23,965 research outputs found
Spectral Motion Synchronization in SE(3)
This paper addresses the problem of motion synchronization (or averaging) and
describes a simple, closed-form solution based on a spectral decomposition,
which does not consider rotation and translation separately but works straight
in SE(3), the manifold of rigid motions. Besides its theoretical interest,
being the first closed form solution in SE(3), experimental results show that
it compares favourably with the state of the art both in terms of precision and
speed
Robust Rotation Synchronization via Low-rank and Sparse Matrix Decomposition
This paper deals with the rotation synchronization problem, which arises in
global registration of 3D point-sets and in structure from motion. The problem
is formulated in an unprecedented way as a "low-rank and sparse" matrix
decomposition that handles both outliers and missing data. A minimization
strategy, dubbed R-GoDec, is also proposed and evaluated experimentally against
state-of-the-art algorithms on simulated and real data. The results show that
R-GoDec is the fastest among the robust algorithms.Comment: The material contained in this paper is part of a manuscript
submitted to CVI
Complete Characterization of Stability of Cluster Synchronization in Complex Dynamical Networks
Synchronization is an important and prevalent phenomenon in natural and
engineered systems. In many dynamical networks, the coupling is balanced or
adjusted in order to admit global synchronization, a condition called Laplacian
coupling. Many networks exhibit incomplete synchronization, where two or more
clusters of synchronization persist, and computational group theory has
recently proved to be valuable in discovering these cluster states based upon
the topology of the network. In the important case of Laplacian coupling,
additional synchronization patterns can exist that would not be predicted from
the group theory analysis alone. The understanding of how and when clusters
form, merge, and persist is essential for understanding collective dynamics,
synchronization, and failure mechanisms of complex networks such as electric
power grids, distributed control networks, and autonomous swarming vehicles. We
describe here a method to find and analyze all of the possible cluster
synchronization patterns in a Laplacian-coupled network, by applying methods of
computational group theory to dynamically-equivalent networks. We present a
general technique to evaluate the stability of each of the dynamically valid
cluster synchronization patterns. Our results are validated in an electro-optic
experiment on a 5 node network that confirms the synchronization patterns
predicted by the theory.Comment: 6 figure
Symmetries, Cluster Synchronization, and Isolated Desynchronization in Complex Networks
Synchronization is of central importance in power distribution,
telecommunication, neuronal, and biological networks. Many networks are
observed to produce patterns of synchronized clusters, but it has been
difficult to predict these clusters or understand the conditions under which
they form, except for in the simplest of networks. In this article, we shed
light on the intimate connection between network symmetry and cluster
synchronization. We introduce general techniques that use network symmetries to
reveal the patterns of synchronized clusters and determine the conditions under
which they persist. The connection between symmetry and cluster synchronization
is experimentally explored using an electro-optic network. We experimentally
observe and theoretically predict a surprising phenomenon in which some
clusters lose synchrony while leaving others synchronized. The results could
guide the design of new power grid systems or lead to new understanding of the
dynamical behavior of networks ranging from neural to social
SPRK: A Low-Cost Stewart Platform For Motion Study In Surgical Robotics
To simulate body organ motion due to breathing, heart beats, or peristaltic
movements, we designed a low-cost, miniaturized SPRK (Stewart Platform Research
Kit) to translate and rotate phantom tissue. This platform is 20cm x 20cm x
10cm to fit in the workspace of a da Vinci Research Kit (DVRK) surgical robot
and costs $250, two orders of magnitude less than a commercial Stewart
platform. The platform has a range of motion of +/- 1.27 cm in translation
along x, y, and z directions and has motion modes for sinusoidal motion and
breathing-inspired motion. Modular platform mounts were also designed for
pattern cutting and debridement experiments. The platform's positional
controller has a time-constant of 0.2 seconds and the root-mean-square error is
1.22 mm, 1.07 mm, and 0.20 mm in x, y, and z directions respectively. All the
details, CAD models, and control software for the platform is available at
github.com/BerkeleyAutomation/sprk
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