444 research outputs found
Manipulating Highly Deformable Materials Using a Visual Feedback Dictionary
The complex physical properties of highly deformable materials such as
clothes pose significant challenges fanipulation systems. We present a novel
visual feedback dictionary-based method for manipulating defoor autonomous
robotic mrmable objects towards a desired configuration. Our approach is based
on visual servoing and we use an efficient technique to extract key features
from the RGB sensor stream in the form of a histogram of deformable model
features. These histogram features serve as high-level representations of the
state of the deformable material. Next, we collect manipulation data and use a
visual feedback dictionary that maps the velocity in the high-dimensional
feature space to the velocity of the robotic end-effectors for manipulation. We
have evaluated our approach on a set of complex manipulation tasks and
human-robot manipulation tasks on different cloth pieces with varying material
characteristics.Comment: The video is available at goo.gl/mDSC4
Generalizations of the Erd\H{o}s-Kac Theorem and the Prime Number Theorem
In this paper, we study the linear independence between the distribution of
the number of prime factors of integers and that of the largest prime factors
of integers. Respectively, under a restriction on the largest prime factors of
integers, we will refine the Erd\H{o}s-Kac Theorem and Loyd's recent result on
Bergelson and Richter's dynamical generalizations of the Prime Number Theorem.
At the end, we will show that the analogue of these results holds with respect
to the Erd\H{o}s-Pomerance Theorem as well.Comment: 20 pages. Accepted by the Communications in Mathematics and
Statistic
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