Showing papers on "Configuration space published in 2015"
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TL;DR: This paper proves asymptotic optimality for a number of variations on FMT*, namely when the configuration space is sampled non-uniformly, when the cost is not arc length, and when connections are made based on the number of nearest neighbors instead of a fixed connection radius.
Abstract: In this paper we present a novel probabilistic sampling-based motion planning algorithm called the Fast Marching Tree algorithm FMT*. The algorithm is specifically aimed at solving complex motion planning problems in high-dimensional configuration spaces. This algorithm is proven to be asymptotically optimal and is shown to converge to an optimal solution faster than its state-of-the-art counterparts, chiefly PRM* and RRT*. The FMT* algorithm performs a 'lazy' dynamic programming recursion on a predetermined number of probabilistically drawn samples to grow a tree of paths, which moves steadily outward in cost-to-arrive space. As such, this algorithm combines features of both single-query algorithms chiefly RRT and multiple-query algorithms chiefly PRM, and is reminiscent of the Fast Marching Method for the solution of Eikonal equations. As a departure from previous analysis approaches that are based on the notion of almost sure convergence, the FMT* algorithm is analyzed under the notion of convergence in probability: the extra mathematical flexibility of this approach allows for convergence rate bounds-the first in the field of optimal sampling-based motion planning. Specifically, for a certain selection of tuning parameters and configuration spaces, we obtain a convergence rate bound of order On −1/d+? , where n is the number of sampled points, d is the dimension of the configuration space, and ? is an arbitrarily small constant. We go on to demonstrate asymptotic optimality for a number of variations on FMT*, namely when the configuration space is sampled non-uniformly, when the cost is not arc length, and when connections are made based on the number of nearest neighbors instead of a fixed connection radius. Numerical experiments over a range of dimensions and obstacle configurations confirm our theoretical and heuristic arguments by showing that FMT*, for a given execution time, returns substantially better solutions than either PRM* or RRT*, especially in high-dimensional configuration spaces and in scenarios where collision-checking is expensive.
369 citations
TL;DR: The theory of FI-modules was introduced and developed in this paper, and it is shown that for any fixed degree the character is given, for n large enough, by a polynomial in the cycle-counting functions that is independent of n.
Abstract: In this paper we introduce and develop the theory of FI-modules. We apply this theory to obtain new theorems about: • the cohomology of the configuration space of n distinct ordered points on an arbitrary (connected, oriented) manifold; • the diagonal coinvariant algebra on r sets of n variables; • the cohomology and tautological ring of the moduli space of n -pointed curves; • the space of polynomials on rank varieties of n × n matrices; • the subalgebra of the cohomology of the genus n Torelli group generated by H 1 ; and more. The symmetric group S n acts on each of these vector spaces. In most cases almost nothing is known about the characters of these representations, or even their dimensions. We prove that in each fixed degree the character is given, for n large enough, by a polynomial in the cycle-counting functions that is independent of n . In particular, the dimension is eventually a polynomial in n . In this framework, representation stability (in the sense of Church–Farb) for a sequence of S n -representations is converted to a finite generation property for a single FI-module.
318 citations
TL;DR: A method for finding minimum energy paths of transitions in magnetic systems, named geodesic nudged elastic band (GNEB), and its implementation are illustrated with calculations of complex transitions involving annihilation and creation of skyrmion and antivortex states.
179 citations
TL;DR: In this article, a permutation blocking path integral Monte Carlo (PIMC) simulation of strongly degenerate non-ideal fermions at finite temperature by combining a fourth-order factorization of the density matrix with antisymmetric propagators between all imaginary time slices is presented.
Abstract: Correlated fermions are of high interest in condensed matter (Fermi liquids, Wigner molecules), cold atomic gases and dense plasmas. Here we propose a novel approach to path integral Monte Carlo (PIMC) simulations of strongly degenerate non-ideal fermions at finite temperature by combining a fourth-order factorization of the density matrix with antisymmetric propagators, i.e., determinants, between all imaginary time slices. To efficiently run through the modified configuration space, we introduce a modification of the widely used continuous space worm algorithm, which allows for an efficient sampling at arbitrary system parameters. We demonstrate how the application of determinants achieves an effective blocking of permutations with opposite signs, leading to a significant relieve of the fermion sign problem. To benchmark the capability of our method regarding the simulation of degenerate fermions, we consider multiple electrons in a quantum dot and compare our results with other ab initio techniques, where they are available. The present permutation blocking PIMC approach allows us to obtain accurate results even for N = 20 electrons at low temperature and arbitrary coupling, where no other ab initio results have been reported, so far.
