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Showing papers on "Configuration space published in 1997"


Proceedings ArticleDOI
20 Apr 1997
TL;DR: The analysis of expansive configuration spaces has inspired a new randomized planning algorithm that tries to sample only the portion of the configuration space that is relevant to the current query, avoiding the cost of precomputing a roadmap for the entire configuration space.
Abstract: We introduce the notion of expansiveness to characterize a family of robot configuration spaces whose connectivity can be effectively captured by a roadmap of randomly-sampled milestones. The analysis of expansive configuration spaces has inspired us to develop a new randomized planning algorithm. This algorithm tries to sample only the portion of the configuration space that is relevant to the current query, avoiding the cost of precomputing a roadmap for the entire configuration space. Thus, it is well-suited for problems where a single query is submitted for a given environment. The algorithm has been implemented and successfully applied to complex assembly maintainability problems from the automotive industry.

500 citations


Journal ArticleDOI
TL;DR: In this paper, a unified construction of the symplectic forms which arise in the solution of both N=2 supersymmetric Yang-Mills theories and soliton equations is provided. But their phase spaces are Jacobian-type bundles over the leaves of a foliation in a universal configuration space.
Abstract: We provide a unified construction of the symplectic forms which arise in the solution of both N=2 supersymmetric Yang-Mills theories and soliton equations. Their phase spaces are Jacobian-type bundles over the leaves of a foliation in a universal configuration space. On one hand, imbedded into finite-gap solutions of soliton equations, these symplectic forms assume explicit expressions in terms of the auxiliary Lax pair, expressions which generalize the well-known Gardner-Faddeev-Zakharov bracket for KdV to a vast class of 2D integrable models; on the other hand, they determine completely the effective Lagrangian and BPS spectrum when the leaves are identified with the moduli space of vacua of an N=2 supersymmetric gauge theory. For SU($N_c$) with $N_f\leq N_c+1$ flavors, the spectral curves we obtain this way agree with the ones derived by Hanany and Oz and others from physical considerations.

145 citations


Journal ArticleDOI
TL;DR: The phase space probability density is at most at (2t) n, where n = dim K and at is a constant which tends to one exponentially fast as t tends to zero as mentioned in this paper.
Abstract: Let K be a compact, connected Lie group and KC its complexification. I consider the Hilbert space HL 2 (KC ; t )of holomorphic functions introduced in (H1), where the parameter t is to be interpreted as Planck's constant. In light of (L-S), the complex group KC may be identified canonically with the cotangent bundle of K. Using this identification I associate to each F 2H L 2 ( K C ; t )a "phase space probability density." The main result of this paper is Theorem 1, which provides an upper bound on this density which holds uniformly over all F and all points in phase space. Specifically, the phase space probability density is at most at (2t) n , where n = dim K and at is a constant which tends to one exponentially fast as t tends to zero. At least for small t, this bound cannot be significantly improved. With t regarded as Planck's constant, the quantity (2t) n is precisely what is ex- pected on physical grounds. Theorem 1 should be interpreted as a form of the Heisenberg uncertainty principle for K, that is, a limit on the concentration of states in phase space. The theorem supports the interpretation of the Hilbert space HL 2 (KC ; t )as the phase space representation of quantum mechanics for a particle with configuration space K. The phase space bound is deduced from very sharp pointwise bounds on functions in HL 2 (KC ; t )(Theorem 2). The proofs rely on precise calculations involving the heat kernel on K and the heat kernel on KC=K.

109 citations


Journal ArticleDOI
TL;DR: In this paper, the structure of the collective bands in a deformed configuration mixing (DCM) shell model based on Hartree - Fock states is investigated, and the calculated collective bands and the B(E2) values are compared with available experimental data.
Abstract: We have investigated the structure of the collective bands in within our deformed configuration mixing (DCM) shell model based on Hartree - Fock states. In our model, the single particle orbits , , and are taken as the configuration space with as the core. A modified Kuo interaction for this basis space is used in our calculation. The different levels are classified into collective bands on the basis of the B(E2) values among them. The calculated collective bands and the B(E2) values are compared with available experimental data. Our calculation is able to reproduce the identical bands observed in , and .

