The deployment of autonomous robots across domains ranging from transportation to human-robot collaboration demands robust safety measures to ensure smooth interaction with the physical world. Traditional safe control algorithms have enabled provable guarantees in structured settings, but they face two persistent challenges in real-world deployments: adaptation to non-stationary objectives and dynamics, and scalability to high-dimensional robots and environments where safety reasoning and enforcement become computationally difficult. This thesis argues that enabling robots to operate safely in everyday life requires stepping beyond traditional robot safety by developing safe control and analysis methods that are both adaptive and scalable.

The thesis addresses adaptive, safety-constrained tasks in a top-down fashion. At the top level, we formulate an optimization problem with (a) an arbitrary control objective, subject to constraints that encode (b) system dynamics and (c) safety requirements. This viewpoint naturally extends to modeling real-world complexity: objectives can vary due to unpredictable factors such as human preferences, dynamics can drift due to changing physical conditions, and safety constraints can become high-dimensional and multi-objective when considering fine-grained robot-environment interactions.

Building on this view, the thesis makes two sets of contributions. First, we develop adaptive methods that preserve safety in interactive operations. To adapt to varying control objectives, we propose the Conditional Collaborative Handling Process (CCHP) to incorporate short contextual demonstrations and enable rapid objective inference and controller adjustment in a physical human-robot collaboration task. We also address adaptation to varying dynamics with safety guarantees by exploiting the structure of provably safe controller synthesis to update safety certificates in real time via Determinant Gradient Ascent (DGA). Second, we shift our focus to high-dimensional systems, where safety reasoning must scale to complex dynamics, rich perception, and coupled constraints. We propose λ-Reachability, a scalable approach to Hamilton-Jacobi safety analysis that interpolates between local consistency and long-horizon safety targets, improving both value approximation accuracy and sample efficiency in high-dimensional humanoid safety value synthesis. In the inevitable case of imperfect safety value functions, we further propose the Projected Safe Set Algorithm (p-SSA) to handle infeasibility in dexterous safe control with dense, multi-body collision constraints, achieving robust collision avoidance in simulation and on a real humanoid robot across cluttered environment tasks.

Collectively, these results broaden the scope of safety-critical robotics from controlled, low-dimensional settings to adaptive and high-dimensional real-world deployments, enabling robots to operate effectively and safely under complex safety requirements.