5,298 research outputs found
The power dissipation method and kinematic reducibility of multiple-model robotic systems
This paper develops a formal connection between the power dissipation method (PDM) and Lagrangian mechanics, with specific application to robotic systems. Such a connection is necessary for understanding how some of the successes in motion planning and stabilization for smooth kinematic robotic systems can be extended to systems with frictional interactions and overconstrained systems. We establish this connection using the idea of a multiple-model system, and then show that multiple-model systems arise naturally in a number of instances, including those arising in cases traditionally addressed using the PDM. We then give necessary and sufficient conditions for a dynamic multiple-model system to be reducible to a kinematic multiple-model system. We use this result to show that solutions to the PDM are actually kinematic reductions of solutions to the Euler-Lagrange equations. We are particularly motivated by mechanical systems undergoing multiple intermittent frictional contacts, such as distributed manipulators, overconstrained wheeled vehicles, and objects that are manipulated by grasping or pushing. Examples illustrate how these results can provide insight into the analysis and control of physical systems
From Proximity to Utility: A Voronoi Partition of Pareto Optima
We present an extension of Voronoi diagrams where when considering which site
a client is going to use, in addition to the site distances, other site
attributes are also considered (for example, prices or weights). A cell in this
diagram is then the locus of all clients that consider the same set of sites to
be relevant. In particular, the precise site a client might use from this
candidate set depends on parameters that might change between usages, and the
candidate set lists all of the relevant sites. The resulting diagram is
significantly more expressive than Voronoi diagrams, but naturally has the
drawback that its complexity, even in the plane, might be quite high.
Nevertheless, we show that if the attributes of the sites are drawn from the
same distribution (note that the locations are fixed), then the expected
complexity of the candidate diagram is near linear.
To this end, we derive several new technical results, which are of
independent interest. In particular, we provide a high-probability,
asymptotically optimal bound on the number of Pareto optima points in a point
set uniformly sampled from the -dimensional hypercube. To do so we revisit
the classical backward analysis technique, both simplifying and improving
relevant results in order to achieve the high-probability bounds
Hiding variables when decomposing specifications into GR(1) contracts
We propose a method for eliminating variables from component specifications during the decomposition of GR(1) properties into contracts. The variables that can be eliminated are identified by parameterizing the communication architecture to investigate the dependence of realizability on the availability of information. We prove that the selected variables can be hidden from other components, while still expressing the resulting specification as a game with full information with respect to the remaining variables. The values of other variables need not be known all the time, so we hide them for part of the time, thus reducing the amount of information that needs to be communicated between components. We improve on our previous results on algorithmic decomposition of GR(1) properties, and prove existence of decompositions in the full information case. We use semantic methods of computation based on binary decision diagrams. To recover the constructed specifications so that humans can read them, we implement exact symbolic minimal covering over the lattice of integer orthotopes, thus deriving minimal formulae in disjunctive normal form over integer variable intervals
Volume-Enclosing Surface Extraction
In this paper we present a new method, which allows for the construction of
triangular isosurfaces from three-dimensional data sets, such as 3D image data
and/or numerical simulation data that are based on regularly shaped, cubic
lattices. This novel volume-enclosing surface extraction technique, which has
been named VESTA, can produce up to six different results due to the nature of
the discretized 3D space under consideration. VESTA is neither template-based
nor it is necessarily required to operate on 2x2x2 voxel cell neighborhoods
only. The surface tiles are determined with a very fast and robust construction
technique while potential ambiguities are detected and resolved. Here, we
provide an in-depth comparison between VESTA and various versions of the
well-known and very popular Marching Cubes algorithm for the very first time.
In an application section, we demonstrate the extraction of VESTA isosurfaces
for various data sets ranging from computer tomographic scan data to simulation
data of relativistic hydrodynamic fireball expansions.Comment: 24 pages, 33 figures, 4 tables, final versio
Structured Decompositions: Structural and Algorithmic Compositionality
We introduce structured decompositions: category-theoretic generalizations of
many combinatorial invariants -- including tree-width, layered tree-width,
co-tree-width and graph decomposition width -- which have played a central role
in the study of structural and algorithmic compositionality in both graph
theory and parameterized complexity. Structured decompositions allow us to
generalize combinatorial invariants to new settings (for example decompositions
of matroids) in which they describe algorithmically useful structural
compositionality. As an application of our theory we prove an algorithmic meta
theorem for the Sub_P-composition problem which, when instantiated in the
category of graphs, yields compositional algorithms for NP-hard problems such
as: Maximum Bipartite Subgraph, Maximum Planar Subgraph and Longest Path
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