Mobile robots equipped with wireless networking capabilities can
provide network connectivity to mobile users.  In this paper, we
present motion planning algorithms for one or more robots to maintain
the connectivity of a single user (target) to a base-station. We study
two target models: in the first model, the target’s trajectory is
known in advance. In the second model, the target moves in an
adversarial fashion and tries to break connectivity.

In the first part of the paper, we present optimal motion strategies
for a single robot to maintain the target’s connectivity for the
maximum time for both types of user models. In the second part, we
extend these results and obtain motion strategies for a team of robots
to maintain the target’s connectivity.