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This paper formulates a two-player zero-sum differential game between an adversarial UAS and a heterogeneous sensor network, where the sensors can be continuously redeployed along building boundaries. They introduce a log-sum-exp smooth approximation to enable gradient-based optimization for sensor placement, and combine STP-RRT* with nonlinear programming for the attacker's trajectory optimization. Alternating bilevel optimization, guided by analytical first-order stationarity conditions, converges to a Local Nash Equilibrium, providing a baseline for CUAS missions.
Continuous sensor redeployment along building boundaries can significantly improve defense against adversarial UAS infiltration, outperforming fixed configurations.
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.
