Autonomous vehicles – aircraft, cars, rovers, over- and underwater vehicles that can move in the real world by themselves without human pilotage – have gained immense importance not only due to the broad spectrum of their potential military and civilian applications, but also due to the concurrent development of sensor technology and embedded systems that enable the realization of true autonomy. These vehicles may be assigned tasks that are dull and/or repetitive, such as mobile surveillance or cleaning and maintenance; tasks that are dangerous for humans, such as military transportation via hostile territory, large-scale ﬁre ﬁghting, and repair and recovery operations in chemical plants and nuclear reactors; or tasks that are prohibitively expensive for humans to execute, such as the exploration of celestial bodies. Unsurprisingly, various theoretical and practical aspects of the development of autonomous mobile vehicles have been vigorously and extensively researched by the robotics, automatic control, and artiﬁcial intelligence communities for over four decades. I am interested in several broad research problems related to autonomous vehicles. Firstly, I am interested in the optimal motion planning and control problem, which involves finding control inputs (e.g. steering, throttle) that enable the vehicle’s desired motion. Optimal control theory has been studied for over three hundred years, but new computational strategies are required to develop real-time algorithms. Secondly, I am interested in the intelligent control problem, which involves developing and integrating artificial intelligence (AI) algorithms with control algorithms to enable the vehicle to achieve complex tasks specified in human-like language (e.g. “get me to my workplace ASAP, drop my friend close to his workplace, find a cheap parking spot and wait until I need you again; also save gasoline as much as possible”). AI and automatic control have been traditionally disparate academic disciplines; furthermore, AI and control problems are formulated using fundamentally different mathematical tools, which makes their integration challenging. These challenges are addressed in the new field of hybrid control, which is the focus of my research. Finally, I am interested in the safety analysis of large-scale systems involving autonomous vehicles. These vehicles must interact with existing infrastructure – unmanned aircraft must share airspace with piloted aircraft in the future – and eventually, with human supervisors. Presently, very little is known about formal (mathematically rigorous) analysis of the safety of such systems involving autonomous agents, humans, and physical infrastructure – now known as cyber-physical systems. My research involves a continuous learning process of mathematically dense topics from AI, dynamics, and control. A by-product of this process is that I have come to appreciate the importance of elucidating such topics in simple, everyday language and diagrams. The most important objective of my teaching is to bring to the students mathematically rich material from dynamics and control in easily digestible forms, to the point where the students can identify the mathematics accentuating the underlying concepts, rather than obscuring them.