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.

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