Showing papers on "Configuration space published in 2000"
07 Dec 2000
TL;DR: A learning approach to model the hand configuration space directly based on the linear behavior observed in the real motion data collected by a CyberGlove, and it is shown that the proposed model is helpful for capturing articulated motion.
Abstract: Hand motion capture is one of the most important parts of gesture interfaces. Many current approaches to this task generally involve a formidable nonlinear optimization problem in a large search space. Motion capture can be achieved more cost-efficiently when considering the motion constraints of a hand. Although some constraints can be represented as equalities or inequalities, there exist many constraints which cannot be explicitly represented. In this paper, we propose a learning approach to model the hand configuration space directly. The redundancy of the configuration space can be eliminated by finding a lower-dimensional subspace of the original space. Finger motion is modeled in this subspace based on the linear behavior observed in the real motion data collected by a CyberGlove. Employing the constrained motion model, we are able to efficiently capture finger motion from video inputs. Several experiments show that our proposed model is helpful for capturing articulated motion.
319 citations
TL;DR: In this paper, a topological hypothesis was proposed to explain the chaotic behavior of the curvature of the configuration space of a dynamical system at a phase transition point, which can be qualitatively reproduced using geometric models.
240 citations
TL;DR: In this paper, controllability tests and motion control algorithms for underactuated mechanical control systems on Lie groups with Lagrangian equal to kinetic energy were provided, and two algebraic tests were derived in terms of the symmetric product and the Lie bracket of the input vector fields.
Abstract: We provide controllability tests and motion control algorithms for underactuated mechanical control systems on Lie groups with Lagrangian equal to kinetic energy. Examples include satellite and underwater vehicle control systems with the number of control inputs less than the dimension of the configuration space. Local controllability properties of these systems are characterized, and two algebraic tests are derived in terms of the symmetric product and the Lie bracket of the input vector fields. Perturbation theory is applied to compute approximate solutions for the system under small-amplitude forcing; in-phase signals play a crucial role in achieving motion along symmetric product directions. Motion control algorithms are then designed to solve problems of point-to-point reconfiguration, static interpolation and exponential stabilization. We illustrate the theoretical results and the algorithms with applications to models of planar rigid bodies, satellites and underwater vehicles.
231 citations
12 Nov 2000
TL;DR: A combinatorial approach to plan noncolliding motions for a polygonal bar-and-joint framework based on a novel class of one-degree-of-freedom mechanisms induced by pseudo triangulations of planar point sets that yields very efficient deterministic algorithms for a category of robot arm motion planning problems with many degrees of freedom.
Abstract: We propose a combinatorial approach to plan noncolliding motions for a polygonal bar-and-joint framework. Our approach yields very efficient deterministic algorithms for a category of robot arm motion planning problems with many degrees of freedom, where the known general roadmap techniques would give exponential complexity. It is based on a novel class of one-degree-of-freedom mechanisms induced by pseudo triangulations of planar point sets, for which we provide several equivalent characterization and exhibit rich combinatorial and rigidity theoretic properties. The main application is an efficient algorithm for the Carpenter's rule problem: convexify a simple bar-and-joint planar polygonal linkage using only non self-intersecting planar motions. A step in the convexification motion consists in moving a pseudo-triangulation-based mechanism along its unique trajectory in configuration space until two adjacent edges align. At that point, a local alteration restores the pseudo triangulation. The motion continues for O(n/sup 2/) steps until all the points are in convex position.
185 citations
TL;DR: In this paper, a selective review of the mathematical theory of the Schrodinger equation for N-body Hamiltonians is presented, focusing on the interplay between the spectral theory of Hamiltonians and the space-time and phase-space analysis of bound states and scattering states.
Abstract: This selective review is written as an introduction to the mathematical theory of the Schrodinger equation for N particles. Characteristic for these systems are the cluster properties of the potential in configuration space, which are expressed in a simple geometric language. The methods developed over the last 40 years to deal with this primary aspect are described by giving full proofs of a number of basic and by now classical results. The central theme is the interplay between the spectral theory of N-body Hamiltonians and the space–time and phase-space analysis of bound states and scattering states.
