Support: NSF grants IIS-0093581 and CCR-0330342
Optimal coverage in a certain region is defined as a function of the density associated to the environment.
Under the assumption of a uniform density the agents would distribute uniformly, in the situation that the densities present some peaks, there will be more agents around the relative position of such peaks rather than in the rest of the environment.
A uniform assumption will not consider the possible appeareance of events in the surface, since the agents will not be reacting to them.
In order to deal with such events, the agents near to the events will detect them, and will try to estimate their relevant characteristics (location, importance, etc).
Under the assumption of a good estimator, asymptotically the estimates of each agent nearby a particular event will converge to the same value.
In principle this convergence might take for too long and each agent will generate its own estimate, hence will generate its own associated density function, depending on the importance of the event which might lead to agents detecting the same source to be reacting differently for long periods of time, hence diminishing the life of the batteries mounted on each robot.
By exchanging messages with its neighbors, the agents can agree faster on the relevant characteristics of each event .
Once the agents have reach agreement on the characteristics of each event, convergence is guaranteed since they will be performing a regular coverage task.
There might be events which importance is negligible and, therefore, no resources are invested on them, there might be cases on which the events that appear in the environment have different degrees of importance, and by reflecting such relative importances in the densities, the robots will distribute themselves accordingly while they try to ensure the optimal coverage of the region under the new denisty.
Such algorithm would be relevant because it will allow the agents in the formation to actually assign a weight to the environment as different events occur without the need of a supervisory level.
The inherent distributed characteristics of the system would make the approach
Robust: By being based only on local information, if an agent fails the other robots in the system can still perform their activities; and
Scalable: Since each agent bases its decision only on its own information and the information from its neighbors, its performance remains invariant under changes in the size of the network or the region on which the sensors have been deployed.
Note: The simulations on this project have been based on the Mathematica code provided by the authors of Coverage Control for Mobile Sensing Networks. IEEE Transactions on Robotics and Automation, 20(2):243--255, 2004.