Effective sensing regions and connectivity of agents undergoing periodic relative motions
Daniel T. Swain, Ming Cao and Naomi Ehrich Leonard
Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico, December 2008.
Time-varying graphs are widely used to model
communication and sensing in multi-agent systems such as mobile
sensor networks and dynamic animal groups. Connectivity
is often determined by the presence of neighbors in a sensing
region defined by relative position and/or bearing. We present a
method for calculating the effective sensing region that defines
the connectivity between agents undergoing periodic relative
motions. This method replaces time-varying calculations with
time-invariant calculations which greatly simplifies studies of
connectivity and convergence of consensus algorithms.We apply
the technique to the case of agents moving in a common fixed
direction with sinusoidal speed oscillations and fixed relative
phases. For agents moving in a straight line, we show analytically
how to select dynamics for fast convergence of consensus.
Further numerical results suggest graph-level connectivity may
be achieved with a sensing radius lower than that predicted by
percolation theory for agents with fixed relative positions.
(492 KB pdf)
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