scholarly journals Free space of rigid objects: caging, path non-existence, and narrow passage detection

2020 ◽  
pp. 027836492093299
Author(s):  
Anastasiia Varava ◽  
J. Frederico Carvalho ◽  
Danica Kragic ◽  
Florian T. Pokorny
Keyword(s):  
Configuration Space ◽  
Three Dimensions ◽  
Robotic Manipulation ◽  
Configuration Spaces ◽  
Finite Sample ◽  
Fine Grained ◽  
Rigid Objects ◽  
Uniform Grids ◽  
Narrow Passage ◽  
Object Shapes

In this work, we propose algorithms to explicitly construct a conservative estimate of the configuration spaces of rigid objects in two and three dimensions. Our approach is able to detect compact path components and narrow passages in configuration space which are important for applications in robotic manipulation and path planning. Moreover, as we demonstrate, they are also applicable to identification of molecular cages in chemistry. Our algorithms are based on a decomposition of the resulting three- and six-dimensional configuration spaces into slices corresponding to a finite sample of fixed orientations in configuration space. We utilize dual diagrams of unions of balls and uniform grids of orientations to approximate the configuration space. Furthermore, we carry out experiments to evaluate the computational efficiency on a set of objects with different geometric features thus demonstrating that our approach is applicable to different object shapes. We investigate the performance of our algorithm by computing increasingly fine-grained approximations of the object’s configuration space. A multithreaded implementation of our approach is shown to result in significant speed improvements.

scholarly journals Stringy canonical forms and binary geometries from associahedra, cyclohedra and generalized permutohedra

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Song He ◽  
Zhenjie Li ◽  
Prashanth Raman ◽  
Chi Zhang
Keyword(s):  
Large Class ◽  
Configuration Space ◽  
Moduli Space ◽  
Cluster Algebras ◽  
Configuration Spaces ◽  
Minkowski Sum ◽  
Canonical Forms ◽  
Infinite Class ◽  
Special Cases ◽  
Generalized Associahedra

Abstract Stringy canonical forms are a class of integrals that provide α′-deformations of the canonical form of any polytopes. For generalized associahedra of finite-type cluster algebras, there exist completely rigid stringy integrals, whose configuration spaces are the so-called binary geometries, and for classical types are associated with (generalized) scattering of particles and strings. In this paper, we propose a large class of rigid stringy canonical forms for another class of polytopes, generalized permutohedra, which also include associahedra and cyclohedra as special cases (type An and Bn generalized associahedra). Remarkably, we find that the configuration spaces of such integrals are also binary geometries, which were suspected to exist for generalized associahedra only. For any generalized permutohedron that can be written as Minkowski sum of coordinate simplices, we show that its rigid stringy integral factorizes into products of lower integrals for massless poles at finite α′, and the configuration space is binary although the u equations take a more general form than those “perfect” ones for cluster cases. Moreover, we provide an infinite class of examples obtained by degenerations of type An and Bn integrals, which have perfect u equations as well. Our results provide yet another family of generalizations of the usual string integral and moduli space, whose physical interpretations remain to be explored.

ADD-RRV for motion planning in complex environments

Robotica ◽  
2021 ◽  
pp. 1-18
Author(s):  
Peng Cai ◽  
Xiaokui Yue ◽  
Hongwen Zhang
Keyword(s):  
Principal Component Analysis ◽  
Motion Planning ◽  
Configuration Space ◽  
Principal Component ◽  
Component Analysis ◽  
Planning Method ◽  
Complex Environments ◽  
Local Configuration ◽  
Narrow Passage

Abstract In this paper, we present a novel sampling-based motion planning method in various complex environments, especially with narrow passages. We use online the results of the planner in the ADD-RRT framework to identify the types of the local configuration space based on the principal component analysis (PCA). The identification result is then used to accelerate the expansion similar to RRV around obstacles and through narrow passages. We also propose a modified bridge test to identify the entrance of a narrow passage and boost samples inside it. We have compared our method with known motion planners in several scenarios through simulations. Our method shows the best performance across all the tested planners in the tested scenarios.

scholarly journals Impact of Position and Orientation of RFID Tags on Real Time Asset Tracking in a Supply Chain

2008 ◽  
Vol 3 (1) ◽  
pp. 1-12
Author(s):  
Sidney D’Mello ◽  
Eric Mathews ◽  
Lee McCauley ◽  
James Markham
Keyword(s):  
Supply Chain ◽  
Real World ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Rfid Tags ◽  
Vertical Orientation ◽  
Fine Grained ◽  
Asset Tracking ◽  
Transverse Electromagnetic ◽  
World Environment

We studied the characteristics of four commercially available RFID tags such as their orientation on an asset and their position in a three dimensional real world environment to obtain comprehensive data to substantiate a baseline for the use of RFID technology in a diverse supply chain management setting. Using RFID tags manufactured by four different vendors and a GHz Transverse Electromagnetic (GTEM) cell, in which an approximately constant electromagnetic (EM) field was maintained, we characterized the tags based on horizontal and vertical orientation on a simulated asset. With these baseline characteristics determined, we moved two of the four tags through a real world environment in three dimensions using an industrial robotic system to determine the effect of asset position in relation to the reader on tag readability. Combining the data collected over these two studies, we provide a rich analysis of the feasibility of asset tracking in a real world supply chain, where there would likely be multiple tag types. We offer fine grained analyses of the tag types and make recommendations for diverse supply chain asset tracking.