126 citations
TL;DR: In this paper, a tracking control scheme for spacecraft formation flying with a decentralized collision-avoidance scheme, using a virtual leader state trajectory, is presented, where each spacecraft tracks a desired relative configuration with respect to the virtual leader in an autonomous manner, to achieve the desired formation.
Abstract: This paper presents a tracking control scheme for spacecraft formation flying with a decentralized collision-avoidance scheme, using a virtual leader state trajectory. The configuration space for a spacecraft is the Lie group SE(3), which is the set of positions and orientations in three-dimensional Euclidean space. A virtual leader trajectory, in the form of attitude and orbital motion of a virtual satellite, is generated offline. Each spacecraft tracks a desired relative configuration with respect to the virtual leader in an autonomous manner, to achieve the desired formation. The relative configuration between a spacecraft and the virtual leader is described in terms of exponential coordinates on SE(3). A continuous-time feedback tracking control scheme is designed using these exponential coordinates and the relative velocities. A Lyapunov analysis guarantees that the spacecraft asymptotically converge to their desired state trajectories. This tracking control scheme is combined with a decentralized co...
121 citations
TL;DR: A novel approach to estimate the distance between a generic point in the Cartesian space and objects detected with a depth sensor and an application to human-robot collision avoidance using a KUKA LWR IV robot and a Microsoft Kinect sensor illustrates the effectiveness of the approach.
Abstract: We present a novel approach to estimate the distance between a generic point in the Cartesian space and objects detected with a depth sensor. This information is crucial in many robotic applications, e.g., for collision avoidance, contact point identification, and augmented reality. The key idea is to perform all distance evaluations directly in the depth space. This allows distance estimation by considering also the frustum generated by the pixel on the depth image, which takes into account both the pixel size and the occluded points. Different techniques to aggregate distance data coming from multiple object points are proposed. We compare the Depth space approach with the commonly used Cartesian space or Configuration space approaches, showing that the presented method provides better results and faster execution times. An application to human-robot collision avoidance using a KUKA LWR IV robot and a Microsoft Kinect sensor illustrates the effectiveness of the approach.
110 citations
TL;DR: In this article, the authors analyse the behavior of the bootstrap current in the configuration space of W7-X by self-consistent neoclassical transport simulations, focusing on high-performance discharge scenarios in magnetic configurations.
Abstract: The neoclassical confinement and the bootstrap current are analysed in the configuration space of W7-X by self-consistent neoclassical transport simulations. Since the establishment of quasi-stationary operation is the most important goal for W7-X, the analysis concentrates on high-performance discharge scenarios in magnetic configurations which are adjusted so that bootstrap current vanishes, or, alternatively, on scenarios where the bootstrap current can be balanced by strong ECCD. Both scenarios lead to restrictions either in the configuration space or in plasma parameters and ECRH heating scenarios. Furthermore, the flexibility of the magnetic configuration space of W7-X is briefly described with emphasis on other physics topics of interest, for example, ballooning unstable configurations as well as configurations with a magnetic hill which might lead to interchange instability.
100 citations
TL;DR: The manifold particle filter is introduced as a principled way of solving the state estimation problem when the state moves between multiple manifolds of different dimensionality and avoids particle starvation during contact by adaptively sampling particles that reside on the contact manifold from the dual proposal distribution.
Abstract: We investigate the problem of using contact sensors to estimate the pose of an object during planar pushing by a fixed-shape hand. Contact sensors are unique because they inherently discriminate between ?contact? and ?no-contact? configurations. As a result, the set of object configurations that activates a sensor constitutes a lower-dimensional contact manifold in the configuration space of the object. This causes conventional state estimation methods, such as the particle filter, to perform poorly during periods of contact due to particle starvation. In this paper, we introduce the manifold particle filter as a principled way of solving the state estimation problem when the state moves between multiple manifolds of different dimensionality. The manifold particle filter avoids particle starvation during contact by adaptively sampling particles that reside on the contact manifold from the dual proposal distribution. We describe three techniques, one analytical and two sample-based, of sampling from the dual proposal distribution and compare their relative strengths and weaknesses. We present simulation results that show that all three techniques outperform the conventional particle filter in both speed and accuracy. In addition, we implement the manifold particle filter on a real robot and show that it successfully tracks the pose of a pushed object using commercially available tactile sensors.
