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Showing papers on "Configuration space published in 2014"


Journal ArticleDOI
TL;DR: In this article, it was shown that the cluster structure on the kinematic configuration space Conf PsyNet n====== (ℙ3) underlies the structure of motivic amplitudes, which are objects which contain all the essential mathematical content of scattering amplitudes in planar SYM theory.
Abstract: In this paper we study motivic amplitudes — objects which contain all of the essential mathematical content of scattering amplitudes in planar SYM theory in a completely canonical way, free from the ambiguities inherent in any attempt to choose particular functional representatives. We find that the cluster structure on the kinematic configuration space Conf n (ℙ3) underlies the structure of motivic amplitudes. Specifically, we compute explicitly the coproduct of the two-loop seven-particle MHV motivic amplitude $ \mathcal{A}_{7,2}^{\mathcal{M}} $ and find that like the previously known six-particle amplitude, it depends only on certain preferred coordinates known in the mathematics literature as cluster $ \mathcal{X} $ -coordinates on Conf n (ℙ3). We also find intriguing relations between motivic amplitudes and the geometry of generalized associahedrons, to which cluster coordinates have a natural combinatoric connection. For example, the obstruction to $ \mathcal{A}_{7,2}^{\mathcal{M}} $ being expressible in terms of classical polylogarithms is most naturally represented by certain quadrilateral faces of the appropriate associahedron. We also find and prove the first known functional equation for the trilogarithm in which all 40 arguments are cluster $ \mathcal{X} $ -coordinates of a single algebra. In this respect it is similar to Abel’s 5-term dilogarithm identity.

192 citations


Journal ArticleDOI
TL;DR: A novel, real-time algorithm to accurately approximate the generalized penetration depth (PDg) between two overlapping rigid or articulated models is presented, based on iterative, constrained optimization on the contact space, defined by the overlapping objects.
Abstract: We present a novel, real-time algorithm to accurately approximate the generalized penetration depth (PDg) between two overlapping rigid or articulated models. Given the high complexity of computing PDg, our algorithm approximates PDg based on iterative, constrained optimization on the contact space, defined by the overlapping objects. The main ingredient of our algorithm is a novel and general formulation of distance metric, the object norm, in a configuration space for articulated models, and a compact closed-form solution for it. Then, we perform constrained optimization, by linearizing the contact constraint, and minimizing the object norm under such a constraint. In practice, our algorithm can compute locally optimal PDg for rigid or articulated models consisting of tens of thousands of triangles in tens of milliseconds. We also suggest three applications using PDg computation: retraction-based motion planning, physically-based animation, and data-driven grasping.

148 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that the modern formulation of Bohm's quantum theory known as Bohmian mechanics is committed only to particles' positions and a law of motion.
Abstract: The paper points out that the modern formulation of Bohm’s quantum theory known as Bohmian mechanics is committed only to particles’ positions and a law of motion. We explain how this view can avoid the open questions that the traditional view faces according to which Bohm’s theory is committed to a wave-function that is a physical entity over and above the particles, although it is defined on configuration space instead of three-dimensional space. We then enquire into the status of the law of motion, elaborating on how the main philosophical options to ground a law of motion, namely Humeanism and dispositionalism, can be applied to Bohmian mechanics. In conclusion, we sketch out how these options apply to primitive ontology approaches to quantum mechanics in general.

140 citations


Proceedings ArticleDOI
Min Li1, Liangzhao Zeng2, Shicong Meng2, Jian Tan2, Li Zhang2, Ali R. Butt1, Nicholas C. M. Fuller2 
23 Jun 2014
TL;DR: This work proposes an online performance tuning system that monitors a job's execution, tunes associated performance-tuning parameters based on collected statistics, and provides fine-grained control over parameter configuration, and designs a gray-box based smart hill climbing algorithm that can efficiently converge to a near-optimal configuration with high probability.
Abstract: MapReduce job parameter tuning is a daunting and time consuming task. The parameter configuration space is huge; there are more than 70 parameters that impact job performance. It is also difficult for users to determine suitable values for the parameters without first having a good understanding of the MapReduce application characteristics. Thus, it is a challenge to systematically explore the parameter space and select a near-optimal configuration. Extant offline tuning approaches are slow and inefficient as they entail multiple test runs and significant human effort.To this end, we propose an online performance tuning system, MRONLINE, that monitors a job's execution, tunes associated performance-tuning parameters based on collected statistics, and provides fine-grained control over parameter configuration. MRONLINE allows each task to have a different configuration, instead of having to use the same configuration for all tasks. Moreover, we design a gray-box based smart hill climbing algorithm that can efficiently converge to a near-optimal configuration with high probability. To improve the search quality and increase convergence speed, we also incorporate a set of MapReduce-specific tuning rules in MRONLINE. Our results using a real implementation on a representative 19-node cluster show that dynamic performance tuning can effectively improve MapReduce application performance by up to 30% compared to the default configuration used in YARN.