177 citations
24 Apr 2000
TL;DR: This paper presents a framework that allows real-time replanning in high-dimensional configuration spaces, using proximity to the environment as a simple and effective heuristic and thereby significantly pruning the search in the configuration space.
Abstract: Real-time replanning is a prerequisite for motion execution in unpredictably changing environments. This paper presents a framework that allows real-time replanning in high-dimensional configuration spaces. Initially, a planning operation generates a path. The path is augmented by a set of paths homotopic to it. This set is represented implicitly by a volume of free space in the work space. Effectively, this corresponds to delaying part of the planning operation for the homotopic paths until motion execution. During execution reactive control algorithms are used to select a valid path from the set of homotopic paths, using proximity to the environment as a simple and effective heuristic and thereby significantly pruning the search in the configuration space. Experimental results are presented to validate the real-time performance of this framework in high-dimensional configuration spaces.
131 citations
TL;DR: In this article, the authors compare three types of 4-node and 9-node finite elements for a recently formulated finite deformation shell theory with seven degrees of freedom, which allows for the applicability of three-dimensional constitutive laws and equipes the configuration space with the structure of a vector space.
Abstract: In this paper we discuss and compare three types of 4-node and 9-node finite elements for a recently formulated finite deformation shell theory with seven degrees of freedom. The shell theory takes thickness change into account and circumvents the use of a rotation tensor. It allows for the applicability of three-dimensional constitutive laws and equipes the configuration space with the structure of a vector space. The finite elements themselves are based either on a hybrid stress functional, on a hybrid strain functional, or on a nonlinear version of the enhanced strain concept. As independent variables either the normal and shear resultants, the strain tensor related to the deformation of the midsurface, or the incompatible enhanced strain field are taken as independent variables. The fields of equivalence of these different formulations, their limitations as well as possible improvements are discussed using different numerical examples.
130 citations
TL;DR: In this article, one-parameter semigroups generated by Schrodinger operators with fairly general electromagnetic potentials were studied and it was shown that the semigroup has a continuous integral kernel given by a Brownian-bridge expectation.
Abstract: The objects of the present study are one-parameter semigroups generated by Schrodinger operators with fairly general electromagnetic potentials. More precisely, we allow scalar potentials from the Kato class and impose on the vector potentials only local Kato-like conditions. The configuration space is supposed to be an arbitrary open subset of multi-dimensional Euclidean space; in case that it is a proper subset, the Schrodinger operator is rendered symmetric by imposing Dirichlet boundary conditions. We discuss the continuity of the image functions of the semigroup and show local-norm-continuity of the semigroup in the potentials. Finally, we prove that the semigroup has a continuous integral kernel given by a Brownian-bridge expectation. Altogether, the article is meant to extend some of the results in B. Simon's landmark paper [Bull. Amer. Math. Soc.7 (1982) 447] to non-zero vector potentials and more general configuration spaces.
118 citations
TL;DR: In this paper, the energy of a simple glass former eIS, in equilibrium and in the out-of-equilibrium situation, is calculated using molecular dynamics computer simulation for the aging system.
Abstract: Using molecular dynamics computer simulation we calculate for a simple glass former eIS, the energy of the inherent structure, in equilibrium and in the out-of-equilibrium situation. We show that eIS can be used to define for the aging system an effective time-dependent temperature Te(t). In particular we demonstrate that during the aging process the system visits at time t configurations which are typical for the equilibrium system at temperature Te(t).
111 citations
TL;DR: This paper studies motion planning from one zero-velocity state to another for a three-joint robot in a horizontal plane with a passive revolute third joint and describes a computationally efficient trajectory planner that finds fast, collision-free trajectories among obstacles.