86 citations
TL;DR: A connection between the kinetic transition network treatment of dynamics and a potential of mean force defined by a reaction coordinate is developed, providing insight into the physical origins of "friction" effects in low-dimensionality descriptions of dynamics based upon a reactioncoordinate.
Abstract: This perspective focuses on conceptual and computational aspects of the potential energy landscape framework. It has two objectives: first to summarise some key developments of the approach and second to illustrate how such techniques can be applied using a specific example that exploits knowledge of pathways. Recent developments in theory and simulation within the landscape framework are first outlined, including methods for structure prediction, analysis of global thermodynamic properties, and treatment of rare event dynamics. We then develop a connection between the kinetic transition network treatment of dynamics and a potential of mean force defined by a reaction coordinate. The effect of projection from the full configuration space to low dimensionality is illustrated for an atomic cluster. In this example, where a relatively successful structural order parameter is available, the principal change in cluster morphology is reproduced, but some details are not faithfully represented. In contrast, a profile based on configurations that correspond to the discrete path defined geometrically retains all the barriers and minima. This comparison provides insight into the physical origins of “friction” effects in low-dimensionality descriptions of dynamics based upon a reaction coordinate.
84 citations
TL;DR: This work discusses how one can combine such local descriptors using a regularized entropy match (REMatch) approach to describe the similarity of both whole molecular and bulk periodic structures, introducing powerful metrics that enable the navigation of alchemical and structural complexities within a unified framework.
Abstract: Evaluating the (dis)similarity of crystalline, disordered and molecular compounds is a critical step in the development of algorithms to navigate automatically the configuration space of complex materials. For instance, a structural similarity metric is crucial for classifying structures, searching chemical space for better compounds and materials, and driving the next generation of machine-learning techniques for predicting the stability and properties of molecules and materials. In the last few years several strategies have been designed to compare atomic coordination environments. In particular, the Smooth Overlap of Atomic Positions (SOAP) has emerged as an elegant framework to obtain translation, rotation and permutation-invariant descriptors of groups of atoms, driven by the design of various classes of machine-learned inter-atomic potentials. Here we discuss how one can combine such local descriptors using a Regularized Entropy Match (REMatch) approach to describe the similarity of both whole molecular and bulk periodic structures, introducing powerful metrics that enable the navigation of alchemical and structural complexity within a unified framework. Furthermore, using this kernel and a ridge regression method we can predict atomization energies for a database of small organic molecules with a mean absolute error below 1kcal/mol, reaching an important milestone in the application of machine-learning techniques to the evaluation of molecular properties.
74 citations
TL;DR: The finite-time convergence of the proposed control scheme for the closed-loop system for autonomous body-fixed hovering of a rigid spacecraft over a tumbling asteroid is proved.
Abstract: A finite-time control scheme for autonomous body-fixed hovering of a rigid spacecraft over a tumbling asteroid is presented. The relative configuration between the spacecraft and asteroid is described in terms of exponential coordinates on the Lie group SE(3), which is the configuration space for the spacecraft. With a Lyapunov stability analysis, the finite-time convergence of the proposed control scheme for the closed-loop system is proved. Numerical simulations validate the performance of the proposed control scheme.
26 May 2015
TL;DR: This paper explores extending the geometric model of the robot beyond the notion of a Cartesian workspace space to fully model and leverage how geometry changes in the presence of obstacles, and develops a general motion optimization framework called Riemannian Motion Optimization (RieMO) to efficiently find motions using the authors' geometric models.
Abstract: What is it that makes movement around obstacles hard? The answer seems clear: obstacles contort the geometry of the workspace and make it difficult to leverage what we consider easy and intuitive straight-line Cartesian geometry. But is Cartesian motion actually easy? It's certainly well-understood and has numerous applications. But beneath the details of linear algebra and pseudoinverses, lies a non-trivial Riemannian metric driving the solution. Cartesian motion is easy only because the pseudoinverse, our powerhouse tool, correctly represents how Euclidean workspace geometry pulls back into the configuration space. In light of that observation, it reasons that motion through a field of obstacles could be just as easy as long as we correctly account for how those obstacles warp the geometry of the space. This paper explores extending our geometric model of the robot beyond the notion of a Cartesian workspace space to fully model and leverage how geometry changes in the presence of obstacles. Intuitively, impenetrable obstacles form topological holes and geodesics curve around them accordingly. We formalize this intuition and develop a general motion optimization framework called Riemannian Motion Optimization (RieMO) to efficiently find motions using our geometric models. Our experiments demonstrate that, for many problems, obstacle avoidance can be much more natural when placed within the right geometric context.