139 citations


Journal ArticleDOI
TL;DR: In this paper, the authors present a new approach to computing event shape distributions or, more precisely, charge flow correlations in a generic conformal field theory (CFT) by using Wightman correlation functions in a certain limit.

121 citations


Journal ArticleDOI
TL;DR: This work develops quantum Monte Carlo schemes to overcome the notoriously difficult study of the ground state complexity for interacting many-body quantum systems, focusing on Shannon-Rényi entropies of ground states of large quantum many- body systems.
Abstract: How many states of a configuration space contribute to a wave function? Attempts to answer this ubiquitous question have a long history in physics and are keys to understanding, e.g., localization phenomena. Beyond single-particle physics, a quantitative study of the ground state complexity for interacting many-body quantum systems is notoriously difficult, mainly due to the exponential growth of the configuration (Hilbert) space with the number of particles. Here we develop quantum Monte Carlo schemes to overcome this issue, focusing on Shannon-R\'enyi entropies of ground states of large quantum many-body systems. Our simulations reveal a generic multifractal behavior while the very nature of quantum phases of matter and associated transitions is captured by universal subleading terms in these entropies.

92 citations


Journal ArticleDOI
TL;DR: In this paper, the authors developed the properties of the n th sequential topological complexity TCn, a homotopy invariant introduced by the third author as an extension of Farber's topological model for studying the complexity of motion planning algorithms in robotics.
Abstract: We develop the properties of the n th sequential topological complexity TCn , a homotopy invariant introduced by the third author as an extension of Farber’s topological model for studying the complexity of motion planning algorithms in robotics. We exhibit close connections of TCn.X/ to the Lusternik‐Schnirelmann category of cartesian powers of X , to the cup length of the diagonal embedding X ,! X n , and to the ratio between homotopy dimension and connectivity of X . We fully compute the numerical value of TCn for products of spheres, closed 1‐connected symplectic manifolds and quaternionic projective spaces. Our study includes two symmetrized versions of TCn.X/. The first one, unlike Farber and Grant’s symmetric topological complexity, turns out to be a homotopy invariant of X ; the second one is closely tied to the homotopical properties of the configuration space of cardinality-n subsets of X . Special attention is given to the case of spheres. 55M30; 55R80

68 citations


Journal ArticleDOI
TL;DR: In this article, the radical nature and spin symmetry of the ground state of the quasi-linear acene and two-dimensional periacene series were examined using the COLUMBUS program package.
Abstract: This study examines the radical nature and spin symmetry of the ground state of the quasi-linear acene and two-dimensional periacene series. For this purpose, high-level ab initio calculations have been performed using the multireference averaged quadratic coupled cluster theory and the COLUMBUS program package. A reference space consisting of restricted and complete active spaces is taken for the π-conjugated space, correlating 16 electrons with 16 orbitals with the most pronounced open-shell character for the acenes and a complete active-space reference approach with eight electrons in eight orbitals for the periacenes. This reference space is used to construct the total configuration space by means of single and double excitations. By comparison with more extended calculations, it is shown that a focus on the π space with a 6-31G basis set is sufficient to describe the major features of the electronic character of these compounds. The present findings suggest that the ground state is a singlet for the smaller members of these series, but that for the larger ones, singlet and triplet states are quasi-degenerate. Both the acenes and periacenes exhibit significant polyradical character beyond the traditional diradical.

