Configuration space

Abstract—Some in-parallel robots, such as the 3-2-1 and the 3/2 manipulators, have attracted attention because their forward kinematics can be solved by three consecutive trilaterations. In this paper, we identify a class of these robots, which we call flagged manipulators, whose singularity loci admit a well-behaved decomposition, i.e., a stratification, derived from that of the flag manifold. Two remarkable properties must be highlighted. First, the decomposition has the same topology for all members in the class, irrespective of the metric details of each particular robot instance. Thus, we provide explicitly all the singular strata and their connectivity, which apply to all flagged manipulators without any tailoring. Second, the strata can be easily characterized geometrically, because it is possible to assign local coordinates to each stratum (in the configuration space of the manipulator) that correspond to uncoupled rotations and/or translations in the workspace. Index Terms—...

We show that the inclusion of topological lagrangians in non-linear sigma models introduces certain topological non-trivial abelian background fields in the configuration space of these theories. In particular, the Hopf and the Wess-Zumino terms lead, respectively, to a vortex and a monopole in the corresponding configuration space for 2+1 and 3+1 dimensional theories. That topological solitons acquire anomalous spin and

1 Supporting Configurability in a tangibly augmented environment for design students THOMAS BINDER 1 , GIORGIO DE MICHELIS 2 , MICHAEL GERVAUTZ 3 , GIULIO ... variety of functions [13]. The backstage and the garage stand for spaces in which everything is possible. ...

An example of mechanical system whose configuration space is direct product of a curved space and the local group of rotations, is presented. The system is considered as a model of spinning particle moving in the space. The Hamiltonian formalism for this system and possible method for its quantization are discussed. It is shown that the Hamilton equations coincide with the Papapetrou equations for spinning test-particle in general relativity.

This paper presents a generalization of symplectic geometry to a principal bundle over the configuration space of a classical field. This bundle, the vertically adapted linear frame bundle, is obtained by breaking the symmetry of the full linear frame bundle of the field configuration space, and it inherits a generalized symplectic structure from the full frame bundle. The geometric structure of the vertically adapted frame bundle admits vector-valued field observables and produces vector-valued Hamiltonian vector fields, from which we can define a Poisson bracket on the field observables. We show that the linear and affine multivelocity spaces and multiphase spaces for geometric field theories are associated to the vertically adapted frame bundle. In addition, the new geometry not only generalizes both the linear and the affine models of multisymplectic geometry but also resolves fundamental problems found in both multisymplectic models.

We derive the q-deformation of the chiral Gross-Taylor holomorphic string large N expansion of two dimensional SU(N) Yang-Mills theory. Delta functions on symmetric group algebras are replaced by the corresponding objects (canonical trace functions) for Hecke algebras. The role of the Schur-Weyl duality between unitary groups and symmetric groups is now played by q-deformed Schur-Weyl duality of quantum groups. The appearance of Euler characters of configuration spaces of Riemann surfaces in the expansion persists. We discuss the geometrical meaning of these formulae.

We describe the representation of the chemical affinity between the antigen-combining site of the immunoglobulin molecule and the antigen molecule as the probability of the two molecules existing in a bound state. Our model is based on the identification of shape attractors in the configuration space for the joint antibody / antigen combining site sequence. We parameterize configuration space in terms of Ramachandran angles. The shape attractors allow us to construct a Markov chain whose steady state distribution gives rise to the desired attachment probability. As a result we are able to delineate the enthalpic, entropic and kinetic components of affinity and study their interactions.

Abstract—This paper describes a scalable method for paral-lelizing sampling-based motion planning algorithms. It subdi-vides configuration space (C-space) into (possibly overlapping) regions and independently, in parallel, uses standard (sequen-tial) sampling-based planners to construct roadmaps in each region. Next, in parallel, regional roadmaps in adjacent regions are connected to form a global roadmap. By subdividing the space and restricting the locality of connection attempts, we reduce the work and inter-processor communication associated with nearest neighbor calculation, a critical bottleneck for scalability in existing parallel motion planning methods. We show that our method is general enough to handle a variety of planning schemes, including the widely used Probabilistic Roadmap (PRM) and Rapidly-exploring Random Trees (RRT) algorithms. We compare our approach to two other existing parallel algorithms and demonstrate that our approach achieves better and more scalable pe...

