FastBridge: Closing the Model-Based Realization Gap in Safety Filters on 3D Gaussian Splatting for Fast Quadrotor Flight

Fast quadrotor flight requires safe obstacle avoidance under tight onboard compute limits. While 3D Gaussian Splatting (3DGS) provides a continuous, geometry-aware scene representation for perception-driven navigation, existing 3DGS safety filters use reduced-order models such as single- and double-integrators that ignore actuator limits and assume commanded accelerations are realized instantaneously. Building on an analytic collision cone barrier for 3DGS, we introduce a nonlinear, actuator-aware safety filter enforced through the full quadrotor dynamics. We derive a high-relative-degree collision cone exponential CBF and a backup CBF that preserves QP feasibility under input constraints using a forward-simulated backup policy. Compared with a state-of-the-art 3DGS safety filter, our approach reduces trajectory jerk by 47% and runs 2.25 times faster. We validate the method in simulation and on hardware for real-time navigation in cluttered, perception-derived environments.