In this dissertation, I present several ideas for building practical algorithms for building more reliable autonomous systems. That is, each of the ideas below is, from the outset, designed to be physically implementable on real hardware and operate in real-time. In Chapter 1, I provide a high-level overview of some of the key challenges in autonomy today and how this work addresses some of those challenges. Chapter 2 presents an approach for reachability-based robust motion planning, which for the first time attains adversarial robustness for real-time motion planning problems. Chapter 3 introduces the prediction problem which arises in multi-agent situations, and describes a Bayesian approach for determining how confident one should be in a given predictive model. Chapter 4 combines elements of the prediction and motion planning problems in a multi-player differential game and presents a novel real-time solution strategy. Finally, Chapter 5 lists several open problems and discusses several exciting next steps.




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