Offensive Robot Cybersecurity introduces a groundbreaking approach by advocating for offensive security methods empowered by means of automation. It emphasizes the necessity of understanding attackers' tactics and identifying vulnerabilities in advance to develop effective defenses, thereby improving robots' security posture. This thesis leverages a decade of robotics experience, employing Machine Learning and Game Theory to streamline the vulnerability identification and exploitation process. Intrinsically, the thesis uncovers a profound connection between robotic architecture and cybersecurity, highlighting that the design and creation aspect of robotics deeply intertwines with its protection against attacks. This duality -- whereby the architecture that shapes robot behavior and capabilities also necessitates a defense mechanism through offensive and defensive cybersecurity strategies -- creates a unique equilibrium. Approaching cybersecurity with a dual perspective of defense and attack, rooted in an understanding of systems architecture, has been pivotal. Through comprehensive analysis, including ethical considerations, the development of security tools, and executing cyber attacks on robot software, hardware, and industry deployments, this thesis proposes a novel architecture for cybersecurity cognitive engines. These engines, powered by advanced game theory and machine learning, pave the way for autonomous offensive cybersecurity strategies for robots, marking a significant shift towards self-defending robotic systems. This research not only underscores the importance of offensive measures in enhancing robot cybersecurity but also sets the stage for future advancements where robots are not just resilient to cyber threats but are equipped to autonomously safeguard themselves.