Robotics and Artificial Intelligence (AI) have been inextricably intertwined since their inception. Today, AI-Robotics systems have become an integral part of our daily lives, from robotic vacuum cleaners to semi-autonomous cars. These systems are built upon three fundamental architectural elements: perception, navigation and planning, and control. However, while the integration of AI in Robotics systems has enhanced the quality of our lives, it has also presented a serious problem -these systems are vulnerable to security attacks. The physical components, algorithms, and data that makeup AI-Robotics systems can be exploited by malicious actors, potentially leading to dire consequences. Motivated by the need to address the security concerns in AI-Robotics systems, this paper presents a comprehensive survey and taxonomy across three dimensions: attack surfaces, ethical and legal concerns, and Human-Robot Interaction (HRI) security. Our goal is to provide readers, developers and other stakeholders with a holistic understanding of these areas to enhance the overall AI-Robotics system security. We begin by identifying potential attack surfaces and provide mitigating defensive strategies. We then delve into ethical issues, such as dependency and psychological impact, as well as the legal concerns regarding accountability for these systems. Besides, emerging trends such as HRI are discussed, considering privacy, integrity, safety, trustworthiness, and explainability concerns. Finally, we present our vision for future research directions in this dynamic and promising field.