A Surveillance Evasion Game with Continuous Sensor Redeployment via Bilevel Optimization

2026-05-26

AI Summary

This study addresses the security threat posed by unmanned aerial systems exploiting spatiotemporal blind spots in sensor networks to infiltrate critical infrastructure airspace. The authors formulate a zero-sum differential game between attacker and defender: the defender continuously redeploys heterogeneous sensors along building perimeters, while the attacker seeks a minimally detectable trajectory. A novel continuously differentiable sensor sliding redeployment mechanism is proposed, operating at the vertices of convex polygons, which overcomes the limitations of traditional discrete placement and establishes a baseline for heterogeneous anti-drone sensor deployment. By integrating log-sum-exp smoothing, STP-RRT* for trajectory initialization, and gradient-based bilevel optimization, the framework jointly converges to a local Nash equilibrium, demonstrating that continuous sensor redeployment significantly enhances airspace surveillance effectiveness.

Abstract

Uncrewed Aerial Systems (UASs) have become a growing threat to the security of critical infrastructure, exploiting spatiotemporal gaps in sensor perimeters to infiltrate restricted airspace undetected. We formulate this interaction as a two-player zero-sum differential game between an adversarial UAS and a heterogeneous sensor network of directional and omnidirectional sensors. Unlike earlier game-theoretic approaches that restrict the defender to discrete placement graphs or fixed configurations, we introduce a continuous sensor redeployment technique in which each sensor slides freely along the convex building boundaries. This is enforced via a log-sum-exp smooth approximation that preserves differentiability at polygon vertices, enabling optimization with gradient-based methods. The attacker's best response is computed via a two-step approach combining STP-RRT* for feasible trajectory initialization and nonlinear programming for detection-minimization refinement. The joint optimization converges to a Local Nash Equilibrium (LNE) via alternating bilevel optimization, with analytical first-order stationarity conditions derived for both players, thereby establishing a deployable baseline for heterogeneous sensor placements in CUAS missions.

Problem

• Surveillance Evasion
• Uncrewed Aerial Systems
• Sensor Redeployment
• Critical Infrastructure Protection
• Differential Game

Innovation

• continuous sensor redeployment
• bilevel optimization
• Local Nash Equilibrium
• log-sum-exp smoothing
• heterogeneous sensor network