234,350 research outputs found
Improved Orientation Sampling for Indexing Diffraction Patterns of Polycrystalline Materials
Orientation mapping is a widely used technique for revealing the
microstructure of a polycrystalline sample. The crystalline orientation at each
point in the sample is determined by analysis of the diffraction pattern, a
process known as pattern indexing. A recent development in pattern indexing is
the use of a brute-force approach, whereby diffraction patterns are simulated
for a large number of crystalline orientations, and compared against the
experimentally observed diffraction pattern in order to determine the most
likely orientation. Whilst this method can robust identify orientations in the
presence of noise, it has very high computational requirements. In this
article, the computational burden is reduced by developing a method for
nearly-optimal sampling of orientations. By using the quaternion representation
of orientations, it is shown that the optimal sampling problem is equivalent to
that of optimally distributing points on a four-dimensional sphere. In doing
so, the number of orientation samples needed to achieve a indexing desired
accuracy is significantly reduced. Orientation sets at a range of sizes are
generated in this way for all Laue groups, and are made available online for
easy use.Comment: 11 pages, 7 figure
Optimal Sampling-Based Motion Planning under Differential Constraints: the Driftless Case
Motion planning under differential constraints is a classic problem in
robotics. To date, the state of the art is represented by sampling-based
techniques, with the Rapidly-exploring Random Tree algorithm as a leading
example. Yet, the problem is still open in many aspects, including guarantees
on the quality of the obtained solution. In this paper we provide a thorough
theoretical framework to assess optimality guarantees of sampling-based
algorithms for planning under differential constraints. We exploit this
framework to design and analyze two novel sampling-based algorithms that are
guaranteed to converge, as the number of samples increases, to an optimal
solution (namely, the Differential Probabilistic RoadMap algorithm and the
Differential Fast Marching Tree algorithm). Our focus is on driftless
control-affine dynamical models, which accurately model a large class of
robotic systems. In this paper we use the notion of convergence in probability
(as opposed to convergence almost surely): the extra mathematical flexibility
of this approach yields convergence rate bounds - a first in the field of
optimal sampling-based motion planning under differential constraints.
Numerical experiments corroborating our theoretical results are presented and
discussed
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