67 citations


Journal ArticleDOI
TL;DR: In this article, an almost global asymptotic tracking control for autonomous body-fixed hovering of a rigid spacecraft over an asteroid is proposed in the framework of geometric mechanics, where the configuration space for the spacecraft is the Lie group SE (3 ), which is the set of positions and orientations of the rigid spacecraft in three-dimensional Euclidean space.

59 citations


Journal ArticleDOI
TL;DR: A permutationally invariant global potential energy surface for the HOCO system is reported by fitting a larger number of high-level ab initio points using the newly proposed permutation invariant polynomial-neural network method.
Abstract: A permutationally invariant global potential energy surface for the HOCO system is reported by fitting a larger number of high-level ab initio points using the newly proposed permutation invariant polynomial-neural network method. The small fitting error (∼5 meV) indicates a faithful representation of the potential energy surface over a large configuration space. Full-dimensional quantum and quasi-classical trajectory studies of the title reaction were performed on this potential energy surface. While the results suggest that the differences between this and an earlier neural network fits are small, discrepancies with state-to-state experimental data remain significant.

58 citations


Journal ArticleDOI
TL;DR: This work presents a randomized path planning algorithm for reaching a desired goal configuration using an integral functional for control effort, called the upstream criterion, that measures the extent to which a path goes against the given vector field.
Abstract: Given a vector field defined on a robot's configuration space, in which the vector field represents the system drift, e.g. a wind velocity field, water current flow, or gradient field for some potential function, we present a randomized path planning algorithm for reaching a desired goal configuration. Taking the premise that moving against the vector field requires greater control effort, and that minimizing the control effort is both physically meaningful and desirable, we propose an integral functional for control effort, called the upstream criterion, that measures the extent to which a path goes against the given vector field. The integrand of the upstream criterion is then used to construct a rapidly exploring random tree (RRT) in the configuration space, in a way such that random nodes are generated with an a priori specified bias that favors directions indicated by the vector field. The resulting planning algorithm produces better quality paths while preserving many of the desirable features of RRT-based planning, e.g. the Voronoi bias property, computational efficiency, algorithmic simplicity, and straightforward extension to constrained and nonholonomic problems. Extensive numerical experiments demonstrate the advantages of our algorithm vis-A -vis existing optimality criterion-based planning algorithms.

Journal ArticleDOI
TL;DR: In this article, the authors derived expressions for the cross power spectrum between the density and momentum field and the auto spectrum of the momentum field in redshift space, by extending the distribution function method to these statistics.
Abstract: Direct measurements of peculiar velocities of galaxies and clusters of galaxies can in principle provide explicit information on the three dimensional mass distribution, but this information is modulated by the fact that velocity field is sampled at galaxy positions, and is thus probing galaxy momentum. We derive expressions for the cross power spectrum between the density and momentum field and the auto spectrum of the momentum field in redshift space, by extending the distribution function method to these statistics. The resulting momentum cross and auto power spectra in redshift space are expressed as infinite sums over velocity moment correlators in real space, as is the case for the density power spectrum in redshift space. We compute each correlator using Eulerian perturbation theory (PT) and halo biasing model and compare the resulting redshift-space velocity statistics to those measured from N-body simulations for both dark matter and halos. We find that in redshift space linear theory predictions for the density-momentum cross power spectrum as well as for the momentum auto spectrum fail to predict the N-body results at very large scales. On the other hand, our nonlinear PT prediction for these velocity statistics, together with real-space power spectrum for dark matter from simulations, improves the accuracy for both dark matter and halos. We also present the same analysis in configuration space, computing the redshift-space pairwise mean infall velocities and velocity correlation function and compare to nonlinear PT.

Journal ArticleDOI
TL;DR: A general Morse-theoretic framework is developed, and the precise threshold radius for a configuration space to be homotopy equivalent to the configuration space of points is found.
Abstract: In this paper we study configuration spaces of hard spheres in a bounded region. We develop a general Morse-theoretic framework and show that mechanically balanced configurations play the role of critical points. As an application, we find the precise threshold radius for a configuration space to be homotopy equivalent to the configuration space of points.

