Encirclement Guaranteed Finite-Time Capture against Unknown Evader Strategies

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.

We study minimum-time escape of an omnidirectional evader from the forward conic field of view of a Reeds-Shepp pursuer with minimum turning radius $r$. For speed ratio $ν$ and cone half-angle $0<α<π/2$, we prove a global escape/holding classification: straight reversal holds the whole cone for $ν\le\sinα$, escape is confined to a barrier-bounded dart for $\sinα<ν\le1$, and escape is possible from every state for $ν>1$. For the slower or equally fast evader, $\sinα<ν\le1$, we construct the solution with Isaacs' characteristics and verify it in feedback form, using a Filippov pursuer relay and a one-sided evader branch. The finite escape time is the first root of one scalar equation, and the holding region is bounded by the nonusable parts of the rays and a barrier that closes with a convex corner on the front axis. Sample-and-hold counter-controls show that this escape time is the value of the game in nonanticipative strategies at every state except the corner. There the two strategy values differ: the pursuer's is infinite, whereas an evader that chooses which barrier branch to cross from the initial germ of the pursuer's control escapes before the barrier time $τ_I$, which is the evader's exact strategy value. An independent level-set solver, refined on fixed comparison points, agrees with the closed-form escape time and reproduces the holding region at the tested parameters.

Safe, real-time motion planning is especially difficult when a dynamic obstacle actively pursues the ego agent, requiring rapid adaptation as the environment changes. We present TrajEdit, a hierarchical trajectory planner for pursuit-evasion that combines flow matching, trajectory editing, and safety filtering. Rather than regenerating trajectories from scratch at every step, TrajEdit follows the current plan under nominal conditions and adapts its remaining portion through FlowEdit as the pursuer approaches, and falls back to a control barrier function safety filter if the adversarial agent is within a safety threshold. Our use of FlowEdit for trajectory editing reduces computation time while maintaining a comparable success rate. We evaluate TrajEdit in 2D pursuit-evasion with static obstacles and an adversarial pursuer, demonstrating high success rates with low capture and collision rates, while achieving computational time savings over full replanning baselines.