Abstract: This paper studies motion planning from one zero velocity state to another for a three-joint robot in a horizontal plane with a passive revolute third joint. Such a robot is small-time locally controllable on an open subset of its zero velocity section, allowing it to follow any path in this subset arbitrarily closely. However, some paths are “preferred” by the dynamics of the manipulator in that they can be followed at higher speeds. In this paper we describe a computationally efficient trajectory planner which finds fast collision-free trajectories among obstacles. We are able to decouple the problem of planning feasible trajectories in the robot’s six-dimensional state space into the computationally simpler problems of planning paths in the three-dimensional configuration space and time scaling the paths according to the manipulator dynamics. This decoupling is made possible by the existence of velocity directions, fixed in the passive link frame, which can be executed at arbitrary speeds. We have demonstrated the motion planner on an experimental underactuated manipulator. To our knowledge, it is the first implementation of a collision-free motion planning algorithm for a manipulator subject to a second-order nonholonomic constraint.
99 citations
TL;DR: In this paper, a criterion is established to be fulfilled by non-adiabatic coupling terms which yields continuous and uniquely diabatic potentials defined throughout configuration space, and it is found that this requirement leads to a kind of ''quantization'' with regard to non-regular NACTs.
TL;DR: The instantaneous normal mode approach is used to provide a description of the local curvature of the potential energy surface of a model for water and finds that the diffusion constant depends on the fraction of directions in configuration space connecting different local minima.
Abstract: We use the instantaneous normal mode approach to provide a description of the local curvature of the potential energy surface of a model for water. We focus on the region of the phase diagram in which the dynamics may be described by mode-coupling theory. We find that the diffusion constant depends on the fraction of directions in configuration space connecting different local minima, supporting the hypothesis that the dynamics are controlled by the geometric properties of configuration space. Furthermore, we find a relation between the number of basins accessed in equilibrium and the connectivity between them.
24 Apr 2000
TL;DR: This paper modifies and extends the previously proposed framework for planning paths for plates under manipulation constraints to handle simple volumes and builds a roadmap in the configuration space that corresponds to equilibrium configurations of the considered volume under the manipulation constraints.
Abstract: This paper addresses the problem of path planning for a class of deformable volumes under fairly general manipulation constraints. The underlying geometric model for the volume is provided by a mass-spring representation. It is augmented by a realistic mechanical model. The latter permits the computation of the shape of the considered object with respect to the grasping constraints by minimizing the energy function of the deformation of the object. Previous research in planning for deformable objects considered the case of elastic plates and proposed a randomized framework for planning paths for plates under manipulation constraints. The present paper modifies and extends the previously proposed framework to handle simple volumes. Our planner builds a roadmap in the configuration space. The nodes of the roadmap are equilibrium configurations of the considered volume under the manipulation constraints, while its edges correspond to quasi-static equilibrium paths. Paths are found by searching the roadmap. We present experimental results that illustrate our approach.
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TL;DR: A class of topological spaces related to motion-planning on graphs that arise naturally in this very context, arising simultaneously in two seemingly disparate fields are described.
Abstract: This expository article describes applications of topological configuration spaces to the control of robotic systems. In particular, we review recent work by the authors on configuration spaces of graphs. These are lovely spaces: we show for example that the configuration space of two points on the complete graph of five vertices is a closed orientable surface of genus six.
TL;DR: In this article, the modern techniques of solution of Faddeev equations are combined to obtain an efficient numerical scheme for bounding states of a three-atomic helium cluster, and the binding energies and other observables for ground and excited states are calculated.
TL;DR: In this article, a time-dependent method to evaluate state-to-state reaction probabilities, based on bond coordinates and an adapted body-fixed frame, is presented, which is expected to be rather efficient to describe A+BC→AB+C reactive collisions.
