Least-Violating Planning in Road Networks from Temporal Logic Specifications

In this paper, we consider the problem of automated plan synthesis for a vehicle operating in a road network, which is modeled as a weighted transition system. The vehicle is assigned a set of demands, each of which involves a task specification in the form of a syntactically co-safe LTL formula, a deadline for achieving this task, and a demand priority. The demands arrive gradually, upon the run of the vehicle, and hence periodical replanning is needed. We particularly focus on cases, where all tasks cannot be accomplished within the desired deadlines and propose several different ways to measure the degree of demand violation that take into account the demand priorities. We develop a general solution to the problem of least-violating planning and replanning based on a translation to linear programming problem. Furthermore, for a particular subclass of demands, we provide a more efficient solution based on graph search algorithms. The benefits of the approach are demonstrated through illustrative simulations inspired by mobility-on-demand scenarios.