  In this paper we present a method for automatically generating optimal robot
trajectories satisfying high level mission specifications. The motion of the
robot in the environment is modeled as a general transition system, enhanced
with weighted transitions. The mission is specified by a general linear
temporal logic formula. In addition, we require that an optimizing proposition
must be repeatedly satisfied. The cost function that we seek to minimize is the
maximum time between satisfying instances of the optimizing proposition. For
every environment model, and for every formula, our method computes a robot
trajectory which minimizes the cost function. The problem is motivated by
applications in robotic monitoring and data gathering. In this setting, the
optimizing proposition is satisfied at all locations where data can be
uploaded, and the entire formula specifies a complex (and infinite horizon)
data collection mission. Our method utilizes B\"uchi automata to produce an
automaton (which can be thought of as a graph) whose runs satisfy the temporal
logic specification. We then present a graph algorithm which computes a path
corresponding to the optimal robot trajectory. We also present an
implementation for a robot performing a data gathering mission in a road
network.