89 citations


Journal ArticleDOI
TL;DR: In this article, the Kirchhoff kinetic analogy relates the governing equations for the statics of elastic rods and the dynamics of rigid bodies and the last three quadratures that are required to reconstruct the rod centreline from the frame variables, which form the complete configuration space.
Abstract: The Kirchhoff kinetic analogy relates the governing equations for the statics of elastic rods and the dynamics of rigid bodies. We discuss the analogy in light of several different Hamiltonian formulations, including a non–canonical description of rod equilibria. We focus on the last three quadratures that are required to reconstruct the rod centreline from the frame variables, which form the complete configuration space in the rigid body interpretation. In particular, we demonstrate that if the frame evolution is formulated as a canonical Hamiltonian system involving quaternions (or Euler parameters), then the last quadratures can all be computed explicitly in terms of algebraic relations involving invariants (or integrals) of the evolution, independent of whether or not the entire system is completely integrable.

68 citations


Journal ArticleDOI
Ruth M. Williams1
01 Aug 1997
TL;DR: In this paper, the Lund-Regge metric on simplicial configuration space is defined and the signature of the simplicial supermetric is investigated. But it is not shown that the signature can be obtained by a combination of analytic and numerical techniques.
Abstract: While there has been some advanced in the use of Regge calculus as a tool in numerical relativity, the main progress in Regge calculus recently has been in quantum gravity. After a brief discussion of this progress, attention is focussed on two particular, related aspects. Firstly, the possible definitions of diffeomorphisms or gauge transformations in Regge calculus are examined and examples are given. Secondly, an investigation of the signature of the simplicial supermetric is described. This is the Lund-Regge metric on simplicial configuration space and defines the distance between simplicial three-geometries. Information on its signature can be used to extend the rather limited results on the signature of the supermetric in the continuum case. This information is obtained by a combination of analytic and numerical techniques. For the three-sphere and the three-torus, the numerical results agree with the analytic ones and show the existence of degeneracy and signature change. Some “vertical” directions in simplicial configuration space, corresponding to simplicial metrics related by gauge transformations, are found for the three-torus.

67 citations


Journal ArticleDOI
TL;DR: It is shown that the combinatorial complexity of the free configuration space of B is O(nk log k), and that it can be $\Omega (nk\alpha(k))$ in the worst case, where n is the total complexity ofthe individual Minkowski sums P1,...,Pk.
Abstract: Let B be a convex polyhedron translating in 3-space amidst k convex polyhedral obstacles A1,...,Ak with pairwise disjoint interiors. The free configuration space (space of all collision-free placements) of B can be represented as the complement of the union of the Minkowski sums $P_i=A_i\oplus (-B)$, for i= 1,...,k. We show that the combinatorial complexity of the free configuration space of B is O(nk log k), and that it can be $\Omega(nk\alpha(k))$ in the worst case, where n is the total complexity of the individual Minkowski sums P1,...,Pk. We also derive an efficient randomized algorithm that constructs this configuration space in expected time O(nk log k log n).

65 citations


Proceedings ArticleDOI
20 Apr 1997
TL;DR: This paper shows a configuration space zone in which no extremal control using five sequences is optimal, and shows that there exist, in a part of this zone, extremal controls requiring seven sequences that are candidates for optimality.
Abstract: This paper deals with the optimal control (time optimal) of a mobile robot moving in an unobstructed planar environment. The mobile robot is equipped with two independent acceleration-driven wheels so that accelerations are bounded. Using the mobile robot's configuration known through its position and orientation, the problem consists of determining the optimal control that allows the robot to move between two imposed configurations, the start and arrival taking place at zero velocity. Our approach is based on analytically extracting as much information as possible from the Pontryagin's maximum principle (PMP) before starting a numerical search. The recently reported numerical result, showing that this extremal control which is of "bang-bang" type and only requires four switch times or five sequences, is invalidated. We show a configuration space zone in which no extremal control using five sequences is optimal. We also show that there exist, in a part of this zone, extremal controls requiring seven sequences that are candidates for optimality.

