Factor Graph-Based Time-Synchronized Trajectory Planning for UAVs in Ground Radar Environment Simulation

The use of unmanned aerial vehicles (UAVs) as mobile sensor platforms has grown significantly in recent years, including applications where drones emulate radar targets or serve as dynamic measurement systems. This paper presents a novel approach to time-synchronized UAV trajectory planning for radar environment simulation. The proposed method considers a UAV equipped with a software-defined radio (SDR) capable of reproducing the radar signature of a simulated airborne object, e.g., a high-maneuverability or high-speed aerial platform. The UAV must follow a spatial trajectory that replicates the viewing geometry-specifically, the observation angles-of the reference target as seen from a ground-based radar. The problem is formulated within a factor graph framework, enabling joint optimization of the UAV trajectory, observation geometry, and temporal synchronization constraints. While factor graphs have been extensively used in robotics and sensor fusion, their application to trajectory planning under temporal and sensing constraints remains largely unexplored. The proposed approach enables unified optimization over space and time, ensuring that the UAV reproduces the target motion as perceived by the radar, both geometrically and with appropriate signal timing.