36,052 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
Colorful Strips
Given a planar point set and an integer , we wish to color the points with
colors so that any axis-aligned strip containing enough points contains all
colors. The goal is to bound the necessary size of such a strip, as a function
of . We show that if the strip size is at least , such a coloring
can always be found. We prove that the size of the strip is also bounded in any
fixed number of dimensions. In contrast to the planar case, we show that
deciding whether a 3D point set can be 2-colored so that any strip containing
at least three points contains both colors is NP-complete.
We also consider the problem of coloring a given set of axis-aligned strips,
so that any sufficiently covered point in the plane is covered by colors.
We show that in dimensions the required coverage is at most .
Lower bounds are given for the two problems. This complements recent
impossibility results on decomposition of strip coverings with arbitrary
orientations. Finally, we study a variant where strips are replaced by wedges
Recommended from our members
What does the future hold for utility electricity efficiency programs?
This study develops projections of future spending and savings from electricity efficiency programs funded by electric utility customers in the United States through 2030 based on three scenarios. Our analysis relies on detailed bottom-up modeling of current state energy efficiency policies, demand-side management and integrated resource plans, and regulatory decisions. The three scenarios represent a range of potential outcomes given the policy environment at the time of the study and uncertainties in the broader economic and state policy environment in each state. We project spending to increase to 11.1 billion in 2030 and remains relatively flat in the low case ($6.8 billion in 2030). Our analysis suggests that electricity efficiency programs funded by utility customers will continue to impact load growth significantly at least through 2030, as savings as a percent of retail sales are forecast at 0.7 percent in the medium scenario and 0.98 percent in the high scenario
The nature of the long time decay at a second order transition point
We show that at a second order phase transition, of \phi^4 like system, a
necessary condition for streched exponential decay of the time structure factor
is obeyed. Using the ideas presented in this proof a crude estimate of the
decay of the structure factor is obtained and shown to yield stretched
exponential decay under very reasonable conditions.Comment: 7 page
Diversidade, síndromes de dispersão e formas de vida vegetal em diferentes estágios sucessionais de florestas secundárias em Tomé-Açu, Pará, Brasil.
Florestas secundárias (capoeiras) são formas de vegetação resultantes de processos sucessionais determinados pelo histórico de uso da terra, distância de florestas primárias bem como fatores estocásticos. O estágio sucessional pode indicar quais as formas de vida vegetal e as síndromes de dispersão dominantes no ambiente. Neste estudo foram avaliados: uma floresta primária (controle) e florestas secundárias de 25, 10 e 5 anos no município de Tomé-Açu, Pará, Brasil. A primeira apresentou 224 espécies e a floresta secundária de cinco anos teve 91, a menor quantidade. O número de espécies diferiu entre ambientes (χ2 = 59,6; p <0,001), mas não a quantidade de famílias (χ2 = 3,6; p = 0,305). O índice de Shannon-Weaner foi alto para todas as florestas, exceto para a capoeira de cinco anos. A distribuição de formas de vida e as síndromes de dispersão diferiram para todas as capoeiras quando comparadas com as distribuições observadas na floresta primária. As formas arbustivas predominaram na capoeira de cinco anos e as arbóreas nas demais. As espécies zoocóricas foram as mais frequentes, enquanto que as autocóricas e hidrocóricas as mais comuns na floresta primária. Devido às boas condições de diversidade das florestas secundárias de Tomé-Açu, sugerimos ações para um manejo florestal sustentável visando retornos econômicos e a conservação destes ambientes
The Induced Magnetic Field of the Moon: Conductivity Profiles and Inferred Temperature
Electromagnetic induction in the moon driven by fluctuations of the interplanetary magnetic field is used to determine the lunar bulk electrical conductivity. The present data clearly show the north-south and east-west transfer function difference as well as high frequency rollover. The difference is shown to be compatible over the mid-frequency range with a noise source associated with the compression of the local remanent field by solar wind dynamic pressure fluctuations. Models for two, three, and four layer; current layer, double current layer, and core plus current layer moons are generated by inversion of the data using a theory which incorporates higher order multipoles. Core radii conductivities generally are in the range 1200 to 1300 km and 0.001 to 0.003 mhos/m; and for the conducting shell 1500 to 1700 km with 0.0001 to 0.0007 mhos/m with an outer layer taken as nonconducting. Core temperature based on available olivine data is 700 to 1000 C
Efficient Multi-Robot Motion Planning for Unlabeled Discs in Simple Polygons
We consider the following motion-planning problem: we are given unit
discs in a simple polygon with vertices, each at their own start position,
and we want to move the discs to a given set of target positions. Contrary
to the standard (labeled) version of the problem, each disc is allowed to be
moved to any target position, as long as in the end every target position is
occupied. We show that this unlabeled version of the problem can be solved in
time, assuming that the start and target positions are at
least some minimal distance from each other. This is in sharp contrast to the
standard (labeled) and more general multi-robot motion-planning problem for
discs moving in a simple polygon, which is known to be strongly NP-hard
Steep sharp-crested gravity waves on deep water
A new type of steady steep two-dimensional irrotational symmetric periodic
gravity waves on inviscid incompressible fluid of infinite depth is revealed.
We demonstrate that these waves have sharper crests in comparison with the
Stokes waves of the same wavelength and steepness. The speed of a fluid
particle at the crest of new waves is greater than their phase speed.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let
- …