59 citations


Journal ArticleDOI
TL;DR: A general method for worst-case limit kinematic tolerance analysis: computing the range of variation in the kinematics function of a mechanism from its part tolerance specifications, which covers fixed and multiple contact mechanisms with parametric or geometric part tolerances.
Abstract: We present a general method for worst-case limit kinematic tolerance analysis: computing the range of variation in the kinematic function of a mechanism from its part tolerance specifications. The method covers fixed and multiple contact mechanisms with parametric or geometric part tolerances. We develop a new model of kinematic variation, called kinematic tolerance space, that generalizes the configuration space representation of nominal kinematic function. Kinematic tolerance space captures quantitative and qualitative variations in kinematic function due to variations in part shape and part configuration. We derive properties of kinematic tolerance space that express the relationship between the nominal kinematics of mechanisms and their kinematic variations. Using these properties, we develop a practical kinematic tolerance space computation algorithm for planar pairs with two degrees of freedom.

56 citations


Journal ArticleDOI
TL;DR: The present code allows detailed spectroscopic calculations for low- and high-spin states in axially deformed nuclei and is written using a very efficient algorithm published earlier and runs extremely fast not only on Mainframes but also on Workstations or even on modern PCs.

53 citations


Journal ArticleDOI
TL;DR: In this paper, the authors proposed a method to extract dynamically important regions in the configuration space between the VRI point and products, and the obtained configuration space is analyzed in terms of the reaction coordinate and the normal coordinate.
Abstract: Theoretical study has been given on bifurcating reaction paths where the intrinsic reaction path (IRP) has a valley-ridge inflection (VRI) point on the way from transition state to product, and leads to another first-order saddle point which connects two symmetrically equivalent products. To extract dynamically important regions in the configuration space between the VRI point and products, a group of steepest descent paths are calculated starting from zero-point energy regions at the VRI point, and the obtained configuration space is analyzed in terms of the reaction coordinate and the normal coordinate. The method is applied to Berry pseudorotations in SiH4F− and PH4F, H3CO→H2COH, and cyclopropylidene→allene, by employing the second-order Mo/ller–Plesset and complete active space self-consistent field ab initio molecular orbital calculations. It is shown that the extension of bifurcating reaction paths largely depends on the position of the VRI point on the IRP. For the respective reactions, non-totally...

Journal ArticleDOI
TL;DR: In this article, a geometrical description of the configuration space is given in terms of integral points in a high-dimensional space, and the entropy is deduced from the integral volume of a convex polytope.
Abstract: The calculation of random tiling configurational entropy amounts to an enumeration of partitions. A geometrical description of the configuration space is given in terms of integral points in a high-dimensional space, and the entropy is deduced from the integral volume of a convex polytope. In some cases the latter volume can be expressed in a compact multiplicative formula, and in all cases in terms of binomial series, the origin of which is given a geometrical meaning. Our results mainly concern codimension-one tilings, but can also be extended to higher codimension tilings. We also discuss the link between freeboundary-and fixed-boundary-condition problems.

Journal ArticleDOI
TL;DR: An algorithm, based on Morse theory, is first developed for objects with smooth, convex hulls and extended to objects with piecewise-smooth hulls using a catalog of critical points from stratified Morse theory.
Abstract: When a three-dimensional object is placed in contact with a supporting plane, gravitational forces move it to one of a finite set of stable poses. For each stable pose, there is a region in the part's configuration space called a capture region; for any initial configuration within the region, the object is guaranteed to converge to that pose. The problem of computing maximal capture regions from an object model is analyzed assuming only that the dynamics are dissipative; the precise equations governing the system are unnecessary. An algorithm, based on Morse theory, is first developed for objects with smooth, convex hulls. The formulation is then extended to objects with piecewise-smooth hulls using a catalog of critical points de rived from stratified Morse theory. Algorithms have been fully implemented for objects with smooth and polyhedral convex hulls. As examples from the implementation demonstrate, calcu lating these regions from a geometric model is computationally practical.