TL;DR: In this article, an exact spatial Kirchhoff rod structural model is considered and the configuration space for this model that has dimension 4 is obtained considering an ad hoc split of the rotation operator that implicitly enforces the constraints on the directors.
Abstract: In the paper, it is considered an exact spatial Kirchhoff rod structural model. The configuration space for this model that has dimension 4 is obtained considering an ad hoc split of the rotation operator that implicitly enforces the constraints on the directors. The tangent stiffness operator, essential for the nonlinear numerical simulations, has been studied. It has been obtained as second covariant gradient of the internal energy functional for the considered structural model that preserves symmetry for any configuration, either equilibrated or not. The result has been reached evaluating the Levi-Civita connection for the tangent space of the configuration manifold. The results obtained extend to the case of Kirchoff -Love rods those presented by Simo (Comput Methods Appl Mech Eng 49:55–70, 1985) for Timoshenko rods. Given the different structure of the tangent spaces in this case, it has been necessary to introduce a specific metric that accounts for the rotation of the intrinsic triad due to the change of the position of the centroid axis of the rod.
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TL;DR: In this article, a permutation blocking path integral Monte Carlo (PIMC) approach is proposed for strongly degenerate non-ideal fermions at finite temperature by combining a fourth-order factorization of the density matrix with antisymmetric propagators, i.e., determinants, between all imaginary time slices.
Abstract: Correlated fermions are of high interest in condensed matter (Fermi liquids, Wigner molecules), cold atomic gases and dense plasmas. Here we propose a novel approach to path integral Monte Carlo (PIMC) simulations of strongly degenerate non-ideal fermions at finite temperature by combining a fourth-order factorization of the density matrix with antisymmetric propagators, i.e., determinants, between all imaginary time slices. To efficiently run through the modified configuration space, we introduce a modification of the widely used continuous space worm algorithm, which allows for an efficient sampling at arbitrary system parameters. We demonstrate how the application of determinants achieves an effective blocking of permutations with opposite signs, leading to a significant relieve of the fermion sign problem. To benchmark the capability of our method regarding the simulation of degenerate fermions, we consider multiple electrons in a quantum dot and compare our results with other ab initio techniques, where they are available. The present permutation blocking path integral Monte Carlo approach allows us to obtain accurate results even for $N=20$ electrons at low temperature and arbitrary coupling, where no other ab initio results have been reported, so far.
TL;DR: In this article, the authors provide a tutorial overview of the Lie bracket techniques and examine how the coordinate-independent nonholonomy of these systems has a coordinate-dependent separation into non-conservative and non-commutative components that respectively capture how the system constraints vary over the shape and position components of the configuration space.
Abstract: Geometric mechanics techniques based on Lie brackets provide high-level characterizations of the motion capabilities of locomoting systems In particular, they relate the net displacement they experience over cyclic gaits to area integrals of their constraints; plotting these constraints thus provides a visual “landscape” that intuitively captures all available solutions of the system’s dynamic equations Recently, we have found that choices of system coordinates heavily influence the effectiveness of these approaches This property appears at first to run counter to the principle that differential geometric structures should be coordinate-invariant In this paper, we provide a tutorial overview of the Lie bracket techniques, then examine how the coordinate-independent nonholonomy of these systems has a coordinate-dependent separation into nonconservative and noncommutative components that respectively capture how the system constraints vary over the shape and position components of the configuration space Nonconservative constraint variations can be integrated geometrically via Stokes’ theorem, but noncommutative effects can only be approximated by similar means; therefore choices of coordinates in which the nonholonomy is primarily nonconservative improve the accuracy of the geometric techniques
TL;DR: It is demonstrated that stacked-slider phases are distinguishable states of matter; they are nonperiodic, statistically anisotropic structures that possess long-range orientational order but have zero shear modulus.