Journal ArticleDOI
TL;DR: In this article, a geometric setting for higher-order La-grangian problems on Lie groups is described, and an intrinsic framework for this type of dynamical systems is deduced using the Skinner-Rusk formalism.
Abstract: In this paper, we describe a geometric setting for higher-order La- grangian problems on Lie groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an adaptation of the classical Skinner-Rusk formalism, we deduce an intrinsic framework for this type of dynamical systems. Interesting applications as, for instance, a geometric derivation of the higher-order Euler-Poincare equations, optimal control of underactuated control systems whose configuration space is a Lie group are shown, among others, along the paper.

Journal ArticleDOI
TL;DR: In this article, a general framework for constructing hybrid Monte Carlo methods under relaxed conditions is presented, where the only geometric property needed is (weakened) reversibility; volume preservation is not needed.
Abstract: One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a Markov chain Monte Carlo method, which converges only in the limit to the prescribed distribution. Such methods typically inch through configuration space step by step, with acceptance of a step based on a Metropolis(-Hastings) criterion. An acceptance rate of 100% is possible in principle by embedding configuration space in a higher dimensional phase space and using ordinary differential equations. In practice, numerical integrators must be used, lowering the acceptance rate. This is the essence of hybrid Monte Carlo methods. Presented is a general framework for constructing such methods under relaxed conditions: the only geometric property needed is (weakened) reversibility; volume preservation is not needed. The possibilities are illustrated by deriving a couple of explicit hybrid Monte Carlo methods, one based on barrier-lowering variable-metric dynamics and another based on isokinetic dynamics.

Journal ArticleDOI
TL;DR: In this article, the authors used the conditional symmetry approach to study the evolution of a minisuperspace spherically symmetric model both at the classical and quantum level, showing that the existence of such symmetries yields solutions to the Wheeler-DeWitt equation which, as a semiclassical analysis shows, exhibit a good correlation with the classical regime.
Abstract: We use the conditional symmetry approach to study the $r$-evolution of a minisuperspace spherically symmetric model both at the classical and quantum level. After integration of the coordinates $t$, $\theta$ and $\phi$ in the gravitational plus electromagnetic action the configuration space dependent dynamical variables turn out to correspond to the $r$-dependent metric functions and the electrostatic field. In the context of the formalism for constrained systems (Dirac - Bergmann, ADM) with respect to the radial coordinate $r$, we set up a point-like reparameterization invariant Lagrangian. It is seen that, in the constant potential parametrization of the lapse, the corresponding minisuperspace is a Lorentzian three-dimensional flat manifold which obviously admits six Killing vector fields plus a homothetic one. The weakly vanishing $r$-Hamiltonian guarantees that the phase space quantities associated to the six Killing fields are linear holonomic integrals of motion. The homothetic field provides one more rheonomic integral of motion. These seven integrals are shown to comprise the entire classical solution space, i.e. the space-time of a Reissner-Nordstrom black hole, the $r$-reparametrization invariance since one dependent variable remains unfixed, and the two quadratic relations satisfied by the integration constants. We then quantize the model using the quantum analogues of the classical conditional symmetries, and show that the existence of such symmetries yields solutions to the Wheeler-DeWitt equation which, as a semiclassical analysis shows, exhibit a good correlation with the classical regime. We use the resulting wave functions to investigate the possibility of removing the classical singularities.

Proceedings ArticleDOI
01 Dec 2014
TL;DR: This paper develops a method for accurately describing the probability density associated with nonlinear measurement models by a second-order approximation of a distribution defined directly on the Lie group configuration space and shows that this density can be described well as a Gaussian distribution in exponential coordinates.
Abstract: Extended Kalman filters on Lie groups arise naturally in the context of pose estimation and more generally in robot localization and mapping. Typically in such settings one deals with nonlinear measurement models that are handled through linearization and linearized uncertainty transformation. To circumvent the loss of accuracy resulting from the typical coordinate-based linearization, this paper develops a method for accurately describing the probability density associated with nonlinear measurement models by a second-order approximation of a distribution defined directly on the Lie group configuration space. We show that, like the case of linearized measurement models, this density can be described well as a Gaussian distribution in exponential coordinates (though with different mean and covariance than those that result from linearized measurement models). And therefore previously developed methods for propagation of uncertainty and fusion of measurements can be applied to this generalized formulation without the a priori assumption of linearized measurement. A case study using a range-bearing model in planar robot localization is presented to demonstrate the method.

