The paparazzi problem

Multiple mobile robots, or robot collectives, have been proposed as solutions to various tasks in which distributed sensing and action are required. Here we consider applying a collective of robots to the paparazzi problem - the problem of providing sensor coverage of a target robot. We demonstrate how the computational task of the collective can be formulated as a global energy minimization task over the entire collective, and show how individual members of the collective can solve the task in a distributed fashion so that the entire collective meets its goal. This result is then extended to consider unbounded communication delays between members and complete failure of individual members of the collective.