Journal ArticleDOI
01 Feb 1997
TL;DR: A motion planning framework is proposed that achieves this with the help of a space called the perceptual control manifold (PCM) defined on the product of the robot configuration space and an image-based feature space, showing how the task of intercepting a moving target can be mapped to the PCM.
Abstract: Visual feedback can play a crucial role in a dynamic robotic task such as the interception of a moving target. To utilize the feedback effectively, there is a need to develop robot motion planning techniques that also take into account properties of the sensed data. We propose a motion planning framework that achieves this with the help of a space called the perceptual control manifold (PCM) defined on the product of the robot configuration space and an image-based feature space. We show how the task of intercepting a moving target can be mapped to the PCM, using image feature trajectories of the robot end-effector and the moving target. This leads to the generation of motion plans that satisfy various constraints and optimality criteria derived from the robot kinematics, the control system, and the sensing mechanism. Specific interception tasks are analyzed to illustrate this vision-based planning technique.

Posted Content
TL;DR: In this paper, the Hitchin connection for rank 2 bundles with trivial determinant over curves of genus 2 is studied. But the connection is not defined in terms of a configuration space, and the corresponding vector bundles are trivial.
Abstract: The aim of this paper is to give an explicit expression for Hitchin's connection in the case of rank 2 bundles with trivial determinant over curves of genus 2. We recall the definition of this connection (which arose in Quantum Field Theory) and characterize it for families of genus two curves. We then consider a particular family (over a configuration space), the corresponding vector bundles are (almost) trivial. The Heat equations which give the connection these bundles are related to the Lie algebra so(6). We compute some local monodromy representations. As a byproduct we obtain, for any representation space V of so(2g+2), a flat connection on the trivial bundle with fiber V over a configuration space and thus a monodromy representation of a pure braid group.

Journal ArticleDOI
TL;DR: In this article, an invariant of rational homology 3-spheres in terms of configuration space integrals is described, which in some sense lies between the invariants of Axelrod and Singer and those of Kontsevich.
Abstract: This note describes an invariant of rational homology 3-spheres in terms of configuration space integrals which in some sense lies between the invariants of Axelrod and Singer and those of Kontsevich.

Book
01 Jan 1997
TL;DR: The story of the configuration space X (2,4) of n Points on the Projective Line: The Configuration Space X ( 2,5), Hypergeometric Functions of Type (3,6), Modular Interpretation of the Configuration Space x (3.6) as mentioned in this paper.
Abstract: Part 1: The Story of the Configuration Space X (2,4) of Four Points on the Projective Line: Configuration Spaces - The Simplest Case Elliptic Curves Modular Interpretations of X (2,4) Hypergeometric Integrals and Loaded Cycles. Part 2: The Story of the Configuration Space X (2,n) of n Points on the Projective Line: The Configuration Space X (2,5) Modular Interpretation of the Configuration Space X (2,n) The Configuration Space X (3,6) Hypergeometric Functions of Type (3,6) Modular Interpretation of the Configuration Space X (3,6)

Book ChapterDOI
01 Jan 1997
TL;DR: In this paper, the authors propose a quantum quantum analog of the orbit method based on the Hilbert space L2(M) of square-integrable half-densities on M.
Abstract: Publisher Summary The orbit method pioneered by Kirillov and Kostant seeks to construct irreducible unitary representations by analogy with quantization procedures in mechanics. A classical physical system may sometimes be modeled by a configuration space M, a manifold the points of which represent the possible positions of the bodies in the system. The corresponding phase space is the cotangent bundle T'M, the points of which represent the possible states (positions and momenta) of the bodies in the system. In this setting, a classical observable is a function on T*M. The quantum mechanical analog of this system is based on the Hilbert space L2(M) of square-integrable half-densities on M. A quantum mechanical observable is an operator T on L2(M); the scalar product (Tv, v) is the expected value of the observable on the state v. Some connection between classical and quantum observables is provided by a symbol calculus; an interesting quantum observable is often a differential operator on M, and the corresponding classical observable is related to the symbol of the differential operator.