Journal ArticleDOI
TL;DR: This work tackles the sampling problem by carrying out driven adiabatic free energy dynamics to obtain converged free energy surfaces of dipeptides in the gas phase and in solution using selected dihedral angles as collective variables and introduces a fuzzy clustering algorithm in collective-variable space.
Abstract: The quality of classical biomolecular simulations is inevitably limited by two problems: the accuracy of the force field used and the comprehensiveness of configuration space sampling. In this work we tackle the sampling problem by carrying out driven adiabatic free energy dynamics to obtain converged free energy surfaces of dipeptides in the gas phase and in solution using selected dihedral angles as collective variables. To calculate populations of conformational macrostates observed in experiment, we introduce a fuzzy clustering algorithm in collective-variable space, which delineates macrostates without prior definition of arbitrary boundaries. With this approach, we calculate the conformational preferences of small peptides with six biomolecular force fields chosen from among the most recent and widely used. We assess the accuracy of each force field against recently published Raman or IR–UV spectroscopy measurements of conformer populations for the dipeptides in solution or in the gas phase.

Journal ArticleDOI
TL;DR: The carbon dioxide Raman spectrum is simulated within an algebraic approach based on curvilinear coordinates in a local representation, obtaining results close to experimental accuracy and providing six new CO2 experimental vibrational terms.
Abstract: The carbon dioxide Raman spectrum is simulated within an algebraic approach based on curvilinear coordinates in a local representation. The two main advantages of the present algebraic approach are a possible connection with configuration space and the correct description of systems with either local or normal mode character. The system Hamiltonian and polarizability tensor are expanded in terms of curvilinear coordinates. The curvilinear coordinates are in turn expanded into normal coordinates, obtaining an algebraic representation in terms of normal bosonic operators. A canonical transformation maps the operators into a local algebraic representation. The final step is an anharmonization procedure to local operators. The Raman spectrum of CO2 has been simulated, obtaining results close to experimental accuracy, and polarizability transition moments for the Raman spectral lines between 1150 cm−1 and 1500 cm−1 are reported. The comparison between experimental and simulated spectra has provided six new CO2 experimental vibrational terms.

Journal ArticleDOI
TL;DR: In this article, the authors considered the U( 1) Chern-Simons gauge theory defined in a general closed oriented 3-manifold M, and the functional integration was used to compute the normalized partition function and the expectation values of the link holonomies.

Journal ArticleDOI
TL;DR: Focusing on periodic domains, the Convected Scheme is applied to the solution of the Vlasov–Poisson system, which describes the evolution of the velocity distribution function of a collection of charged particles subject to reciprocal Coulomb interactions.

Proceedings ArticleDOI
01 Jul 2014
TL;DR: This work focuses on trajectory classification and presents a sampling-based approach which can handle noise, which is applicable to general configuration spaces and which relies only on the availability of collision free samples, and obtains a multiscale classification algorithm for trajectories in configuration spaces of arbitrary dimension.
Abstract: Topological approaches to studying equivalence classes of trajectories in a configuration space have recently received attention in robotics since they allow a robot to reason about trajectories at a high level of abstraction. While recent work has approached the problem of topological motion planning under the assumption that the configuration space and obstacles within it are explicitly described in a noise-free manner, we focus on trajectory classification and present a sampling-based approach which can handle noise, which is applicable to general configuration spaces and which relies only on the availability of collision free samples. Unlike previous sampling-based approaches in robotics which use graphs to capture information about the path-connectedness of a configuration space, we construct a multiscale approximation of neighborhoods of the collision free configurations based on filtrations of simplicial complexes. Our approach thereby extracts additional homological information which is essential for a topological trajectory classification. By computing a basis for the first persistent homology groups, we obtain a multiscale classification algorithm for trajectories in configuration spaces of arbitrary dimension. We furthermore show how an augmented filtration of simplicial complexes based on a cost function can be defined to incorporate additional constraints. We present an evaluation of our approach in 2, 3, 4 and 6 dimensional configuration spaces in simulation and using a Baxter robot.

