Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 24 for “"configuration spaces"”.
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Topological Complexity of Configuration Spaces
… topological complexity of projective and lens spaces. In particular, we introduce a class of navigation functions on projective and lens spaces. It is known ([25]) that the topological complexity of a real projective space equals one plus its immersion dimension. A similar approach to the …
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Permutohedra, configuration spaces and spineless cacti
<p>It has been known that the configuration space F(R<sup>2</sup>, <em>n)</em> of <em>n</em> distinct ordered points in R<sup>2</sup> deformation retracts to a regular CW complex with <em>n!</em>permutohedra <em>P<sub>n</sub></em> as the top dimensional cells. In this paper, we show that there …
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Configuration spaces of thick particles on graphs
In this thesis, we study the topology of configuration spaces of particles of variable radius r>0 moving on a metric graph. Our main tool is a piecewise linear (PL) Morse-Bott theory for affine polytope complexes, which extends the Morse theory for such complexes introduced by M. Bestvina and N. …
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Two Aspects of Topology in Graph Configuration Spaces
A graph configuration space is generated by the movement of a finite number of robots on a graph. These configuration spaces of points in a graph are topologically interesting objects. By using local, combinatorial properties, we define a new classification of graphs whose configuration spaces are …
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Connecting models of configuration spaces: From double loops to strings
… They are central to the study of iterated loop spaces, and the specific case of <em>n</em> = 2 is key in the solution of the Deligne Conjecture. In this paper we examine the connection between two <em>E</em> 2 operads, namely the little 2-cubes operad <em>C</em> 2 itself and the operad of …
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Homology of Configuration Spaces of Surfaces as Mapping Class Group Representations
In this thesis, we study the homology of configuration spaces of surfaces viewed as representations of the mapping class group of the surface, distinguishing between various flavours: ordered and unordered configurations, of closed surfaces and surfaces with boundary, and with different homology …
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Motion Planning along Manifolds with Geodesic Convexity and Analytic Inverse Kinematics
… Most motion planning algorithms operate in the configuration space of a robot, where each dimension corresponds to an individual degree of freedom. Oftentimes, these configuration spaces can be viewed as Euclidean spaces, and many motion planning algorithms treat them as such. However, many …
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Automorphisms of free products of groups
… structure and with strong links to geometric configuration spaces. In this thesis I describe in detail and for the first time the (co)homology of the symmetric automorphism groups. To this end I construct a classifying space for the Fouxe-Rabinovitch automorphism group, a large normal subgroup …
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Topology of configuration space on trees
Configuration Space on trees comes naturally from problems in engineering and has its own importance in mathematics. This paper reviewed the existing research results on the topological properties of classic configuration spaces and generalized some of them for the no-k-equal configuration space on …
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Proving infeasibility in motion planning
… a closed manifold in the obstacle region of the configuration space that separates the start and goal into disconnected components of the free configuration space. We introduce two algorithms for generating infeasibility proofs. The first algorithm grows facets of the infeasibility proof manifold …
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Generalizations of no k-equal spaces
We consider generalizations of no $k$-equal spaces as well as their relations to other concepts. For any topological space $X$, the $n^{th}$ no $k$-equal space of $X$ is the space of $n$ points from $X$ such that no $k$ are the same. First, we consider a generalization where each of the points is …
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On THH and TAQ of Commutative S-Algebras
… n-Poisson algebras in terms of the homology of configuration spaces.
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On the topology of the spaces of coverings
The spaces of coverings (SoC) arise from various configuration spaces of the covering problems. We study the topology of these spaces for different domains and covering agents. In particular, we study the SoCs for grid domains and metric trees covered by balls. Characterizations of their topology …
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Derived algebraic geometry over En̳-rings
… is, rings with multiplication parametrized by configuration spaces of points in Rn. As n increases, these theories converge to the derived algebraic geometry of Tobn-Vezzosi and Lurie. The class of spaces obtained by gluing En-rings form a geometric counterpart to En-categories, which are …
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Koszul duality and the bar spectral sequence
… certain spectral Lie algebras models labeled configuration spaces by a theorem of Knudsen. The associated bar spectral sequence yields new results on their mod p homology at low weights, as well as interesting patterns of universal differentials. We also record an attempt with Andrew Senger on …
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Rare events and dynamics in non-equilibrium systems
… systems. Specifically, we consider systems with configuration spaces that are either Lie groups, or homogeneous spaces. We demonstrate that this theory, which we call a generalised geometric Cosserat theory (GGCT), can be seen as a unifying framework with which to study classical Cosserat …
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Aggregation for modular robots in the pivoting cube model
… algorithms for self-aggregation and self-reconfiguration of modular robots in the pivoting cube model. First, we provide generic algorithms for aggregation of robots following integrator dynamics in arbitrary dimensional configuration spaces. We describe solutions to the problem under …
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Configuration-aware software documentation
… is pervasive, it can also lead to faults (or misconfigurations) and make program evolution challenging. Dependencies can be missed, essential code can be left in place when a configuration option is removed, or code can be deleted or changed when still in use by other configuration options. One …
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Learning Probabilistic Generative Models For Fast Sampling-Based Planning
… fast collision detection in high dimensional configuration spaces based on Gaussian Mixture Models (GMMs) for Rapidly-exploring Random Trees (RRT). In addition, we introduce a new probabilistically safe local steering primitive based on the probabilistic model. Our local steering procedure is …
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Interactive Bayesian identification of kinematic mechanisms
… behave different in different parts of their configuration spaces. The results also show that active action selection can significantly decrease the number of actions required to gather the same information while the racing technique does so without increasing step time of the filter over …
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