cs.ROMay 27, 2026

A Surveillance Evasion Game with Continuous Sensor Redeployment via Bilevel Optimization

Authors: Jaehyeok KimKartik A. PantJoseph KinersonKylie Sommer-KohrtWorawis SribunmaLi-Yu LinJames M. Goppert

Organizations: School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47906

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.

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