Brownian ratchets have recently been considered as models to describe the ability of certain systems to locate very specific states in multidimensional configuration spaces. This directional process has particularly been proposed as an alternative explanation for the protein folding problem, in which the polypeptide is driven toward the native state by a multidimensional Brownian ratchet. Recognizing the relevance of robustness in biological systems, in this work we analyze such a property of Brownian ratchets by pushing to the limits all the properties considered essential to produce directed transport. Based on the results presented here, we can state that Brownian ratchets are able to deliver current and locate funnel structures under a wide range of conditions. As a result, they represent a simple model that solves the Levinthal's paradox with great robustness and flexibility and without requiring any ad hoc biased transition probability. The behavior of Brownian ratchets shown in this article considerably enhances the plausibility of the model for at least part of the structural mechanism behind protein folding process.

This article develops a global fields approach for conceptualizing the global arena. The approach builds upon existing approaches to the world system and world society while articulating them with the field theory of Bourdieu and organizational sociology. It highlights particular structural configurations (“spaces of relations”) and the specific cultural content (“rules of the game” and “symbolic capital”) of global systems. The utility of the approach is demonstrated through an analysis of the different forms of the two hegemonic empires of the past centuries, Great Britain and the United States. The British state tended toward formal imperialism in the 19th century, characterized by direct territorial rule, while the United States since WWII has tended toward informal imperialism. The essay shows that the difference can be best explained by considering the different historical global fields in which the two empires operated.

We study the problem of identification of a proper state-space for the stochastic dynamics of free particles in continuum, with their possible birth and death. In this dynamics, the motion of each separate particle is described by a fixed Markov process M on a Riemannian manifold X. The main problem arising here is a possible collapse of the system, in the sense that, though the initial configuration of particles is locally finite, there could exist a compact set in X such that, with probability one, infinitely many particles will arrive at this set at some time t>0. We assume that X has infinite volume and, for each α>1, we consider the set Θ_α of all infinite configurations in X for which the number of particles in a compact set is bounded by a constant times the α-th power of the volume of the set. We find quite general conditions on the process M which guarantee that the corresponding infinite particle process can start at each configuration from Θ_α, will never leave Θ_α,...

We study how micromagnetic calculations can be applied to processes that involve a singularity of the magnetization field, namely, the Bloch point. In order to allow for comparison with recent experiments, we consider Permalloy thin-film disks supporting a vortex magnetic configuration. The structure of the Bloch point at rest in the middle of the core of the vortex is studied first, comparing the evolution of the calculation results under decreasing mesh size to analytical results. The reversal of the core of the vortex under a field applied perpendicularly to the disk plane is then investigated. We apply two different procedures to evaluate switching fields and processes: direct micromagnetic time-dependent calculation, and the evaluation of the energy barrier that separates the two orientations of the vortex core in the configuration space, using a path method. Both methods show the occurrence of Bloch points during reversal. Special attention is paid to the extrapolation towards...

We present an approach to the problem of mobile robot motion planning in arbitrary cost fields subject to differential constraints. Given a model of vehicle maneuverability, a trajectory generator solves the two point boundary value problem of connecting two points in state space with a feasible motion. We use this capacity to compute a control set which connects any state to its reachable neighbors in a limited neighborhood. Equivalence classes of paths are used to implement a path sampling policy which preserves expressiveness while eliminating redundancy. The implicit repetition of the resulting minimal control set throughout state space produces a reachability graph that encodes all feasible motions consistent with this sampling policy. The graph encodes only feasible motions by construction and, by appropriate choice of state space dimension, can permit full configuration space collision detection while imposing heading and curvature continuity constraints at nodes. Nonholonomi...