Intelligent Robot Systems for Manipulation of Non-Rigid Objects

2017 ◽  
Vol 260 ◽  
pp. 20-29 ◽  
Author(s):  
Nikos A. Aspragathos
Keyword(s):  
Main Part ◽  
State Of The Art ◽  
Robotic Manipulation ◽  
Robotic Systems ◽  
Elastic Behavior ◽  
Intelligent Robot ◽  
Bending Rigidity ◽  
Future Directions ◽  
Rigid Objects ◽  
Robot Systems

In this paper, methodologies are presented for the development of intelligent robot systems for the manipulation of linear and sheet like objects with low and/or very low bending rigidity. In the introduction the non-rigid objects are defined and classified considering their shape, bending rigidity and extensibility. The industrial and service applications of these systems are presented and the state of the art approaches for the manipulation of various categories of the non-rigid objects are presented. A brief State-of the-Art on the manipulation of the deformable objects with relatively low bending rigidity and presenting elastic behavior like foam, sheet metal is presented as well.The main part of the paper is devoted to the robotic manipulation of the sheet-like objects with very low rigidity such as fabrics and leather. Laboratory demonstrators accompany the presentation of the developed intelligent robotic systems for manipulation of non-rigid objects and the paper concludes with hints for the future directions of the research and development in robotic systems for handling non-rigid objects.

scholarly journals On the Cohomology of the Mapping Class Group of the Punctured Projective Plane

2020 ◽  
Vol 71 (2) ◽  
pp. 539-555
Author(s):  
Miguel A Maldonado ◽  
Miguel A Xicoténcatl
Keyword(s):  
Exact Sequence ◽  
Configuration Space ◽  
Mapping Class Group ◽  
Homotopy Theory ◽  
Class Group ◽  
Orientable Surface ◽  
Configuration Spaces ◽  
Mapping Class ◽  
Serre Spectral Sequence ◽  
Classical Homotopy

Abstract The mapping class group $\Gamma ^k(N_g)$ of a non-orientable surface with punctures is studied via classical homotopy theory of configuration spaces. In particular, we obtain a non-orientable version of the Birman exact sequence. In the case of ${\mathbb{R}} \textrm{P}^2$, we analyze the Serre spectral sequence of a fiber bundle $F_k({\mathbb{R}}{\textrm{P}}^{2}) / \Sigma _k \to X_k \to BSO(3)$ where $X_k$ is a $K(\Gamma ^k({\mathbb{R}} \textrm{P}^2),1)$ and $F_k({\mathbb{R}}{\textrm{P}}^{2}) / \Sigma _k$ denotes the configuration space of unordered $k$-tuples of distinct points in ${\mathbb{R}} \textrm{P}^2$. As a consequence, we express the mod-2 cohomology of $\Gamma ^k({\mathbb{R}} \textrm{P}^2)$ in terms of that of $F_k({\mathbb{R}}{\textrm{P}}^{2}) / \Sigma _k$.

TURBULENT DIFFUSION IN TWO AND THREE DIMENSIONS BY THE RANDOM-WALK MODEL WITH MEMORY

1961 ◽  
Vol 39 (1) ◽  
pp. 133-140 ◽  
Author(s):  
R. C. Bourret
Keyword(s):  
Random Walk ◽  
Lattice Model ◽  
Turbulent Diffusion ◽  
Telegraph Equation ◽  
Three Dimensions ◽  
Autocorrelation Functions ◽  
Fine Grained ◽  
Velocity Autocorrelation ◽  
With Memory ◽  
Velocity Autocorrelation Functions

A lattice model used for the derivation of the telegraph equation for diffusion is extended to two and three dimensions. Appropriate generalizations of the telegraph equation are obtained. These equations give a fine-grained chronological description of diffusion. From these equations, the velocity autocorrelation functions of the diffusing particles are obtained.

MEASURING PROTEST FOR COMPARISONS: MULTIDIMENSIONAL SCALING OF ACTION, MESSAGE, AND COMMUNITY*

2020 ◽  
Vol 25 (3) ◽  
pp. 339-363
Author(s):  
Kevin Reuning ◽  
Lee Ann Banaszak
Keyword(s):  
Public Discourse ◽  
Three Dimensions ◽  
Multidimensional Space ◽  
Social Movement Organizations ◽  
Fine Grained ◽  
Multidimensional Measure ◽  
Multiple Dimensions ◽  
Confirmatory Factor ◽  
Movement Organizations ◽  
Direct Change

We introduce a fine-grained method of categorizing protests by their strategies and tactics that places protests in a multidimensional space based on motivations—direct change towards a policy or goal; changing public discourse narratives; and building movement identities or communities. This technique recognizes that multiple motivations may exist and allows protests to be compared based on where they are in multiple dimensions. To test our method and the theoretical dimensions we hypothesize, we surveyed protesters at the 2016 Republican and Democratic National Conventions. Using questions about participant goals and targets, and confirmatory factor analysis, we corroborate the existence of three dimensions. We show these dimensions provide real information about the differences between protests outside the two conventions. We conclude by discussing how our multidimensional measure can be extended to other events, social movement organizations, or whole movements to facilitate comparisons of events, organizations, or movements across time and space.

