Migration Dynamics for Adapting Sensor Coverage on the Line

A method is developed for using the diffusive flow of migration dynamics to adapt the locations of sensors that are positioned along a line to provide coverage along that line. Such an adaptive adjustment of the locations of sensors positioned along a line can provide an opportunity to change the relative amount of coverage to achieve some desired (potentially nonuniform) coverage pattern. An important feature of the migration dynamics approach is that it is a provably convergent local adaptation approach, in that it provides a solution that is guaranteed to yield a coverage pattern that approaches the shape of the goal coverage pattern using only local observations of the locations of neighboring sensors and no data sharing. From applying the migration dynamics approach with a specifically chosen fitness function, a rule is created for individual sensors to move to create the desired adaptation based on only local observations. A formal analysis of the dynamics that result from the chosen fitness function shows that the resulting approach converges to approximate the shape of the desired coverage function. Thus, position adjustment to achieve group coverage goals is shown to be possible without sharing information across the entire group of sensors. Numerical simulations are provided to support the analytical claims.