An Automata-Theoretic Approach to the Vehicle Routing Problem

We propose a new formulation and algorithms for the Vehicle Routing Problem (VRP). To accommodate persistent surveillance missions, which require executions in infinite time, we define Persistent VRP (P-VRP). The vehicles consume a resource, such as gas or battery charge, which can be replenished when they visit replenish stations. The mission specifications are given as rich, temporal logic statements about the sites, their service durations, and the time intervals in which services should be provided. We define a temporal logic, called Time-Window Temporal Logic (TWTL), whose formulae allow for simple, intuitive descriptions of such specifications. Two different optimization criteria are considered. The first is the infinite-time limit of the duration needed for the completion of a surveillance round. The second penalizes the long-term average of the same quantity. The proposed algorithms, which are based on concepts and tools from formal verification and optimization, generate collision-free motion plans automatically from the temporal logic statements and vehicle characteristics such as maximum operation time and minimum replenish time. Illustrative simulations and experimental trials for a team of quadrotors involved in persistent surveillance missions are included.