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

TL;DR

The paper addresses inferring pursuer parameters under turn-rate-limited dynamics from binary sacrificial-agent outcomes to construct engagement zones and safe trajectories. It combines a geometrically grounded RR/EZ model with gradient-based, multi-start optimization to recover pursuer state and kinematic limits under several learning scenarios, including boundary and interior interception. To accelerate information gain, it introduces two sacrificial-trajectory selection strategies: a geometric exploration method for boundary interception and a Bayesian experimental-design approach with a Gauss–Newton information surrogate for interior interception. The learned parameter sets are then used to plan time-optimal, safe trajectories that avoid all feasible engagement zones, with Monte Carlo results demonstrating rapid convergence and substantial path-time improvements, even with limited data. The approach offers a principled framework for inferring adversarial capabilities from sparse, binary observations and integrating them into real-time safety-aware planning.

Abstract

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.

Figures (13)

• Figure 1: Reachable region (RR) of the pursuer (magenta) and the corresponding CSBEZ (green) for an evader heading along the $x$-axis. Sample evader (blue) and pursuer (red) trajectories are also shown.
• Figure 2: Sacrificial trajectories (blue), along with the true (red), potential (magenta), and learned mean (orange) pursuer reachable regions.
• Figure 3: Learned parameter values (points) and the mean learned parameter value (blue), along with the true parameter value (red).
• Figure 4: Median absolute error (solid) and IQR (shaded) across 500 MC runs for Cases 1A and 1B under the boundary-interception assumption. Blue indicates no measurement noise, and orange indicates noisy measurements.
• Figure 5: Median absolute error (solid) and IQR (shaded) across 500 runs for Cases 2A and 2B under the boundary-interception assumption. Blue indicates no measurement noise, and orange indicates noisy measurements.