Vehicle Routing Problem Formulation for Efficient Tracking of Objects in Low Earth Orbit

Abstract

The increasing number of resident space objects (RSOs) in low Earth orbit (LEO) endangers the sustainable use of space and necessitates continuous surveillance to prevent collisions. The U.S. Space Surveillance Network (SSN) tracks tens of thousands of LEO RSOs using a suite of ground-based sensors; however, the algorithms that task and schedule these sensors have not improved significantly in the last twenty years. In that time, the number of catalogued LEO RSOs has more than doubled, calling for more efficient tasking algorithms. Prior research has primarily focused on improving the tasking of ground-based sensors for tracking RSOs in geosynchronous Earth orbit (GEO). In this paper, we extend recent work on a vehicle routing problem (VRP) formulation for optimal tasking and scheduling of ground-based radars for tracking GEO RSOs and apply it to tracking LEO RSOs. We introduce a modified VRP formulation, which features discrete time indexing and leverages sparse, binary feasibility matrices for reduced computation time, and present results for several simulations. We show that our approach can compute global and regional optima for tracking (a) 100 targets using 4 ground-based sensors over a 5-hour time horizon in under 5 minutes on a laptop computer and (b) 10,000 targets using 27 ground-based sensors over a 24-hour time horizon in about 4 hours on a high-performance computing cluster.