Explore a comprehensive robotics lecture on hierarchical reasoning, abstractions, and geometry in autonomous systems. Delve into the advancements in robotic understanding and operation, including self-driving cars, robot mapping, and home service robots. Examine the limitations of current geometric models used by robots and discover the need for abstract concepts in long-term planning and complex mission execution. Learn about recent developments in combining semantic and physical representations for improved planning and decision-making. Gain insights from Nicholas Roy, the Bisplinghoff Professor at MIT, as he shares his expertise in aeronautics, astronautics, and artificial intelligence. Understand the implications of these advancements for the future of robotics and AI.