Optimal path planning for surveillance with temporal-logic constraints

In this paper we present a method for automatically generating optimal robot paths satisfying high level mission specifications. The motion of the robot in the environment is modeled as a weighted transition system. The mission is specified by an arbitrary linear temporal logic (LTL) formula over propositions satisfied at the regions of a partitioned environment. The mission specification contains an optimizing proposition which 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 path 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 LTL formula specifies a complex data collection mission. Our method utilizes Büchi 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 run corresponding to the optimal robot path. We present an implementation for a robot performing data collection in a road network platform.