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Driving safely, efficiently, and smoothly in mixed traffic is a crucial capability of autonomous vehicles. It is also very challenging, because of the uncertainties in future motions of the nearby traffic agents, constantly changing environments, etc.. In this thesis, we develop an autonomous driving system that takes those uncertainties into account. We proposed GAMMA, a general agent motion prediction model for autonomous driving, to predict the motions of heterogeneous traffic agents. GAMMA incorporates kinematics, geometry, intention, responsibility, and attention in a unified framework for prediction and achieves a high prediction accuracy on multiple real-world datasets. We then embed GAMMA into a partially observable Markov decision process (POMDP) to plan optimal vehicle control under uncertainty. We proposed IS-DESPOT for solving the POMDP. Our autonomous driving system enables safe, smooth, and …