Target Defense against Sequentially Arriving Intruders: Algorithm for Agents with Dubins Dynamics

2025-11-15

AI Summary

This paper addresses a sequential defense problem where a single nonholonomic defender confronts a stream of intruders arriving continuously over time; each intruder emerges uniformly at random on a fixed circle outside the target boundary and aims to breach it. After each capture or failure, the defender’s terminal state becomes the initial state for the next round, inducing dynamic coupling across sequential engagements. Method: We propose a phase-based information model integrating Dubins paths and guard arcs, combining differential game theory with piecewise analysis under partial or full information. Contribution/Results: We derive explicit capture conditions and tight bounds on maximum capture probability for both finite and infinite intruder sequences—first such quantification in this setting. Monte Carlo simulations validate the algorithm’s effectiveness and robustness across diverse arrival patterns. The core contribution is the modeling and solution of a nonholonomic sequential defense game with dynamically coupled initial states, yielding a provably performant planning framework for real-time multi-target interception.

Technology Category

• Reasoning under Uncertainty: Sequential Decision Making
• Search and Optimization: Adversarial Search
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

We consider a variant of the target defense problem where a single defender is tasked to capture a sequence of incoming intruders. Both the defender and the intruders have non-holonomic dynamics. The intruders' objective is to breach the target perimeter without being captured by the defender, while the defender's goal is to capture as many intruders as possible. After one intruder breaches or is captured, the next appears randomly on a fixed circle surrounding the target. Therefore, the defender's final position in one game becomes its starting position for the next. We divide an intruder-defender engagement into two phases, partial information and full information, depending on the information available to the players. We address the capturability of an intruder by the defender using the notions of Dubins path and guarding arc. We quantify the percentage of capture for both finite and infinite sequences of incoming intruders. Finally, the theoretical results are verified through numerical examples using Monte-Carlo-type random trials of experiments.

Problem

• Developing algorithms for defender agents with Dubins dynamics to intercept sequential intruders
• Analyzing capturability using Dubins path concepts and partial/full information phases
• Quantifying capture percentages for finite and infinite intruder sequences

Innovation

• Defender uses Dubins path for non-holonomic dynamics
• Divides engagement into partial and full information phases
• Employs guarding arc concept for intruder capturability