1,360 research outputs found
k-Color Multi-Robot Motion Planning
We present a simple and natural extension of the multi-robot motion planning
problem where the robots are partitioned into groups (colors), such that in
each group the robots are interchangeable. Every robot is no longer required to
move to a specific target, but rather to some target placement that is assigned
to its group. We call this problem k-color multi-robot motion planning and
provide a sampling-based algorithm specifically designed for solving it. At the
heart of the algorithm is a novel technique where the k-color problem is
reduced to several discrete multi-robot motion planning problems. These
reductions amplify basic samples into massive collections of free placements
and paths for the robots. We demonstrate the performance of the algorithm by an
implementation for the case of disc robots and polygonal robots translating in
the plane. We show that the algorithm successfully and efficiently copes with a
variety of challenging scenarios, involving many robots, while a simplified
version of this algorithm, that can be viewed as an extension of a prevalent
sampling-based algorithm for the k-color case, fails even on simple scenarios.
Interestingly, our algorithm outperforms a well established implementation of
PRM for the standard multi-robot problem, in which each robot has a distinct
color.Comment: 2
Algorithms for detecting dependencies and rigid subsystems for CAD
Geometric constraint systems underly popular Computer Aided Design soft-
ware. Automated approaches for detecting dependencies in a design are critical
for developing robust solvers and providing informative user feedback, and we
provide algorithms for two types of dependencies. First, we give a pebble game
algorithm for detecting generic dependencies. Then, we focus on identifying the
"special positions" of a design in which generically independent constraints
become dependent. We present combinatorial algorithms for identifying subgraphs
associated to factors of a particular polynomial, whose vanishing indicates a
special position and resulting dependency. Further factoring in the Grassmann-
Cayley algebra may allow a geometric interpretation giving conditions (e.g.,
"these two lines being parallel cause a dependency") determining the special
position.Comment: 37 pages, 14 figures (v2 is an expanded version of an AGD'14 abstract
based on v1
Motioning connected subgraphs into a graph
In this paper we study connected subgraphs and how to motion them inside a
connected graph preserving the connectivity. We determine completely the group
of movements.Comment: 17 pages, 18 figure
Kinematic Flexibility Analysis: Hydrogen Bonding Patterns Impart a Spatial Hierarchy of Protein Motion
Elastic network models (ENM) and constraint-based, topological rigidity
analysis are two distinct, coarse-grained approaches to study conformational
flexibility of macromolecules. In the two decades since their introduction,
both have contributed significantly to insights into protein molecular
mechanisms and function. However, despite a shared purpose of these approaches,
the topological nature of rigidity analysis, and thereby the absence of motion
modes, has impeded a direct comparison. Here, we present an alternative,
kinematic approach to rigidity analysis, which circumvents these drawbacks. We
introduce a novel protein hydrogen bond network spectral decomposition, which
provides an orthonormal basis for collective motions modulated by non-covalent
interactions, analogous to the eigenspectrum of normal modes, and decomposes
proteins into rigid clusters identical to those from topological rigidity. Our
kinematic flexibility analysis bridges topological rigidity theory and ENM, and
enables a detailed analysis of motion modes obtained from both approaches. Our
analysis reveals that collectivity of protein motions, reported by the Shannon
entropy, is significantly lower for rigidity theory versus normal mode
approaches. Strikingly, kinematic flexibility analysis suggests that the
hydrogen bonding network encodes a protein-fold specific, spatial hierarchy of
motions, which goes nearly undetected in ENM. This hierarchy reveals distinct
motion regimes that rationalize protein stiffness changes observed from
experiment and molecular dynamics simulations. A formal expression for changes
in free energy derived from the spectral decomposition indicates that motions
across nearly 40% of modes obey enthalpy-entropy compensation. Taken together,
our analysis suggests that hydrogen bond networks have evolved to modulate
protein structure and dynamics
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