Inferring Turn-Rate-Limited Engagement Zones with Sacrificial Agents for Safe Trajectory Planning

This paper presents a learning-based framework for estimating pursuer parameters in turn-rate-limited pursuit-evasion scenarios using sacrificial agents. Each sacrificial agent follows a straight-line trajectory toward an adversary and reports whether it was intercepted or survived. These binary outcomes are related to the pursuer's parameters through a geometric reachable-region (RR) model. Two formulations are introduced: a boundary-interception case, where capture occurs at the RR boundary, and an interior-interception case, which allows capture anywhere within it. The pursuer's parameters are inferred using a gradient-based multi-start optimization with custom loss functions tailored to each case. Two trajectory-selection strategies are proposed for the sacrificial agents: a geometric heuristic that maximizes the spread of expected interception points, and a Bayesian experimental-design method that maximizes the D-score of the expected Gauss-Newton information matrix, thereby selecting trajectories that yield maximal information gain. Monte Carlo experiments demonstrate accurate parameter recovery with five to twelve sacrificial agents. The learned engagement models are then used to generate safe, time-optimal paths for high-value agents that avoid all feasible pursuer engagement regions.

Systematic Constraint Formulation and Collision-Free Trajectory Planning Using Space-Time Graphs of Convex Sets

In this paper, we create optimal, collision-free, time-dependent trajectories through cluttered dynamic environments. The many spatial and temporal constraints make finding an initial guess for a numerical solver difficult. Graphs of Convex Sets (GCS) and the recently developed Space-Time Graphs of Convex Sets formulation (ST-GCS) enable us to generate optimal minimum distance collision-free trajectories without providing an initial guess to the solver. We also explore the derivation of general GCS-compatible constraints and document an intuitive strategy for adapting general constraints to the framework. We show that ST-GCS produces equivalent trajectories to the standard GCS formulation when the environment is static. We then show ST-GCS operating in dynamic environments to find minimum distance collision-free trajectories.