TrajEdit: Real-Time Flow-Matching Trajectory Adaptation via FlowEdit and CBF Safety Filter

We consider a planar pursuit-evasion problem in which a Dubins pursuer seeks to capture a slower first-order point-mass evader that can change its heading instantaneously. First, we propose a turn-rate feedback law with a single tunable gain and derive an explicit admissible gain interval that guarantees finite-time capture against any admissible evader strategy while satisfying the turn-rate constraint. Next, we obtain an explicit capture-time bound and characterize the turning authority required for the gain interval to be non-empty. Finally, we show that the dependence on the evader's speed bound can be removed by deriving a speed ceiling, computable solely from the pursuer's parameters, below which the guarantees hold at the maximum allowable gain. Numerical simulations illustrate the effectiveness of the proposed approach.

Safe navigation in dynamic environments requires robots to plan under obstacle predictions whose errors are uncertain, non-stationary, and can induce rare but safety-critical failures. Existing control-barrier-function safety filters can reject immediately unsafe controls, but they provide little guidance on when the current finite-horizon planning mode itself is becoming unsafe as prediction uncertainty evolves. We propose Conformal Event-Triggered Risk-Certified Replanning (CERT-Replan), a framework that uses calibrated barrier risk as an early-warning signal for replanning. CERT-Replan calibrates horizon-indexed obstacle-prediction residuals online and uses the resulting uncertainty radii to evaluate dynamic-obstacle safety margins. A one-step safety filter protects the next applied control, while a horizon-level risk monitor evaluates the upper-tail CVaR of predicted barrier-violation losses along the current MPC rollout. When this risk exceeds an allocated budget, CERT-Replan rejects the current planning mode and selects a lower-risk alternative, such as a different speed profile, corridor, or homotopy class, rather than repeatedly correcting the same nominal plan. In a non-stationary benchmark, CERT-Replan achieves an $83.3\%$ collision reduction relative to the safety-filter-only baseline \textcolor{black}{and a $77.8\%$ reduction relative to simple replanning triggers}, while reducing average safety-filter intervention by $32.4\%$. \textcolor{black}{With Trajectron++, CERT-Replan achieves $96\%$ collision-free operation. Hardware experiments and onboard runtime profiling demonstrate computational feasibility.}

Autonomous high-speed navigation through large, complex environments requires real-time generation of agile trajectories that are dynamically feasible, collision-free, and satisfy state or actuator constraints. Modern trajectory planning techniques primarily use numerical optimization, as they enable the systematic computation of high-quality, expressive trajectories that satisfy various constraints. However, stringent requirements on computation time and the risk of numerical instability can limit the use of optimization-based planners in safety-critical scenarios. This work presents an optimization-free planning framework called STITCHER that stitches short trajectory segments together with graph search to compute long-range, expressive, and near-optimal trajectories in real-time. STITCHER outperforms modern optimization-based planners through our innovative planning architecture and several algorithmic developments that make real-time planning possible. Extensive simulation testing is performed to analyze the algorithmic components that make up STITCHER, along with a thorough comparison with three state-of-the-art optimization planners. Simulation tests show that safe trajectories can be created within a few milliseconds for paths that span the entirety of two 50 m x 50 m environments. Hardware tests with a custom quadrotor verify that STITCHER can produce trackable paths in real-time while respecting nonconvex constraints, such as limits on tilt angle and motor forces, with flight speeds up to 63 km/h.