Journal ArticleDOI
TL;DR: In this article, the authors extend ideas developed for the loop representation of quantum gravity to diffeomorphism-invariant gauge theories coupled to fermions, and construct a Hilbert space L^2(a x f) for the quantum theory on which all automorphisms of P act as unitary operators.
Abstract: We extend ideas developed for the loop representation of quantum gravity to diffeomorphism-invariant gauge theories coupled to fermions. Let P -> Sigma be a principal G-bundle over space and let F be a vector bundle associated to P whose fiber is a sum of continuous unitary irreducible representations of the compact connected gauge group G, each representation appearing together with its dual. We consider theories whose classical configuration space is A x F, where A is the space of connections on P and F is the space of sections of F, regarded as a collection of Grassmann-valued fermionic fields. We construct the `quantum configuration space a x f as a completion of A x F. Using this we construct a Hilbert space L^2(a x f) for the quantum theory on which all automorphisms of P act as unitary operators, and determine an explicit `spin network basis' of the subspace L^2((a x f)/G) consisting of gauge-invariant states. We represent observables constructed from holonomies of the connection along paths together with fermionic fields and their conjugate momenta as operators on L^2((a x f)/G). We also construct a Hilbert space H_diff of diffeomorphism-invariant states using the group averaging procedure of Ashtekar, Lewandowski, Marolf, Mourao and Thiemann.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the 3-body trigonometric G_2 integrable system is exactly solvable if the configuration space is parametrized by certain symmetric functions of the coordinates, and if the Hamiltonian can be expressed as a quadratic polynomial in the generators of some Lie algebra of differential operators in a finite-dimensional representation.
Abstract: It is shown that the 3-body trigonometric G_2 integrable system is exactly-solvable. If the configuration space is parametrized by certain symmetric functions of the coordinates then, for arbitrary values of the coupling constants, the Hamiltonian can be expressed as a quadratic polynomial in the generators of some Lie algebra of differential operators in a finite-dimensional representation. Four infinite families of eigenstates, represented by polynomials, and the corresponding eigenvalues are described explicitly.

Journal ArticleDOI
TL;DR: In this article, the authors studied the dynamics of a spherically symmetric thin shell with arbitrary rest mass and surface tension interacting with a central black hole and proved that the true Hamiltonians are uniquely determined by the equations of motion of the shell, the value of the total energy of the system, and the choice of time coordinate along the shell.
Abstract: The dynamics of a spherically symmetric thin shell with arbitrary rest mass and surface tension interacting with a central black hole is studied. A careful investigation of all classical solutions reveals that the value of the radius of the shell and of the radial velocity as an initial datum does not determine the motion of the shell; another configuration space must, therefore, be found. A different problem is that the shell Hamiltonians used in the literature are complicated functions of momenta (nonlocal) and they are gauge dependent. To solve these problems, the existence is proved of a gauge-invariant super-Hamiltonian that is quadratic in momenta and that generates the shell equations of motion. The true Hamiltonians are shown to follow from the super-Hamiltonian by a reduction procedure including a choice of gauge and solution of constraint; one important step in the proof is a lemma stating that the true Hamiltonians are uniquely determined (up to a canonical transformation) by the equations of motion of the shell, the value of the total energy of the system, and the choice of time coordinate along the shell. As an example, the Kraus-Wilczek Hamiltonian is rederived from the super-Hamiltonian. The super-Hamiltonian coincides with that of a fictitious particle moving in a fixed two-dimensional Kruskal spacetime under the influence of two effective potentials. The pair consisting of a point of this spacetime and a unit timelike vector at the point, considered as an initial datum, determines a unique motion of the shell.

Book
01 May 1997
TL;DR: In this paper, Lagrangian and Hamiltonian dynamics and transformations in phase space have been studied and compared with noncanonical flows and non-canonical canonical flows in generalized and nonholonomic coordinates.
Abstract: Introduction 1. Universal laws of nature 2. Lagrange's and Hamilton's equations 3. Flows in phase space 4. Motion in a central potential 5. Small oscillations about equilibria 6. Integrable and chaotic oscillations 7. Parameter-dependent transformations 8. Linear transformations, rotations and rotating frames 9. Rigid body dynamics 10. Lagrangian dynamics and transformations in configuration space 11. Relativity, geometry, and gravity 12. Generalized vs. nonholonomic coordinates 13. Noncanonical flows 14. Damped driven Newtonian systems 15. Hamiltonian dynamics and transformations in phase space 16. Integrable canonical flows 17. Nonintegrable canonical flows 18. Simulations, complexity, and laws of nature.

