Optimality and robustness in multi-robot path planning 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 that 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 that computes a run corresponding to the optimal robot path. We present an implementation for a robot performing data collection in a road-network platform.This work was supported in part by the Office of Naval Research (grant number MURI N00014-09-1051), Army Research Office (grant number W911NF-09-1-0088), Air Force Office of Scientific Research (grant number YIP FA9550-09-1-020), National Science Foundation (grant number CNS-0834260), Singapore-MIT Alliance for Research and Technology (SMART) Future of Urban Mobility Project and by Natural Sciences and Engineering Research Council of Canada. (MURI N00014-09-1051 - Office of Naval Research; W911NF-09-1-0088 - Army Research Office; YIP FA9550-09-1-020 - Air Force Office of Scientific Research; CNS-0834260 - National Science Foundation; Singapore-MIT Alliance for Research and Technology (SMART); Natural Sciences and Engineering Research Council of Canada