45,293 research outputs found
Optimal Paths on the Space-Time SINR Random Graph
We analyze a class of Signal-to-Interference-and-Noise-Ratio (SINR) random
graphs. These random graphs arise in the modeling packet transmissions in
wireless networks. In contrast to previous studies on the SINR graphs, we
consider both a space and a time dimension. The spatial aspect originates from
the random locations of the network nodes in the Euclidean plane. The time
aspect stems from the random transmission policy followed by each network node
and from the time variations of the wireless channel characteristics. The
combination of these random space and time aspects leads to fluctuations of the
SINR experienced by the wireless channels, which in turn determine the
progression of packets in space and time in such a network. This paper studies
optimal paths in such wireless networks in terms of first passage percolation
on this random graph. We establish both "positive" and "negative" results on
the associated time constant. The latter determines the asymptotics of the
minimum delay required by a packet to progress from a source node to a
destination node when the Euclidean distance between the two tends to infinity.
The main negative result states that this time constant is infinite on the
random graph associated with a Poisson point process under natural assumptions
on the wireless channels. The main positive result states that when adding a
periodic node infrastructure of arbitrarily small intensity to the Poisson
point process, the time constant is positive and finite
Active Markov Information-Theoretic Path Planning for Robotic Environmental Sensing
Recent research in multi-robot exploration and mapping has focused on
sampling environmental fields, which are typically modeled using the Gaussian
process (GP). Existing information-theoretic exploration strategies for
learning GP-based environmental field maps adopt the non-Markovian problem
structure and consequently scale poorly with the length of history of
observations. Hence, it becomes computationally impractical to use these
strategies for in situ, real-time active sampling. To ease this computational
burden, this paper presents a Markov-based approach to efficient
information-theoretic path planning for active sampling of GP-based fields. We
analyze the time complexity of solving the Markov-based path planning problem,
and demonstrate analytically that it scales better than that of deriving the
non-Markovian strategies with increasing length of planning horizon. For a
class of exploration tasks called the transect sampling task, we provide
theoretical guarantees on the active sampling performance of our Markov-based
policy, from which ideal environmental field conditions and sampling task
settings can be established to limit its performance degradation due to
violation of the Markov assumption. Empirical evaluation on real-world
temperature and plankton density field data shows that our Markov-based policy
can generally achieve active sampling performance comparable to that of the
widely-used non-Markovian greedy policies under less favorable realistic field
conditions and task settings while enjoying significant computational gain over
them.Comment: 10th International Conference on Autonomous Agents and Multiagent
Systems (AAMAS 2011), Extended version with proofs, 11 page
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