Posted Content
TL;DR: In this paper, a new method of computing cohomology groups of spaces of knots was proposed, based on the topology of configuration spaces and two-connected graphs, and calculated all such classes of order 3.
Abstract: We propose a new method of computing cohomology groups of spaces of knots in $\R^n$, $n \ge 3$, based on the topology of configuration spaces and two-connected graphs, and calculate all such classes of order $\le 3.$ As a byproduct we define the higher indices, which invariants of knots in $\R^3$ define at arbitrary singular knots. More generally, for any finite-order cohomology class of the space of knots we define its principal symbol, which lies in a cohomology group of a certain finite-dimensional configuration space and characterizes our class modulo the classes of smaller filtration.

Journal ArticleDOI
TL;DR: In this paper, a model of assisted diffusion of hard core particles on a line is studied, where the configuration space breaks up into an exponentially large number of disconnected sectors whose number and sizes are determined.
Abstract: We study a model of assisted diffusion of hard-core particles on a line. Our model is a special case of a multispecies exclusion process, but the long-time decay of correlation functions can be qualitatively different from that of the simple exclusion process, depending on initial conditions. This behavior is a consequence of the existence of an infinity of conserved quantities. The configuration space breaks up into an exponentially large number of disconnected sectors whose number and sizes are determined. The decays of autocorrelation functions in different sectors follow from an exact mapping to a model of the diffusion of hard-core random walkers with conserved spins. These are also verified numerically. Within each sector the model is reducible to the Heisenberg model and hence is fully integrable. We discuss additional symmetries of the equivalent quantum Hamiltonian which relate observables in different sectors. We also discuss some implications of the existence of an infinity of conservation laws for a hydrodynamic description.

Proceedings ArticleDOI
20 Apr 1997
TL;DR: This work proposes a new approach to solving the point-to-point inverse kinematics problem for highly redundant manipulators that explicitly takes into account constraints due to joint limits and self-collisions and central to this approach is the novel notion of kinematic roadmap for a manipulator.
Abstract: We propose a new approach to solving the point-to-point inverse kinematics problem for highly redundant manipulators. It is inspired by recent motion planning research and explicitly takes into account constraints due to joint limits and self-collisions. Central to our approach is the novel notion of kinematic roadmap for a manipulator. The kinematic roadmap captures the connectivity of the configuration space of a manipulator in a finite graph like structure. The standard formulation of inverse kinematics problem is then solved using this roadmap. Our current implementation, based on Ariadne's clew algorithm, is composed of two sub-algorithms: EXPLORE, a simple algorithm that builds the kinematic roadmap by placing landmarks in the configuration space; and SEARCH, a local planner that uses this roadmap to reach the desired end-effector configuration. Our implementation of SEARCH is an extremely efficient closed form solution, albeit local, to inverse kinematics that exploits the serial kinematic structure of serial manipulator arms. Initial experiments with a 7-DOF manipulator have been extremely successful.

Journal ArticleDOI
TL;DR: Theulting approach provides a new decision process that can be used as an observer for event-driven manipulation program ming, and makes the system robust to alignment errors.
Abstract: This article describes a new statistical, model-based approach to building a contact-state observer for time-invariant con straints for a point in three dimensions. Three-dimensional constraint estimation and selection, and the application of these procedures to a planar, two-dimensional maze is described in detail. The observer uses measurements of the contact force and position, and prior information about the task encoded in a network, to determine the current location of the robot in the task-configuration space. Each node represents what the measurements will look like in a small region of configuration space by storing a predictive, statistical, measurement model. Construction of the task network requires a model of both the grasped part and the environment. The model makes the system robust to alignment errors, however, gross errors can occur if the topology of the modeled configuration space differs from the true topology. Arcs in the task network represent possible transitions between models. Bea...

