Book Description

Integrating autonomous robots into safety-critical settings requires reasoning about uncertainty at all levels of the autonomy stack. This thesis presents novel algorithmic tools for imbuing robustness within two hierarchically complementary areas, namely: motion planning and decision-making. In Part I of the thesis, by harnessing the theories of contraction and semi-infinite convex optimization and the computational tool of sum-of-squares programming, we present a unified framework for robust real-time motion planning for complex underactuated nonlinear systems. Broadly, the approach entails pairing open-loop motion planning algorithms that neglect uncertainty and are optimized for generating trajectories for simple kinodynamic models in real-time, with robust nonlinear trajectory-tracking feedback controllers. We demonstrate how to systematically synthesize these controllers and integrate them within planning to generate and execute certifiably safe trajectories that are robust to the closed-loop effects of disturbances and planning with simplified models. In Part II of the thesis, we demonstrate how to embed the control-theoretic advancements developed in Part I as constraints within a novel semi-supervised algorithm for learning dynamical systems from user demonstrations. The constraints act as a form of context-driven hypothesis pruning to yield learned models that jointly balance regression performance and stabilizability, ultimately resulting in generated trajectories for the robot that are conditioned for feedback control. Experimental results on a quadrotor testbed illustrate the efficacy of the proposed algorithms in Parts I and II of the thesis, and clear connections between theory and hardware. Finally, in Part III of the thesis, we describe a framework for lifting notions of robustness from low-level motion planning to higher-level sequential decision-making using the theory of risk measures. Leveraging a class of risk measures with favorable axiomatic foundations, we demonstrate how to formulate decision-making algorithms with tunable robustness properties. In particular, we focus on a novel application of this framework to inverse reinforcement learning where we learn predictive motion models for humans in safety-critical scenarios, and illustrate their effectiveness within a commercial driving simulator featuring humans in-the-loop. The contributions within this thesis constitute an important step towards endowing modern robotic systems with the ability to systematically and hierarchically reason about safety and efficiency in the face of uncertainty, which is crucial for safety-critical applications.