Abstract: Stealthy potentials, a family of long-range isotropic pair potentials, produce infinitely degenerate disordered ground states at high densities and crystalline ground states at low densities in d-dimensional Euclidean space R^{d}. In the previous paper in this series, we numerically studied the entropically favored ground states in the canonical ensemble in the zero-temperature limit across the first three Euclidean space dimensions. In this paper, we investigate using both numerical and theoretical techniques metastable stacked-slider phases, which are part of the ground-state manifold of stealthy potentials at densities in which crystal ground states are favored entropically. Our numerical results enable us to devise analytical models of this phase in two, three, and higher dimensions. Utilizing this model, we estimated the size of the feasible region in configuration space of the stacked-slider phase, finding it to be smaller than that of crystal structures in the infinite-system-size limit, which is consistent with our recent previous work. In two dimensions, we also determine exact expressions for the pair correlation function and structure factor of the analytical model of stacked-slider phases and analyze the connectedness of the ground-state manifold of stealthy potentials in this density regime. We demonstrate that stacked-slider phases are distinguishable states of matter; they are nonperiodic, statistically anisotropic structures that possess long-range orientational order but have zero shear modulus. We outline some possible future avenues of research to elucidate our understanding of this unusual phase of matter.
TL;DR: A single level nonlinear controller is proposed for the point stabilization of MIP to move the MIP from one point to another point in the configuration space while stabilizing the pendulum.
TL;DR: In this article, a suite of relational notions of shape are presented at the level of configuration space geometry, with corresponding new theories of shape mechanics and shape statistics, which reveal compatibility between supersymmetry and GR-based conceptions of Background Independence.
Abstract: A suite of relational notions of shape are presented at the level of configuration space geometry, with corresponding new theories of shape mechanics and shape statistics. These further generalize two quite well known examples: --1) Kendall's (metric) shape space with his shape statistics and Barbour's mechanics thereupon. 0) Leibnizian relational space alias metric scale-and-shape space to which corresponds Barbour-Bertotti mechanics. This paper's new theories include, using the invariant and group namings, 1) $Angle$ alias $conformal$ $shape$ $mechanics$. 2) $Area ratio$ alias $affine$ $shape$ $mechanics$. 3) $ Area$ alias $affine$ $scale$-$and$-$shape$ $mechanics$. 1) to 3) rest respectively on angle space, area-ratio space, and area space configuration spaces. Probability and statistics applications are also pointed to in outline.
4) Various supersymmetric counterparts of -1) to 3) are considered. Since supergravity differs considerably from GR-based conceptions of Background Independence, some of the new supersymmetric shape mechanics are compared with both. These reveal compatibility between supersymmetry and GR-based conceptions of Background Independence, at least within these simpler model arenas.
15 Apr 2015
TL;DR: In this paper, the authors elucidate relations between different approaches to describing the non-associative deformations of geometry that arise in non-geometric string theory and demonstrate how to derive configuration space triproducts exactly from non-aggregated phase space star products and extend the relationship in various directions.
Abstract: We elucidate relations between different approaches to describing the nonassociative deformations of geometry that arise in non-geometric string theory. We demonstrate how to derive configuration space triproducts exactly from nonassociative phase space star products and extend the relationship in various directions. By foliating phase space with leaves of constant momentum we obtain families of Moyal-Weyl type deformations of triproducts, and we generalize them to new triproducts of differential forms and of tensor fields. We prove that nonassociativity disappears on-shell in all instances. We also extend our considerations to the differential geometry of nonassociative phase space, and study the induced deformations of configuration space diffeomorphisms. We further develop general prescriptions for deforming configuration space geometry from the nonassociative geometry of phase space, thus paving the way to a nonassociative theory of gravity in non-geometric flux compactifications of string theory.
TL;DR: In this paper, a short review describes singularities appearing in both types of systems under a unified framework, presenting a classification of singularities into two broad categories: weak-noise limit singularities and large deviation functions.
Abstract: Large deviation functions of configurations exhibit very different behaviors in and out of thermal equilibrium. In particular, they exhibit singularities in a broad range of non-equilibrium models, which are absent in equilibrium. These singularities were first identified in finite-dimensional systems in the weak-noise limit. Recent studies have shown that they are also present in driven diffusive systems with an infinite-dimensional configuration space. This short review describes singularities appearing in both types of systems under a unified framework, presenting a classification of singularities into two broad categories. The types of singularities which were identified for finite-dimensional cases are compared to those found in driven diffusive systems.
TL;DR: In this paper, the authors present new configuration space construction algorithms based on machine learning and geometric approximation techniques, which perform collision queries on many configuration samples and use the collision query results to compute an approximate representation for the configuration space, which quickly converge to the exact configuration space.