We define and study exact, efficient representations of realization spaces of a natural class of underconstrained 2D Euclidean Distance Constraint Systems(EDCS) or Frameworks based on 1-dof Henneberg-I graphs. Each representation corresponds to a choice of parameters and yields a different parametrized configuration space. Our notion of efficiency is based on the algebraic complexities of sampling the configuration space and of obtaining a realization from the sample (parametrized) configuration. Significantly, we give purely combinatorial characterizations that capture (i) the class of graphs that have efficient configuration spaces and (ii) the possible choices of representation parameters that yield efficient configuration spaces for a given graph. Our results automatically yield an efficient algorithm for sampling realizations, without missing extreme or boundary realizations. In addition, our results formally show that our definition of efficient configuration space is robust a...

This paper presents a contact analysis algorithm for pairs of rigid, curved, planar parts based on configuration space computation. The algorithm is part of a dynamical simulator for planar systems with changing contact topologies. The configuration space of a pair of parts is a data structure that encodes the contact configurations for all pairs of part features. The configuration spaces of the interacting pairs in the mechanical system are constructed before the simulation. At each time step, the simulator queries the configuration spaces for contact changes instead of performing collision detection. The simulator demonstrates the efficacy of the configuration space approach to contact analysis. It achieves real-time performance on systems with complex contact geometry, curved parts, and changing contacts.

Some algebraic properties of integralsover configuration spaces are investigated in order to better understandquantization and the Connes-Kreimer algebraic approach to renormalization. <BR>In order to isolate the mathematical-physics interface toquantum field theory independent from the specifics of the variousimplementations, the sigma model of Kontsevich is investigated in moredetail. Due to the convergence of the configuration space integrals, themodel allows to study the Feynman rules independently, from an axiomaticpoint of view, avoiding the intricacies of renormalization, unavoidablewithin the traditional quantum field theory. <BR>As an application, a combinatorial approach to constructingthe coefficients of formality morphisms is suggested, as an alternative tothe analytical approach used by Kontsevich. These coefficients are "Feynman integrals", although not quite typical since they do converge. <BR>A second example of "Feynman integrals&quo...

We present a new approach to the problem of detecting point diffractors from active source surface seismic data. We formulate an optimization problem in the configuration space of possible collections of scatterers and construct a birth-and-death spatial dynamic, which converges to the optimal solution. By design, this dynamic does not have resolution limits typical of migration based techniques, which allows for subwavelength sensing.

The harmonic oscillator as a distinguished dynamical system can be defined not only on the Euclidean plane but also on the sphere and on the hyperbolic plane, and more generally on any configuration space with constant curvature and with a metric of any signature, either Riemannian (definite positive) or Lorentzian (indefinite). In this paper we study the main properties of these `curved' harmonic oscillators simultaneously on any such configuration space, using a Cayley-Klein (CK) type approach, with two free parameters , which altogether correspond to the possible values for curvature and signature type: the generic Riemannian and Lorentzian spaces of constant curvature (sphere S^2, hyperbolic plane H^2, AntiDeSitter sphere AdS^ and DeSitter sphere dS^) appear in this family, with the Euclidean and Minkowski spaces as flat limits. We solve the equations of motion for the `curved' harmonic oscillator and obtain explicit expressions for the orbits by using three different me...

A concise but general derivation of Lagrange's equations is given for a system of finitely many particles subject to holonomic and nonholonomic constraints. Based directly on Newton's second law, it takes advantage of an inertia-based metric to obtain a geometrically transparent ...

ABSTRACT This paper presents a reactive navigation algorithm for wheeled mobile robots in an unknown environment populated by obstacles. The presented approach incorporates the dimensions and shape of the robot to determine the set of all possible collision-free steering angles. The steering angle that falls in the widest gap and is dosest to the target is selected. The next stage in the algorithm takes into account the non-holonomic constraints of differentially steered robots by computing circular trajectories with adaptive radius of curvature. Actual experimental tests on a real mobile robot are presented. The results demonstrate the algorithm capabilities of driving a mobile robot safely through different obstacles arrangements.