Topic
Configuration space
About: Configuration space is a research topic. Over the lifetime, 5873 publications have been published within this topic receiving 136193 citations.
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07 Mar 2022TL;DR: In this paper , the authors show that a topological change is often associated with a dramatic change in the configuration space geometry, and that the geometric change is the actual driver of the phase transition.
Abstract: As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests that the existence of a phase transition could perhaps be inferred from changes to the topology of the accessible part of the configuration space. This paper instead suggests that such a topological change is often associated with a dramatic change in the configuration space geometry, and that the geometric change is the actual driver of the phase transition. More precisely, a geometric change that brings about a discontinuity in the mixing time required for an initial probability distribution on the configuration space to reach steady-state is conjectured to be related to the onset of a phase transition in the thermodynamic limit. This conjecture is tested by evaluating the diffusion diameter and $\epsilon$-mixing time of the configuration spaces of hard disk and hard sphere systems of increasing size. Explicit geometries are constructed for the configuration spaces of these systems, and numerical evidence suggests that a discontinuity in the $\epsilon$-mixing time coincides with the solid-fluid phase transition in the thermodynamic limit.
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TL;DR: In this paper , the authors investigate the space of configurations, described in terms of joint angles of its spherical joints, that satisfy the loop closure constraint, meaning that the kinematic chain is closed.
Abstract: A kinematic chain in three-dimensional Euclidean space consists of $n$ links that are connected by spherical joints. Such a chain is said to be within a closed configuration when its link lengths form a closed polygonal chain in three dimensions. We investigate the space of configurations, described in terms of joint angles of its spherical joints, that satisfy the the loop closure constraint, meaning that the kinematic chain is closed. In special cases, we can find a new set of parameters that describe the diagonal lengths (the distance of the joints from the origin) of the configuration space by a simple domain, namely a cube of dimension $n-3$. We expect that the new findings can be applied to various problems such as motion planning for closed kinematic chains or singularity analysis of their configuration spaces. To demonstrate the practical feasibility of the new method, we present numerical examples.
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01 Oct 2018TL;DR: A new method for computing the error range (or area of acceptance) for a pair of rigid connector objects with self-aligning geometry capable of higher dimensional analysis which was previously limited to three.
Abstract: Physical connectors with self-aligning geometry aid in the docking process for many robotic and automatic control systems such as robotic self-reconfiguration and air-to-air refueling. This self-aligning geometry provides a wider range of acceptable error tolerance in relative pose between the two rigid objects, increasing successful docking chances. We present a new method for computing the error range (or area of acceptance) for a pair of rigid connector objects with self-aligning geometry capable of higher dimensional analysis which was previously limited to three. The method is based on the configuration space obstacle model, which gives us a representation of the space of contact states between the two objects. Using an approach direction as analogous to gravity, and assuming the target docked configuration is stable, the set of misaligned points that lead to docking is the target configuration's watershed for an arbitrarily dimensioned configuration space obstacle. It is well known that the watershed of a height map on a discrete grid can be found using any number of algorithms from image segmentation. We present an implementation based on Meyer's flooding algorithm to determine this watershed and measure the AA for simple connectors in 2D and 3D. Results are presented for systems including unconstrained motion in SE(2) and motion constrained to four dimensions (ie. x,y,z,pitch) in SE(3).
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TL;DR: In this article, the Coulomb gauge has been studied and the entanglement entropy has been shown to behave very similar to a single scalar degree of freedom if we do not include further centers, but approaches that of a gauge field if we include non-trivial centers.
Abstract: In this paper, we explore the question of how different gauge choices in a gauge theory affect the tensor product structure of the Hilbert space in configuration space. In particular, we study the Coulomb gauge and observe that the naive gauge potential degrees of freedom cease to be local operators as soon as we impose the Dirac brackets. We construct new local set of operators and compute the entanglement entropy according to this algebra in $2+1$ dimensions. We find that our proposal would lead to an entanglement entropy that behave very similar to a single scalar degree of freedom if we do not include further centers, but approaches that of a gauge field if we include non-trivial centers. We explore also the situation where the gauge field is Higgsed, and construct a local operator algebra that again requires some deformation. This should give us some insight into interpreting the entanglement entropy in generic gauge theories and perhaps also in gravitational theories.
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01 Jan 2005
TL;DR: A calculation path technique based on the configuration space in the case of an articulated robot of two degrees of freedom is used, choosing in each case the best option for each one of the techniques for the combination.
Abstract: In this paper, we use a calculation path technique based on the configuration space in the case of an articulated robot of two degrees of freedom. We propose the use of artificial potential fields to represent the configuration space and the use of techniques of artificial intelligence like A* and D* to search a free collision path into the configuration space. This combination of techniques can be used in static and dynamic environments with more than three dimensions without considering the geometry of the obstacles. The results for this combination of techniques are presented, choosing in each case the best option for each one of the techniques for the combination.