Journal ArticleDOI
TL;DR: In this paper, a renormalization invariant residue is defined for any amplitude without subdivergences and its vanishing is a necessary and sufficient condition for the convergence of such an amplitude.
Abstract: A systematic study of recursive renormalization of Feynman amplitudes is carried out both in Euclidean and in Minkowski configuration spaces. For a massless quantum field theory (QFT), we use the technique of extending associate homogeneous distributions to complete the renormalization recursion. A homogeneous (Poincare covariant) amplitude is said to be convergent if it admits a (unique covariant) extension as a homogeneous distribution. For any amplitude without subdivergences — i.e. for a Feynman distribution that is homogeneous off the full (small) diagonal — we define a renormalization invariant residue. Its vanishing is a necessary and sufficient condition for the convergence of such an amplitude. It extends to arbitrary — not necessarily primitively divergent — Feynman amplitudes. This notion of convergence is finer than the usual power counting criterion and includes cancellation of divergences.

Journal ArticleDOI
TL;DR: In this paper, the importance of the c-space for constraint satisfaction in numerical time stepping schemes is analyzed for holonomically constrained MBS modeled with the absolute coordinate approach, i.e. using the Newton-Euler equations for the individual bodies subjected to geometric constraints.

Journal ArticleDOI
TL;DR: This work gives theoretical and practical insights on how to efficiently check a large number of configurations for collision and cost and presents two efficient algorithms for their calculation: FAMOD, an approximate method based on convolution, which is independent of the size and the shape of the robot mask, and vHGW-360, an exact method based upon the van Herk-Gil-Werman morphological dilation algorithm.
Abstract: Collision checking is the major computational bottleneck for many robot path and motion planning applications, such as for autonomous vehicles, particularly with grid-based environment representations. Apart from collisions, many applications benefit from incorporating costs into planning; cost functions or cost maps are a common tool. Similar to checking a single configuration for collision, evaluating its cost using a grid-based cost map also requires examining every cell under the robot footprint. This work gives theoretical and practical insights on how to efficiently check a large number of configurations for collision and cost. As part of this work, configuration space costs are formulated, which can be seen as generalization of configuration space obstacles allowing a complete configuration check incorporating the robot geometry to be done using a single lookup. Furthermore, this paper presents two efficient algorithms for their calculation: FAMOD, an approximate method based on convolution, which is independent of the size and the shape of the robot mask, and vHGW-360, an exact method based on the van Herk-Gil-Werman morphological dilation algorithm, which can be used if the robot shape is rectangular. Both algorithms were implemented and evaluated on graphics hardware to demonstrate the applicability and benefit to real-time path and motion planning systems.

Posted Content
TL;DR: This work introduces an alternative approach which aims at achieving empirical adequacy with a more modest ontological complexity, and provides some preliminary evidence for optimism regarding the (once popular but prematurely-abandoned) program of trying to replace the configuration space wave function with a (totally unproblematic) set of fields in ordinary physical space.
Abstract: The ontology of Bohmian mechanics includes both the universal wave function (living in 3N-dimensional configuration space) and particles (living in ordinary 3-dimensional physical space). Proposals for understanding the physical significance of the wave function in this theory have included the idea of regarding it as a physically-real field in its 3N-dimensional space, as well as the idea of regarding it as a law of nature. Here we introduce and explore a third possibility in which the configuration space wave function is simply eliminated -- replaced by a set of single-particle pilot-wave fields living in ordinary physical space. Such a re-formulation of the Bohmian pilot-wave theory can exactly reproduce the statistical predictions of ordinary quantum theory. But this comes at the rather high ontological price of introducing an infinite network of interacting potential fields (living in 3-dimensional space) which influence the particles' motion through the pilot-wave fields. We thus introduce an alternative approach which aims at achieving empirical adequacy (like that enjoyed by GRW type theories) with a more modest ontological complexity, and provide some preliminary evidence for optimism regarding the (once popular but prematurely-abandoned) program of trying to replace the (philosophically puzzling) configuration space wave function with a (totally unproblematic) set of fields in ordinary physical space.

