Ergodic Trajectory Design by Learned Pushforward Maps: Provable Coverage via Conditional Flow Matching

ArXi:2605.13063v1 Announce Type: new Designing continuous trajectories whose time-averaged occupancy provably matches a prescribed spatial density (the \emph{ergodic coverage} problem) is central to UAV-assisted data collection and sensing, robotic exploration, and mobile monitoring. For flying agents in particular, this challenge is acute: trajectories must balance coverage fidelity against tight energy budgets, no-fly zones, and acceleration limits.