TL;DR: In this article, a 3-SPS/S redundant motion mechanism with kinematic redundancy is proposed to reduce the unnecessary degree of freedom for the yaw and pitch motions in the configuration space.
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TL;DR: A suite of relational notions of shape are presented at the level of configuration space geometry, with corresponding new theories of shape mechanics and shape statistics as mentioned in this paper, which reveal compatibility between supersymmetry and GR-based conceptions of background independence.
Abstract: A suite of relational notions of shape are presented at the level of configuration space geometry, with corresponding new theories of shape mechanics and shape statistics. These further generalize two quite well known examples: -1) Kendall's (metric) shape space with his shape statistics and Barbour's mechanics thereupon. 0) Leibnizian relational space alias metric scale-and-shape space to which corresponds Barbour--Bertotti mechanics. This paper's new theories include, using the invariant and group namings, 1) $Angle$ alias $conformal$ $shape$ $mechanics$. 2) $Area$ $ratio$ alias $affine$ $shape$ $mechanics$. 3) $Area$ alias $affine$ $scale$-$and$-$shape$ $mechanics$. 1) to 3) rest respectively on angle space, area-ratio space, and area space configuration spaces. Affine shape matching and affine shape statistics are argued to be of value to the theory of image analysis, as are in another sense their projective counterparts which rest on the geometry of cross-ratio space (another configuration space). The shape statistics of -1) and 0) are argued to be of value in robotics.
4) Various supersymmetric counterparts of -1) to 3) are considered. Since supergravity differs considerably from GR-based conceptions of background independence, some of the new supersymmetric shape mechanics are compared with both. These reveal compatibility between supersymmetry and GR-based conceptions of background independence, at least within these simpler model arenas.
TL;DR: In this paper, the Penetration Depth (PD) between general polygonal models based on iterative and local optimization techniques is found. But, the method requires a large number of triangles and is computationally expensive.
Abstract: We present a real-time algorithm that finds the Penetration Depth (PD) between general polygonal models based on iterative and local optimization techniques. Given an in-collision configuration of an object in configuration space, we find an initial collision-free configuration using several methods such as centroid difference, maximally clear configuration, motion coherence, random configuration, and sampling-based search. We project this configuration on to a local contact space using a variant of continuous collision detection algorithm and construct a linear convex cone around the projected configuration. We then formulate a new projection of the in-collision configuration onto the convex cone as a Linear Complementarity Problem (LCP), which we solve using a type of Gauss-Seidel iterative algorithm. We repeat this procedure until a locally optimal PD is obtained. Our algorithm can process complicated models consisting of tens of thousands triangles at interactive rates.
TL;DR: In this paper, the authors introduce and explore a third possibility in which the configuration space wave function is simply eliminated and replaced by a set of single-particle pilot-wave fields living 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.
01 Dec 2015
TL;DR: This thesis presents a new framework for multirobot path planning called subdimensional expansion, which initially plans for each robot individually, and then coordinates motion among the robots as needed, and presents the Constraint Manifold Subsearch (CMS) algorithm to solve problems where robots must dynamically form and dissolve teams with other robots to perform cooperative tasks.
Abstract: Planning optimal paths for large numbers of robots is computationally expensive. In this thesis, we present a new framework for multirobot path planning called subdimensional expansion, which initially plans for each robot individually, and then coordinates motion among the robots as needed. More specifically subdimensional expansion initially creates a one-dimensional search space embedded in the joint configuration space of the multirobot system. When the search space is found to be blocked during planning by a robot-robot collision, the dimensionality of the search space is locally increased to ensure that an alternative path can be found. As a result, robots are only coordinated when necessary, which reduces the computational cost of finding a path. Subdimensional expansion is a exible framework that can be used with multiple planning algorithms. For discrete planning problems, subdimensional expansion can be combined with A* to produce the M* algorithm, a complete and optimal multirobot path planning problem. When the configuration space of individual robots is too large to be explored effectively with A*, subdimensional expansion can be combined with probabilistic planning algorithms to produce sRRT and sPRM. M* is then extended to solve variants of the multirobot path planning algorithm. We present the Constraint Manifold Subsearch (CMS) algorithm to solve problems where robots must dynamically form and dissolve teams with other robots to perform cooperative tasks. Uncertainty M* (UM*) is a variant of M* that handles systems with probabilistic dynamics. Finally, we apply M* to multirobot sequential composition. Results are validated with extensive simulations and experiments on multiple physical robots.
