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

Obstacle avoidance is essential for safe navigation and motion planning. Recent radiance field reconstruction methods enable object detection and modeling with high fidelity, but remain too memory- and compute-intensive for on-board perception-based path planning. To address these limitations, we propose PolyMerge to convert a large, photorealistic 3D Gaussian Splatting (3DGS) model of a scene into a lightweight representation of convex polytopes whose union provably over-approximates all obstacles in the original 3DGS model. PolyMerge tunes the polytope count to trade off conservativeness and compute cost, and integrates with control barrier functions (CBFs) to plan collision-free paths. We showcase PolyMerge in simulation and hardware experiments on a Crazyflie drone, which uses PolyMerge to compute and follow safe trajectories in real time under severe onboard compute constraints, outperforming baselines in speed while guaranteeing safety. For our code and videos, visit https://athlon76.github.io/PolyMerge-website/.

We study high-order safety-critical control of quadrotor teams under bounded inputs and pairwise collision-avoidance constraints. Squared-distance barriers may lose thrust effectiveness when the relative displacement is orthogonal to the available thrust directions, while nonsingular constraints may still be jointly infeasible under shared bounds. We characterize both phenomena through pairwise effectiveness and aggregate feasibility measures. A torque-aware dynamic extension exposes attitude torques in a fourth-order barrier and prevents the extended-input row from vanishing under positive thrust. Gaussian processes directly learn the fourth-order HOCBF residual, providing robust margins without differentiating unknown perturbations. Under residual-bound and persistent-feasibility assumptions, the resulting QP guarantees collision avoidance and recovers the nominal input whenever it satisfies the robust safety and actuator constraints.

Control barrier functions for input-constrained systems place the admissible input set inside the definition of the safe set, yet the resulting barrier is almost always a function of the state alone; On a quadrotor this is not cosmetic: because the thrust vector must be reoriented before it can decelerate an approach, and reorientation is limited by the attainable body rate, a state-only barrier certifies states from which no escape is reachable in time; We characterize the certification gap in closed form and show its width is proportional to closing speed and inversely proportional to the body-rate limit; We then define an escape barrier on the augmented pair of state and previously applied input, with escape authority measured over the one-step reachable thrust cap; It admits a closed form and an analytic inverse for the maximum certifiable closing speed, and embeds in a predictive controller at no additional state cost; Across 550 paired closed-loop episodes on a 13-state quadrotor, the proposed controller completes every tested scenario, whereas the stopping-distance barrier enforced over the same horizon fails 15% and 25% of episodes in exactly the two scenarios that enter the predicted gap; Against an online backup-CBF baseline enforcing the same escape condition at the reached state, it holds a 29-74 degree larger directional margin and 3-18 times the clearance, and an independent conservative rollout referee finds no certified state from which escape fails.