Abstract: In this work we present a time-dependent method to evaluate state-to-state reaction probabilities, based on bond coordinates and an adapted body-fixed frame. Such a method is expected to be rather efficient to describe A+BC→AB+C reactive collisions. In addition, the apparent complexity of the Hamiltonian expressed in these coordinates is reduced when applied to a wave packet represented in grids for the internal coordinates. The efficiency of this method as compared to the use of the most adapted Jacobi coordinates increases as the masses of the satellite atoms approach that of the heavier central atom and, what may be more important, avoids the problems associated with the singularities of the radial kinetic terms in the region of configuration space of interest. This method is used to study the Li+HF(v=0,1,j=0,J=0) reactive collision and the structure of the final state distribution of the LiF products is interpreted in terms of transition state resonances.
TL;DR: This work considers the nonlinear dynamic interpolation problem on Riemannian manifolds and, in particular, on connected and compact Lie groups and forces the dynamic variables of a control system to pass through specific points in the configuration space, while minimizing a certain energy function.
Abstract: We consider the nonlinear dynamic interpolation problem on Riemannian manifolds and, in particular, on connected and compact Lie groups. Basically we force the dynamic variables of a control system to pass through specific points in the configuration space, while minimizing a certain energy function, by a suitable choice of the controls. The energy function we consider depends on the velocity and acceleration along trajectories. The solution curves can be seen as generalizations of the classical splines in tension for the Euclidean space. The relations with sub-Riemannian optimal control problems are explained.
TL;DR: In this paper, the configurational entropy changes in model glass-forming liquids have been evaluated using computer simulations, using the Lennard-Jones potential energy topology as a parameter.
Abstract: Computer simulations have been employed in recent years to evaluate the configurational entropy changes in model glass-forming liquids. We consider two methods, both of which involve the calculation of the `intra-basin' entropy as a means for obtaining the configurational entropy. The first method involves the evaluation of the intra-basin entropy from the vibrational frequencies of inherent structures, by making a harmonic approximation of the local potential energy topography. The second method employs simulations that confine the liquid within a localized region of configuration space by the imposition of constraints; apart from the choice of the constraints, no further assumptions are made. We compare the configurational entropies estimated for a model liquid (binary mixture of particles interacting {\it via} the Lennard-Jones potential) for a range of temperatures, at fixed density.
TL;DR: In this paper, the authors apply the line-integral technique to study possible geometric phase effects in 2×2 diabatic double many-body expansion (DMBE) potential energy surface of three hydrogenic systems, namely, H3, DH2, and HD2.
Abstract: In this work we apply the line-integral technique to study possible geometric phase effects in the 2×2 diabatic double many-body expansion (DMBE) potential energy surface of three hydrogenic systems, namely, H3, DH2, and HD2. First, we show that the phase obtained by employing the line-integral method is identical (up to a constant) to the ordinary diabatic angle of the orthogonal transformation that diagonalizes the diabatic potential matrix. Next this angle is studied numerically along the line formed by fixing the two hyperspherical coordinates ρ and θ and letting φ change along the interval [0, 2π]. We find that in the H3 system, where this line always encircles the seam, the corresponding line integral always produces the value π for the geometric (Berry) phase. In the cases of the two isotopic systems we usually find the same results, but we also verify that for substantial regions in configuration space these lines do not encircle the seam and that, therefore, the line integrals produce the value of zero for the geometric phase. Analyzing the results, we establish that the Longuet-Higgins phase, which is usually assumed to be equal to φ/2, is in general significantly different from this value for all studied mass combinations.
TL;DR: In this article, the ideal-valued index of the G-space with filtration is studied and numerical indices are introduced for estimating the critical points of a G-invariant functional defined on a manifold.
Abstract: With a G-space, where G is a compact Lie group, one can associate an ideal in the cohomology ring of the classifying space for G. It is called the ideal-valued index of the G-space. A filtration of the ideal-valued index that arises in a natural way from the Leray spectral sequence is considered. Properties of the index with filtration are studied and numerical indices are introduced. These indices are convenient for estimates of the G-category and the study of the set of critical points of a G-invariant functional defined on a manifold.A generalization of the Bourgin-Yang theorem for the index with filtration is proved. This result is used for estimates of the index of the space of partial coincidences for a map of a space with p-torus action in a Euclidean space.
