This award supports research that addresses critical vulnerabilities in remotely controlled robotic systems through a comprehensive study of a particularly sophisticated class of cyber attacks, thereby advancing the national health, promoting the progress of science, advancing prosperity and welfare, and securing the national defense. Modern robotic systems rely heavily on networked communication for coordination and control, creating opportunities for malicious actors to inject false data that can cause robots to perform unintended and potentially dangerous actions. Traditional cybersecurity approaches designed for computer networks are insufficient for robotic systems because robots operate in physical environments where security breaches can result in property damage, personal injury, or disruption of essential services. This project looks to address this critical gap by studying affine transformation-based perfectly undetectable attacks that exploit the geometric properties inherent in robotic systems to remain completely undetectable by conventional security measures. Understanding and defending against these attacks is crucial for maintaining public trust in robotic technologies and ensuring their safe deployment in critical applications. The project seeks to advance fundamental knowledge in robotic cybersecurity while training graduate students in interdisciplinary research combining robotics, cybersecurity, and mathematical theory, thereby strengthening the national w