scholarly journals Space-filling trees: A new perspective on incremental search for motion planning

2011 ◽  
Author(s):  
J. J. Kuffner ◽  
S. M. LaValle
Keyword(s):  
Motion Planning ◽  
Space Filling ◽  
Incremental Search ◽  
New Perspective

scholarly journals New perspective on sampling-based motion planning via random geometric graphs

2018 ◽  
Vol 37 (10) ◽  
pp. 1117-1133 ◽  
Author(s):  
Kiril Solovey ◽  
Oren Salzman ◽  
Dan Halperin
Keyword(s):  
Motion Planning ◽  
Geometric Graphs ◽  
Optimal Motion ◽  
Random Geometric Graphs ◽  
Probabilistic Roadmaps ◽  
Optimal Motion Planning ◽  
Unit Hypercube ◽  
Standard Models ◽  
New Perspective ◽  
Near Optimality

Roadmaps constructed by many sampling-based motion planners coincide, in the absence of obstacles, with standard models of random geometric graphs (RGGs). Those models have been studied for several decades and by now a rich body of literature exists analyzing various properties and types of RGGs. In their seminal work on optimal motion planning, Karaman and Frazzoli conjectured that a sampling-based planner has a certain property if the underlying RGG has this property as well. In this paper, we settle this conjecture and leverage it for the development of a general framework for the analysis of sampling-based planners. Our framework, which we call localization–tessellation, allows for easy transfer of arguments on RGGs from the free unit hypercube to spaces punctured by obstacles, which are geometrically and topologically much more complex. We demonstrate its power by providing alternative and (arguably) simple proofs for probabilistic completeness and asymptotic (near-)optimality of probabilistic roadmaps (PRMs) in Euclidean spaces. Furthermore, we introduce three variants of PRMs, analyze them using our framework, and discuss the implications of the analysis.

Simulation of 3-Dimensional Cell Population Growth Processes in Polyhedral Cellular Systems

2007 ◽  
Vol 537-538 ◽  
pp. 579-590
Author(s):  
Tamás Réti ◽  
Ibolya Zsoldos
Keyword(s):  
Population Growth ◽  
Cell Population ◽  
Cell Decomposition ◽  
Cellular Systems ◽  
Space Filling ◽  
Growth Processes ◽  
Cell Nucleation ◽  
Cell Population Growth ◽  
Polyhedral Cells ◽  
New Perspective

In order to simulate the polyhedral grain nucleation in alloys, 3-D cell population growth processes are studied in space-filling periodic cellular systems. We discussed two different methods by which space-filling polyhedral cellular systems can be constructed by topological transformations performed on “stable” 3-D cellular systems. It has been demonstrated that an infinite sequence of stable periodic space-filling polyhedral systems can be generated by means of a simple recursion procedure based on a vertex based tetrahedron insertion. On the basis of computed results it is conjectured that in a 3-D periodic, topologically stable cellular system the minimum value of the average face number 〈f〉 of polyhedral cells is larger than eight (i.e. 〈f〉 > 8). The outlined algorithms (which are based on cell decomposition and/or cell nucleation) provide a new perspective to simulate grain population growth processes in materials with polyhedral microstructure.

Matrix completion as a post-processing technique for probabilistic roadmaps

2019 ◽  
Vol 38 (2-3) ◽  
pp. 388-400 ◽  
Author(s):  
Joel M. Esposito ◽  
John N. Wright
Keyword(s):  
Motion Planning ◽  
Sparse Matrices ◽  
Matrix Completion ◽  
Processing Technique ◽  
Low Rank ◽  
Post Processing ◽  
Probabilistic Roadmaps ◽  
The Status ◽  
New Perspective ◽  
The Cost

Inspired by the recent literature on matrix completion, this paper describes a novel post-processing algorithm for probabilistic roadmaps (PRMs). We argue that the adjacency matrix associated with real roadmaps can be decomposed into the sum of low-rank and sparse matrices. Given a PRM with n vertices and only [Formula: see text] collision-checked candidate edges, our algorithm numerically computes a relaxation of this decomposition, which estimates the status of all [Formula: see text] possible edges in the full roadmap with high accuracy, without performing any additional collision checks. Typical results from our experiments on problems from the Open Motion Planning Library indicate that after checking [Formula: see text] of the possible edges, the algorithm estimates the full visibility graph with [Formula: see text] accuracy. The practical utility of the algorithm is that the average path length across the resulting denser edge set is significantly shorter (at the cost of somewhat increased spatial complexity and query times). An ancillary benefit is that the resulting low-rank plus sparse decomposition readily reveals information that would be otherwise difficult to compute, such as the number of convex cells in free configuration space and the number of vertices in each. We believe that this novel connection between motion planning and matrix completion provides a new perspective on sampling-based planning and may guide future algorithm development.

SREM observation of the interaction between the in-situ deposited Pd small particles and MgO cleavage surface

1986 ◽  
Vol 44 ◽  
pp. 382-383
Author(s):  
H.-J. Ou
Keyword(s):  
Electron Microscopy ◽  
Small Particle ◽  
Small Particles ◽  
Cleavage Surface ◽  
Metallic Particles ◽  
Microscopy Technique ◽  
Ceramic Surfaces ◽  
Reflection Electron Microscopy ◽  
New Perspective

The understanding of the interactions between the small metallic particles and ceramic surfaces has been studied by many catalyst scientists. We had developed Scanning Reflection Electron Microscopy technique to study surface structure of MgO hulk cleaved surface and the interaction with the small particle of metals. Resolutions of 10Å has shown the periodic array of surface atomic steps on MgO. The SREM observation of the interaction between the metallic particles and the surface may provide a new perspective on such processes.

Articulation Training: A New Perspective

1979 ◽  
Vol 10 (3) ◽  
pp. 145-151 ◽  
Author(s):  
Sallie W. Hillard ◽  
Laura P. Goepfert
Keyword(s):  
Life Experience ◽  
Remediation Measures ◽  
New Perspective

This paper describes the concept of teaching articulation through words which have inherent meaning to a child’s life experience, such as a semantically potent word approach. The approach was used with six children. Comparison of pre/post remediation measures indicated that it has promise as a technique for facilitating increased correct phoneme production.

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