In this work, we propose a two-phase game-theoretic framework to model and defend against Advanced Persistent Threat (APT) attacks in Autonomous Ground Robots (AGRs) running a ROS2-based autonomy stack for safety-critical navigation. In our scenario, the attacker seeks to penetrate the autonomous navigation system and take control over the AGR, causing it to crash into obstacles or fail in its navigation mission, potentially causing catastrophic damage. We use an attack tree abstraction to break the APT attack into two phases and analyze it using appropriate game-theoretical models and solutions to determine the optimal defense strategy for the defenders. For the first phase, we propose a variation of the popular cut-the-rope (CTR) security model by extending it to a probabilistic setting in which applying a spot-check at a given attack tree node does not necessarily result in a “cut” of the “rope”. We model this attack tree based on a curated library of real-world exploits in robotic systems and potential security measures that can counter these exploits. We show that this formulation admits a unique mixed Nash Equilibrium (NE) and determines the optimal defense policy for the first phase. Next, we address the scenario in which the defense mechanisms against the APT attack have failed to prevent the attacker from reaching the safety-critical target node in the network and the robotic asset is commandeered. We equip the robot system with a data-driven end-point Anomaly Detection System (ADS) that monitors the robot odometry data and detects anomalous entities being injected into the autonomy stack. We model this phase of the attack using a two-player zero-sum game where the defender needs to select optimal thresholds for the ADS monitor to balance the need for detecting data-poisoning attacks quickly while minimizing the possibility of false alarms and the attacker needs to select the intensity of the attack for the opposing objectives. We use experiments on a Nova Carter AGR running a Nav2-based autonomy stack within a Secure-ROS2 (SROS2) framework to inform the second-phase game-theoretic model and demonstrate the attack and defense mechanisms.