TL;DR: The hypothesis that the mode-coupling critical temperature is the T at which the dynamics crosses over from free to activated exploration of configuration space is confirmed.
Abstract: The connectivity of the potential energy landscape in supercooled atomic liquids is investigated through a calculation of the instantaneous normal modes spectrum and a detailed analysis of the unstable directions in configuration space. We confirm the hypothesis that the mode-coupling critical temperature is the T at which the dynamics crosses over from free to activated exploration of configuration space. We also observe changes in the local connectivity of configuration space sampled during aging, following a temperature jump from a liquid to a glassy state.
TL;DR: In this article, unstable D-branes play the role of "D-sphalerons" in string theory and their existence implies that the configuration space of type-II string theory has a complicated homotopy structure, similar to that of an infinite grassmannian.
Abstract: We show that unstable D-branes play the role of ``D-sphalerons'' in string theory. Their existence implies that the configuration space of type-II string theory has a complicated homotopy structure, similar to that of an infinite grassmannian. In particular, the configuration space of type-IIA (-IIB) string theory on Bbb R10 has non-trivial homotopy groups πk for all k even (odd).
TL;DR: In this paper, the rational Betti numbers of the configuration space C-k(M) of k points in an even-dimensional orientable closed manifold M and prove that these numbers depend only on the rational cohomology algebra of the manifold.
TL;DR: For n-body dynamics an analysis is made of the properties of configuration space within a symmetric hyperspherical framework as discussed by the authors, where coordinates are conveniently broken up into spatial (or external) rotations, kinematic invariants (related to the inertia moments) and internal (or internal) rotation.
Abstract: For n-body dynamics an analysis is made of the properties of configuration space within a symmetric hyperspherical framework. Coordinates are conveniently broken up into spatial (or external) rotations, kinematic invariants (related to the inertia moments) and kinematic (or internal) rotations. Their usefulness is demonstrated for the study of constrained intramolecular motions and of concerted reactions and for collective modes of polyatomic molecules and clusters. For a fixed hyperradius, which is a measure of total inertia, the space of kinematic invariants is the surface of a right spherical triangle that leads to the tetrahedral (for n = 4) or octahedral (for n ≥ 5) tessellation of the sphere. Alternative parametrizations are discussed, including the proper one to deal with the umbrella inversion motion of ammonia.
TL;DR: Spatial discretization of axially moving media eigenvalue problems is examined from the perspectives of moving versus stationary system basis functions, configuration space versus state space form discretizations, and subcritical versus supercritical speed conver-.
Abstract: Spatial discretization of axially moving media eigenvalue problems is examined from the perspectives of moving versus stationary system basis functions, configuration space versus state space form discretization, and subcritical versus supercritical speed conver-. gence. The moving string eigenfunctions, which have previously been shown to give excellent discretization convergence under certain conditions, become linearly dependent and cause numerical problems as the number of terms increases. This problem does not occur in a discretization of the state space form of the eigenvalue problem, although convergence is slower, not monotonic, and not necessarily from above. Use of the moving string basis at supercritical speeds yields strikingly poor results with either the configuration or state space discretizations. The stationary system eigenfunctions provide reliable eigenvalue predictions across the range of problems examined. Because they have known exact solutions, the moving string on elastic foundation and the traveling, tensioned beam are used as illustrative examples. Many of the findings, however, apply to more complex moving media problems, including nontrivial equilibria of nonlinear models.
01 Jun 2000
TL;DR: This paper considers an approach to operator-guided real time motion control of robot arm manipulators that's based on the use of configuration space (C-space), and results in a significant improvement in performance: shorter path, less time to complete the task, and virtually no arm-obstacle collisions.