HARMONIC ANALYSIS ON CONFIGURATION SPACE I: GENERAL THEORY

2002 ◽  
Vol 05 (02) ◽  
pp. 201-233 ◽  
Author(s):  
YURI G. KONDRATIEV ◽  
TOBIAS KUNA
Keyword(s):  
Fourier Transform ◽  
Harmonic Analysis ◽  
Configuration Space ◽  
Riemannian Manifolds ◽  
Characterization Theorem ◽  
Configuration Spaces ◽  
Probability Measures ◽  
Correlation Measures ◽  
Underlying Manifold ◽  
Lifting Operator

We develop a combinatorial version of harmonic analysis on configuration spaces over Riemannian manifolds. Our constructions are based on the use of a lifting operator which can be considered as a kind of (combinatorial) Fourier transform in the configuration space analysis. The latter operator gives us a natural lifting of the geometry from the underlying manifold onto the configuration space. Properties of correlation measures for given states (i.e. probability measures) on configuration spaces are studied including a characterization theorem for correlation measures.

scholarly journals MORSE THEORY AND THE TOPOLOGY OF CONFIGURATION SPACE

1996 ◽  
Vol 11 (05) ◽  
pp. 823-843
Author(s):  
W.D. McGLINN ◽  
L. O’RAIFEARTAIGH ◽  
S. SEN ◽  
R.D. SORKIN
Keyword(s):  
Potential Function ◽  
Configuration Space ◽  
Morse Theory ◽  
Three Dimensional ◽  
Configuration Spaces ◽  
Arbitrary Field ◽  
Two Dimensional ◽  
Point Particles ◽  
Homology Groups ◽  
Fermi Statistics

The first and second homology groups, H1 and H2, are computed for configuration spaces of framed three-dimensional point particles with annihilation included, when up to two particles and an antiparticle are present, the types of frames considered being S2 and SO(3). Whereas a recent calculation for two-dimensional particles used the Mayer–Vietoris sequence, in the present work Morse theory is used. By constructing a potential function none of whose critical indices is less than four, we find that (for coefficients in an arbitrary field K) the homology groups H1 and H2 reduce to those of the frame space, S2 or SO(3) as the case may be. In the case of SO(3) frames this result implies that H1 (with coefficients in ℤ2) is generated by the cycle corresponding to a 2π rotation of the frame. (This same cycle is homologous to the exchange loop: the spin-statistics correlation.) It also implies that H2 is trivial, which means that there does not exist a topologically nontrivial Wess–Zumino term for SO(3) frames [in contrast to the two-dimensional case, where SO(2) frames do possess such a term]. In the case of S2 frames (with coefficients in ℝ), we conclude H2=ℝ, the generator being in effect the frame space itself. This implies that for S2 frames there does exist a Wess–Zumino term, as indeed is needed for the possibility of half-integer spin and the corresponding Fermi statistics. Taken together, these results for H1 and H2 imply that our configuration space “admits spin 1/2” for either choice of frame, meaning that the spin-statistics theorem previously proved for this space is not vacuous.

scholarly journals Topological complexity of collision-free motion planning on surfaces

2010 ◽  
Vol 147 (2) ◽  
pp. 649-660 ◽  
Author(s):  
Daniel C. Cohen ◽  
Michael Farber
Keyword(s):  
Motion Planning ◽  
Configuration Space ◽  
Main Tool ◽  
Orientable Surface ◽  
Configuration Spaces ◽  
Topological Complexity ◽  
Algebraic Varieties ◽  
Hodge Structures ◽  
Lusternik Schnirelmann ◽  
Mixed Hodge Structures

AbstractThe topological complexity$\mathsf {TC}(X)$is a numerical homotopy invariant of a topological spaceXwhich is motivated by robotics and is similar in spirit to the classical Lusternik–Schnirelmann category ofX. Given a mechanical system with configuration spaceX, the invariant$\mathsf {TC}(X)$measures the complexity of motion planning algorithms which can be designed for the system. In this paper, we compute the topological complexity of the configuration space ofndistinct ordered points on an orientable surface, for both closed and punctured surfaces. Our main tool is a theorem of B. Totaro describing the cohomology of configuration spaces of algebraic varieties. For configuration spaces of punctured surfaces, this is used in conjunction with techniques from the theory of mixed Hodge structures.

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