We consider the problem of exploring an unknown
environment with a pair of mobile robots. The goal is to make
the robots meet (or rendezvous) in minimum time such that
there is a maximum speed gain of the exploration task. The
key challenge in achieving this goal is to rendezvous with
the least possible dependency on communication. This single
constraint involves several sub-problems: finding unique potential
rendezvous locations in the environment, ranking these locations
based on their uniqueness and synchronizing with the other robot
to meet at one of the locations at a scheduled time. In addition,
these tasks are to be performed simultaneously while exploring
and mapping the environment. We propose an approach for
efficiently combining the exploration and rendezvous tasks by
considering the cost of reaching a rendezvous location and
the reward of its uniqueness. This cost and reward model is
combined with a set of deterministic and probabilistic rendezvous
strategies for the robots to meet during exploration. Experimental
results suggest that the joint tasks of exploration and rendezvous
are substantially improved by ranking the potential rendezvous
locations based on the combined cost-reward criterion when
compared to the ranking solely based on the uniqueness of the
location.