Abstract: This paper considers an approach to operator-guided real time motion control of robot arm manipulators that's based on the use of configuration space (C-space). The goal is to improve operator performance in a complex environment with obstacles, In such tasks, traditional teleoperation techniques, which are all based on control in work space (W-space), suffer from human errors tied to deficiencies in human spatial reasoning. The C-space approach transforms the problem into one humans are much better equipped to handle-moving a point in a maze-and results in a significant improvement in performance: shorter path, less time to complete the task, and virtually no arm-obstacle collisions. Versions of the approach are described for two-dimensional (2-D) and three-dimensional (3-D) tasks, and tools are developed to efficiently interface the human and machine intelligence. Effectiveness of the C-space approach is demonstrated by a series of experiments, showing an improvement in performance on the order of magnitude in the 2-D case and a factor of two to four in the 3-D case, compared to usual work space control.
TL;DR: In this paper, a computationally efficient molecular dynamics method, based on holonomic constraints, devised to estimate the rate constants of rare activated events of short duration is presented, where the process is described by a reaction coordinate ξ(r), a well-defined function in configuration space.
24 Apr 2000
TL;DR: This paper presents a randomized framework for computing feedback motion strategies, by defining a global navigation function over a collection of spherical balls in the configuration space, and presents a construction algorithm that includes a Bayesian termination condition based on the probability that a specified fraction of the free space is covered.
Abstract: This paper presents a randomized framework for computing feedback motion strategies, by defining a global navigation function over a collection of spherical balls in the configuration space. If the goal is changed, an updated navigation function can be quickly computed, offering benefits similar to the fast multiple queries permitted by the probabilistic roadmap approach to path planning. Our choice of balls is motivated in part by recent tools from computational geometry which compute point locations and arrangements efficiently without significant dependence on dimension. We present a construction algorithm that includes a Bayesian termination condition based on the probability that a specified fraction of the free space is covered. A basic implementation illustrates the framework for rigid and articulated bodies with up to five-dimensional configuration spaces.
TL;DR: In this article, the dynamics of N 3 interacting particles are investigated in the non-relativistic context of the Barbour-Bertotti theories, and the reduction process on this constrained system yields a Lagrangian in the form of a Riemannian line element.
Abstract: The dynamics of N 3 interacting particles is investigated in the non-relativistic context of the Barbour-Bertotti theories. The reduction process on this constrained system yields a Lagrangian in the form of a Riemannian line element. The involved metric, degenerate in the flat configuration space, is the first fundamental form of the space of orbits of translations and rotations (the Leibniz group). The Riemann tensor and the scalar curvature are computed using a generalized Gauss formula in terms of the vorticity tensors of generators of the rotations. The curvature scalar is further given in terms of the principal moments of inertia of the system. Line configurations are singular for N 3. A comparison with similar methods in molecular dynamics is traced.
TL;DR: In this paper, a unified R -matrix-Floquet theory is proposed to analyze both multiphoton ionization of diatomic molecules and laser-assisted electron-diatomic molecule scattering.
Abstract: In this paper we describe a unified R -matrix-Floquet theory which can be used to analyse both multiphoton ionization of diatomic molecules and laser-assisted electron-diatomic molecule scattering Our treatment is non-perturbative and can be applied to arbitrary multi-electron diatomic molecules We assume that the laser field is monochromatic, monomode, spacially homogeneous and linearly polarized, where the molecular axis can be oriented in an arbitrary direction relative to this polarization direction The theory takes advantage of the natural division of configuration space into internal and external regions occurring in the R -matrix method, to choose the most appropriate form of the interaction Hamiltonian in each region This enables standard multi-centre electron-molecule scattering programs to be modified in a straightforward way to solve the problem in the internal region and single-centre atomic multiphoton propagator programs to be extended to solve the problem in the external region We illustrate our theory by considering the form of the equations for homonuclear diatomic molecules We also present results for H2 using a simple target wavefunction which provides an important test of the theory and the computer programs and illustrates the role of resonances in two-photon ionization