graph representation of the free space. Solving the second planning problem makes it necessary to construct an explicit representation of the involved contacts along with their associated moving constraints. It leads to reason on the morphological properties of the manipulated objects.

Gravitational theta states and the wave function of the universe.

Abstract: The naive no-boundary wave function of the universe is shown to be invariant under diffeomorphisms only for the simplest spacetime topologies. A more general construction which does give an invariant wave function of the universe is exhibited. Similar problems, some familiar, some not, are encountered in a wide range of theories whose physical configuration space is topologically nontrivial. These include the theory of identical particles, Yang-Mills theory, higher-dimensional gravity, and membrane theories. The sum-over-histories formulation of quantum mechanics provides a unified approach to these problems and their resolution.

Gauge Theory in a Finite Volume

Abstract: In these lecture notes we discuss an analytic calculational scheme for SU($N$) gauge theories in a finite volume. We will mainly concentrate on pure SU(2) gauge theory. The method relies on using an effective Hamiltonian for the zero momentum modes. The notorious problem of Gribov horizons is evaded by encoding the topological nontrivial nature of configuration space into boundary conditions for the zero momentum modes. This system then allows us to compute the low-lying energy spectrum in volumes up to about five times the size of the scalar glueball. These continuum results agree in general well with the lattice Monte Carlo results. We discuss in some detail the resolution of a discrepancy with Monte Carlo results for the $T^+_2$ glueball.

Model-Based Vision By Cooperative Processing Of Evidence And Hypotheses Using Configuration Spaces

Abstract: This paper presents a model-based object recognition method which combines a bottom-up evidence accumulation process and a top-down hypothesis verification process. The hypothesize-and-test paradigm is fundamental in model-based vision. However, research issues remain on how the bottom-up process gathers pieces of evidence and when the top-down process should take the lead. To accumulate pieces of evidence, we use a configuration space whose points represent a configuration of an object (ie. position and orientation of an object in an image). If a feature is found which matches a part of an object model, the configuration space is updated to reflect the possible configurations of the object. A region in the configuration space where multiple pieces of evidence from such feature-part matches overlap suggests a high probability that the object exists in an image with a configuration in that region. The cost of the bottom-up process to further accumulate evidence for localization, and that of the top-down process to recognize the object by verification, are compared by considering the size of the search region and the probability of success of verification. If the cost of the top-down process becomes lower, hypotheses are generated and their verification processes are started. The first version of the recognition program has been written and applied to the recognition of a jet airplane in synthetic aperture radar (SAR) images. In creating a model of an object, we have used a SAR simulator as a sensor model, so that we can predict those object features which are reliably detectable by the sensors. The program is being tested with simulated SAR images, and shows promising performance.

Implementation of an adaptive, constant thermodynamic speed simulated annealing schedule

Abstract: We present a new implementation of simulated annealing. It calculates its own cooling schedule from thermodynamic information computed enroute. Our schedule proceeds at constant “thermodynamic speed” to minimize the entropy produced along the way. It is based on finite time thermodynamics and is, in some sense, optimal. We use ensembles over the entire configuration space to compute thermodynamic averages. Ensembles provide good statistics for the thermodynamic process as well as a direct, instantaneous measures of the nature of the configuration space with Hamming distances. We compare our implementation with some others on a random graph problem. It is found to produce superior results.

The continuum and the alpha-particle formation

Abstract: The absolute α-decay width of 212Po is calculated within a harmonic oscillator representation. Clustering features induced by the nuclear interaction appear by considering a large configuration space. The role of the neutronproton interaction is analysed and a reasonable account of the experimental alpha-decay width is given.

Motion planning for manipulators in complex environments

Abstract: Difficulties we are faced with in order to solve the motion-planning problem for manipulators are twofold : 1) the practical difficulty of dealing with rotations in a three dimensional space, 2) the inherent exponential complexity of the Free Space construction with the number of degrees of freedom.

Planning collision free trajectories by a configuration space approach

Abstract: This paper addresses the motion planning problem. We present a simple and efficient algorithm for generating a approximate representation of the free Configuration Space for a robot moving in a workspace with obstacles. The algorithms presented in this paper have been implemented and can deal with all robots made of revolute or prismatic joints. We present an exemple of collision-free trajectories computed by the system for a manipulator with 4 degrees of freedom.

Finite-element analysis of low-energy e+-H scattering.

Abstract: Accurate $S$-wave phase shifts for low-energy ($0.1\ensuremath{\le}k\ensuremath{\le}0.7$) positron-hydrogen scattering have been calculated by use of the finite-element method. Simple criteria are developed for which the truncation of the relevant configuration space and its subsequent discretization appear to be optimized. These criteria are expected to be independent of the details of the collision system.