Journal ArticleDOI
TL;DR: Jorgensen et al. as discussed by the authors presented a structural analysis of TIP4P water based on the choice of restricted ranges of the pair angular configuration space, referred to as states or configurations Γ, are used to obtain restricted averages, gΓ(r), of the angular correlation function g(r,ω1,ω2).
Abstract: A structural study of TIP4P [W. L. Jorgensen et al., J. Chem. Phys. 79, 926 (1983)] water is presented. The method of structural analysis is based on the choice of restricted ranges of the pair angular configuration space. Such ranges, referred to as states or configurations Γ, are used to obtain restricted averages, gΓ(r), of the angular correlation function g(r,ω1,ω2). Eulerian angles are used to define molecular orientations. This allows one to analyze all the geometries of the configuration space and to pay due attention to the nonhydrogen bonded configurations. The local structures and their temperature evolution are studied using the restricted distribution functions of oxygen–oxygen, gOOΓ(r), and of oxygen–hydrogen gOHΓ(r) of the different configurations. As the temperature rises, the local population of nonhydrogen bonded configurations increases owing to the breakdown of the tetrahedral network. By comparing the gOOΓ(r) to the g(r) of simple fluids, scaled from liquid argon, the evidence of a res...

Journal ArticleDOI
TL;DR: This paper addresses manipulator redundancy from a global perspective, aiming at kinematic control through the exploration of self-motion topology, with significant improvement in the search for globally optimum solutions of path planning when compared to traditional approaches.
Abstract: This paper addresses manipulator redundancy from a global perspective, aiming at kinematic control through the exploration of self-motion topology The methodology is based on collecting information about the structure of the kinematic map with the use of topological tools, providing an overall view of the configuration space and its relationship to the work space – a suitable framework for the efficient implementation of global approaches A space discretization method has been developed to benefit from the topological structure, embedding kinematics in its representation This method enables an efficient exploration of global redundancy resolution and path planning, offering the means to avoid local minima and deadlocks with minimum effort The discretization was implemented for a planar manipulator, demonstrating significant improvement in the search for globally optimum solutions of path planning when compared to traditional approaches

Journal ArticleDOI
TL;DR: A computerised method of retrieving mechanism concepts from a library by specifying a required behaviour using qualitative configuration space as a retrieval index is proposed and applied to simple mechanism design problems as examples to confirm the effectiveness of the approach.
Abstract: When designing mechanisms, making use of examples in past designs and handbooks should lead to cost reduction by promoting the sharing of parts and subassemblies among the products as well as reduction of time and effort. At present, however, the process of surveying design examples is left almost entirely to human designers and little computerised aid has been developed. We propose a computerised method of retrieving mechanism concepts from a library by specifying a required behaviour using qualitative configuration space as a retrieval index. First, mechanism concepts and their kinematics characteristics are described and stored in a computerised library using qualitative configuration spaces accompanined by additional information such as motion type and motion transmission direction. To retrieve mechanism concepts which realise specific kinematic behaviour, designers specify the required behaviour as timing charts of given input and intended output motions. Motion types, motion transmission direction, and motion speed dependence of the input and output motions can also be specified. Computer programs translate the required timing charts into required locus patterns in motion parameter space, and then available mechanism concepts to realise the behaviour are retrieved based on pattern matching between the qualitative configuration spaces and the locus patterns. The method is implemented as an experimental computer program written in Prolog and applied to simple mechanism design problems as examples to confirm the effectiveness of the approach.

Proceedings ArticleDOI
20 Apr 1997
TL;DR: This paper presents a systematic approach for quantifying the quality of compliant grasps using a frame-invariant quality measure, and grasp optimization using this quality measure is discussed with examples.
Abstract: This paper presents a systematic approach for quantifying the quality of compliant grasps. Appropriate tangent and cotangent subspaces to the object's configuration space are studied, from which frame-invariant characteristic compliance parameters are defined. Physical and geometric interpretations are given to these parameters, and a practically meaningful method is proposed to make the parameters comparable. A frame-invariant quality measure is then defined, and grasp optimization using this quality measure is discussed with examples.