TL;DR: Applications are given to LE/CT mixing in π-stacked systems, charge-recombination matrix elements in a hetero-dimer, and excitonic couplings in multi-chromophoric systems.
Abstract: We present a general method for analyzing the character of singly excited states in terms of charge transfer (CT) and locally excited (LE) configurations. The analysis is formulated for configuration interaction singles (CIS) singly excited wave functions of aggregate systems. It also approximately works for the second-order approximate coupled cluster singles and doubles and the second-order algebraic-diagrammatic construction methods [CC2 and ADC(2)]. The analysis method not only generates a weight of each character for an excited state, but also allows to define the related quasi-diabatic states and corresponding coupling matrix elements. In the character analysis approach, we divide the target system into domains and use a modified Pipek-Mezey algorithm to localize the canonical MOs on each domain, respectively. The CIS wavefunction is then transformed into the localized basis, which allows us to partition the wavefunction into LE configurations within domains and CT configuration between pairs of different domains. Quasi-diabatic states are then obtained by mixing excited states subject to the condition of maximizing the weight of one single LE or CT configuration (localization in configuration space). Different aims of such a procedure are discussed, either the construction of pure LE and CT states for analysis purposes (by including a large number of excited states) or the construction of effective models for dynamics calculations (by including a restricted number of excited states). Applications are given to LE/CT mixing in π-stacked systems, charge-recombination matrix elements in a hetero-dimer, and excitonic couplings in multi-chromophoric systems.
TL;DR: In this paper, the authors show that the pseudogenerators up to order 4 in the Taylor expansion of this family have particularly simple explicit expressions involving no momentum averaging, which makes collocation methods particularly easy to implement and computationally efficient, which in turn may open the door for furt.
Abstract: Metastable behavior in dynamical systems may be a significant challenge for a simulation-based analysis. In recent years, transfer operator--based approaches to problems exhibiting metastability have matured. In order to make these approaches computationally feasible for larger systems, various reduction techniques have been proposed: For example, Schutte introduced a spatial transfer operator which acts on densities on configuration space, while Weber proposed to avoid trajectory simulation (like Froyland, Junge, and Koltai) by considering a discrete generator. In this paper, we show that even though the family of spatial transfer operators is not a semigroup, it possesses a well-defined generating structure. What is more, the pseudogenerators up to order 4 in the Taylor expansion of this family have particularly simple explicit expressions involving no momentum averaging. This makes collocation methods particularly easy to implement and computationally efficient, which in turn may open the door for furt...
TL;DR: In this article, a sliding mode control scheme for autonomous spacecraft formation flying via a virtual leader state trajectory is presented, where each spacecraft tracks a desired relative configuration with respect to the virtual leader in a decentralized and autonomous manner.
Abstract: This paper presents a sliding mode control scheme on for autonomous spacecraft formation flying via a virtual leader state trajectory. The configuration space for a spacecraft is the Lie group SE(3), which is the set of positions and orientations of the rigid spacecraft in three-dimensional (3D) Euclidean space. A virtual leader trajectory, in the form of natural attitude and translational (orbital) motion of a satellite, is generated offline. Each spacecraft tracks a desired relative configuration with respect to the virtual leader in a decentralized and autonomous manner to achieve the desired formation. The relative configuration between each spacecraft and the virtual leader is described in terms of exponential coordinates on SE(3). A new feedback control scheme is proposed for coupled translational and rotational maneuver using a new sliding surface, which is defined as the exponential coordinates and velocity tracking errors such that the sliding surface converges to zero without explicit re...
TL;DR: It is shown that spurious oscillations in the transient phase result from order reduction that may be avoided by a perturbation of starting values or by index reduction, and is analysed by a coupled one-step error recursion for differential and algebraic solution components.
Abstract: Generalized- $$\alpha $$ ? methods are very popular in structural dynamics. They are methods of Newmark type and combine favourable stability properties with second order convergence for unconstrained second order systems in linear spaces. Recently, they were extended to constrained systems in flexible multibody dynamics that have a configuration space with Lie group structure. In the present paper, the convergence of these Lie group methods is analysed by a coupled one-step error recursion for differential and algebraic solution components. It is shown that spurious oscillations in the transient phase result from order reduction that may be avoided by a perturbation of starting values or by index reduction. Numerical tests for a benchmark problem from the literature illustrate the results of the theoretical investigations.