Dynamic Safety Under Uncertainty: A Control Barrier Function Approach

Modern technological achievements in robotics, machine learning, and control promise an exciting future where autonomous robots are a useful part of everyday life, from automated manufacturing and driverless cars to robotic healthcare and autonomous delivery drones. However, as robots are deployed in increasingly complex, uncertain, and human-interactive environments, safety becomes paramount; we cannot deploy these systems at scale unless we are rigorously assured of their safety. Despite the capabilities of modern robotics, practical real-world safety is often achieved through conservative hardware designs, confining deployment regulations, or restrictive assumptions that severely limit a robot's capabilities. The goal of this thesis is to develop methods for achieving dynamic safety: formal safety guarantees that preserve system performance and remain valid under uncertainty. To this end, this thesis advances the theory and practice of control barrier functions (CBFs), a leading framework for enforcing safety constraints on dynamical systems. While CBF-based methods offer strong theoretical guarantees, they do so by relying on several restrictive assumptions. Namely, they assume that the safety requirement and the system dynamics are compatible and that the dynamics model and state are perfectly known. These assumptions rarely hold in real-world settings and can result in false confidence and catastrophic safety failures when violated. This thesis addresses these gaps by systematically relaxing these assumptions and developing new theory to retain rigorous, deployable guarantees. By leveraging structural properties of several relevant classes of system dynamics, I first present a myriad of constructive synthesis methods that make CBF design feasible for a wide range of robots. I then develop robust control methods that retain their safety guarantees in the presence of bounded dynamics and measurement uncertainty. However, despite the utility of these methods in guaranteeing safety, they often lead to highly conservative behavior that compromises system performance. Thus, to mitigate this conservatism, I leverage machine learning techniques to reduce uncertainty and determine desired levels of robustness. While this unification of machine learning techniques with safety-critical control may sacrifice formal guarantees, it enables safe and performant behavior in practice. Moreover, the robust CBF framework provides a valuable degree of interpretability absent from typical end-to-end approaches. Next, seeking a middle ground between conservative absolute guarantees and capable-but-heuristic methods, I adopt a probabilistic notion of safety that provides risk-based guarantees in the presence of unbounded disturbances. In particular, by illustrating the fundamental connection between DCBFs and supermartingales, I develop new theoretical guarantees and propose several algorithms to achieve safety in the presence of stochastic uncertainty. I then deploy these methods on several complex systems experiencing significant uncertainty, including a quadrotor robot with a slung payload, a humanoid robot walking in unstructured environments, and multiple robots performing dynamic collision avoidance. To achieve this, we use generative modeling techniques to capture the necessary understanding of the uncertainty distribution. Here, I also forego the traditional CBF-based safety filter paradigm and show the performance and safety improvements that can be gained through the unification of CBFs and horizon-based methods such as model predictive control (MPC). Together, the contributions of this thesis represent an advancement towards dynamic, safe, and capable robotic autonomy under uncertainty. The risk-aware, robust safety-critical control methods proposed here help close the gap between theoretical safety guarantees and the demands of real-world deployment.