Energy-Based Voronoi Partition in Constant Flow Environments

As is well known, energy cost can greatly impact the deployment of battery-powered sensor networks in remote environments such as rivers or oceans. Motivated by this, we propose here an energy-based metric and associate energy-based Voronoi partitions with mobile vehicles in constant flows. The metric corresponds to the minimum energy that a vehicle requires to move from one point to another in the flow environment, and the resulting partition can be used by the vehicles in cooperative control tasks such as task assignment and coverage. Based on disk-based and asymptote-based approximations of the Voronoi regions, we determine a subset (or lower bound) and superset (or upper bound) of an agent's Voronoi neighbors. We then show that, via simulations, the upper bound is tight and its cardinality remains bounded as the number of generators increases. Finally, we propose efficient algorithms to compute the upper bound (especially when the generators dynamically change), which enables the fast calculation of Voronoi regions.