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Explore cutting-edge research in robotic manipulation through this keynote address from the 2017 Research Showcase. Delve into Siddhartha Srinivasa's work on bridging the gap between current robotic capabilities and human-level dexterity in manipulation tasks. Learn about nonprehensile physics-based manipulation models that enable robots to push, pull, and slide objects in cluttered environments. Discover the mathematics behind human-robot interaction and collaborative manipulation, including Bayesian inference for modeling human collaborators and trajectory optimization for generating fluent collaborative plans. Gain insights into a new initiative on assistive care that combines physics, human-robot collaboration, control theory, and rehabilitation engineering to develop caregiving systems. Understand the importance of integrating perception, planning, and control in real-world robotic systems, and how this approach has led to state-of-the-art algorithms in object recognition, pose estimation, and dense 3D modeling.