Patent
19 Nov 2014
TL;DR: In this article, a path planning method for robot fast collision avoidance using a BBRrt algorithm and a collision detection algorithm based on the convex set theory, extending alternatively from initial configuration and target configuration to opposite configuration form two balance RRT trees, quickly finding, in a configuration space, a collision-free motion path connecting the original configuration and the target configuration.
Abstract: An embodiment of the invention provides a path planning method for robot fast collision avoidance. The method comprises using a BBRrt algorithm and a collision detection algorithm based on the convex set theory, extending alternatively from initial configuration and target configuration to opposite configuration form two balance RRT trees, quickly finding, in a configuration space, a collision-free motion path connecting the initial configuration and the target configuration, effectively passing through a narrow channel and avoiding collision with obstacles in the environment, making full use of a multi-step expansion method and a balance extension method with an inspiring purpose, and thus effectively improving the convergence and repeatability of the RRT algorithm. Based on the convex set theory, a convex hull fast collision detection algorithm constituted by a linear inequation group is provided, and the efficiency and performance of a collision detection module in the path planning method for collision avoidance can be improved. The method provided by the invention can be extended to high-dimensional robot multi-tree RRT path planning.

Journal ArticleDOI
Jie Xu1, Pingwen Zhang1
TL;DR: In this paper, the authors proposed a minimal set of order parameters for bent-core molecules with C 2v symmetry, based on the analysis of the impact of coefficients, which helps to choose independent variables in the moments as order parameters.
Abstract: Density functional theory is used to describe the phase behaviors of rigid molecules. The construction of the kernel function is discussed. Excluded-volume potential is calculated for two types of molecules with C 2v symmetry. Molecular symmetries lead to the symmetries of the kernel function and the density function, enabling a reduction of configuration space. By approximating the kernel function with a polynomial, the system can be fully characterized by some moments corresponding to the form of the kernel function. The symmetries of the kernel function determine the form of the polynomial, while the coefficients are determined by the temperature and molecular parameters. The analysis of the impact of coefficients helps us to choose independent variables in the moments as order parameters. Combining the analysis and some simulation results, we propose a minimal set of order parameters for bent-core molecules.

Journal ArticleDOI
28 Aug 2014
TL;DR: In this article, the authors consider path following control of planar snake robots using virtual holonomic constraints and derive the Euler-Lagrange equations of motion of the system.
Abstract: This paper considers path following control of planar snake robots using virtual holonomic constraints. In order to present a model-based path following control design for the snake robot, we first derive the Euler-Lagrange equations of motion of the system. Subsequently, we define geometric relations among the generalized coordinates of the system, using the method of virtual holonomic constraints. These appropriately defined constraints shape the geometry of a constraint manifold for the system, which is a submanifold of the configuration space of the robot. Furthermore, we show that the constraint manifold can be made invariant by a suitable choice of feedback. In particular, we analytically design a smooth feedback control law to exponentially stabilize the constraint manifold. We show that enforcing the appropriately defined virtual holonomic constraints for the configuration variables implies that the robot converges to and follows a desired geometric path. Numerical simulations and experimental results are presented to validate the theoretical approach.

Journal ArticleDOI
TL;DR: In this article, the configuration space and kinematic symmetry groups for identical particles in one-dimensional traps experiencing Galilean-invariant two-body interactions were analyzed. But the authors focused on the symmetries of one, two and three particles in asymmetric, symmetric, and harmonic traps.
Abstract: This is the first in a pair of articles that classify the configuration space and kinematic symmetry groups for $N$ identical particles in one-dimensional traps experiencing Galilean-invariant two-body interactions. These symmetries explain degeneracies in the few-body spectrum and demonstrate how tuning the trap shape and the particle interactions can manipulate these degeneracies. The additional symmetries that emerge in the non-interacting limit and in the unitary limit of an infinitely strong contact interaction are sufficient to algebraically solve for the spectrum and degeneracy in terms of the one-particle observables. Symmetry also determines the degree to which the algebraic expressions for energy level shifts by weak interactions or nearly-unitary interactions are universal, i.e.\ independent of trap shape and details of the interaction. Identical fermions and bosons with and without spin are considered. This article sequentially analyzes the symmetries of one, two and three particles in asymmetric, symmetric, and harmonic traps; the sequel article treats the $N$ particle case.