629 research outputs found
A Smooth Distributed Feedback for Global Rendezvous of Unicycles
This paper presents a solution to the rendezvous control problem for a
network of kinematic unicycles in the plane, each equipped with an onboard
camera measuring its relative displacement with respect to its neighbors in
body frame coordinates. A smooth, time-independent control law is presented
that drives the unicycles to a common position from arbitrary initial
conditions, under the assumption that the sensing digraph contains a
reverse-directed spanning tree. The proposed feedback is very simple, and
relies only on the onboard measurements. No global positioning system is
required, nor any information about the unicycles' orientations
Rearranging trees for robust consensus
In this paper, we use the H2 norm associated with a communication graph to
characterize the robustness of consensus to noise. In particular, we restrict
our attention to trees and by systematic attention to the effect of local
changes in topology, we derive a partial ordering for undirected trees
according to the H2 norm. Our approach for undirected trees provides a
constructive method for deriving an ordering for directed trees. Further, our
approach suggests a decentralized manner in which trees can be rearranged in
order to improve their robustness.Comment: Submitted to CDC 201
Collective optimization over average quantities
peer reviewedThis paper addresses the design of algorithms
for the collective optimization of a cost function defined over
average quantities in the presence of limited communication.
We argue that several meaningful collective optimization problems
can be formulated in this way. As an application of
the proposed approach, we propose a novel algorithm that
achieves synchronization or balancing in phase models of
coupled oscillators under mild connectedness assumptions on
the (possibly time-varying and unidirectional) communication
graphs
Starling flock networks manage uncertainty in consensus at low cost
Flocks of starlings exhibit a remarkable ability to maintain cohesion as a
group in highly uncertain environments and with limited, noisy information.
Recent work demonstrated that individual starlings within large flocks respond
to a fixed number of nearest neighbors, but until now it was not understood why
this number is seven. We analyze robustness to uncertainty of consensus in
empirical data from multiple starling flocks and show that the flock
interaction networks with six or seven neighbors optimize the trade-off between
group cohesion and individual effort. We can distinguish these numbers of
neighbors from fewer or greater numbers using our systems-theoretic approach to
measuring robustness of interaction networks as a function of the network
structure, i.e., who is sensing whom. The metric quantifies the disagreement
within the network due to disturbances and noise during consensus behavior and
can be evaluated over a parameterized family of hypothesized sensing strategies
(here the parameter is number of neighbors). We use this approach to further
show that for the range of flocks studied the optimal number of neighbors does
not depend on the number of birds within a flock; rather, it depends on the
shape, notably the thickness, of the flock. The results suggest that robustness
to uncertainty may have been a factor in the evolution of flocking for
starlings. More generally, our results elucidate the role of the interaction
network on uncertainty management in collective behavior, and motivate the
application of our approach to other biological networks.Comment: 19 pages, 3 figures, 9 supporting figure
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