Control tasks with safety requirements under high levels of model uncertainty are increasingly common. Machine learning techniques are frequently used to address such tasks, typically by leveraging model error bounds to specify robust constraint-based safety filters. However, if the learned model uncertainty is very high, the corresponding filters are potentially invalid, meaning no control input satisfies the constraints imposed by the safety filter. While most works address this issue by assuming some form of safe backup controller, ours tackles it by collecting additional data on the fly using a Gaussian process bandit-type algorithm. We combine a control barrier function with a learned model to specify a robust certificate that ensures safety if feasible. Whenever infeasibility occurs, we leverage the control barrier function to guide exploration, ensuring the collected data contributes toward the closed-loop system safety. By combining a safety filter with exploration in this manner, our method provably achieves safety in a general setting that does not require any prior model or backup controller, provided that the true system lies in a reproducing kernel Hilbert space. To the best of our knowledge, it is the first safe learning-based control method that achieves this.

Robot learning has produced remarkably effective "black-box" controllers for complex tasks such as dynamic locomotion on humanoids. Yet ensuring dynamic safety, i.e., constraint satisfaction, remains challenging for such policies. Reinforcement learning (RL) embeds constraints heuristically through reward engineering, and adding or modifying constraints requires retraining. Model-based approaches, like control barrier functions (CBFs), enable runtime constraint specification with formal guarantees but require accurate dynamics models. This paper presents SHIELD, a layered safety framework that bridges this gap by: (1) training a generative, stochastic dynamics residual model using real-world data from hardware rollouts of the nominal controller, capturing system behavior and uncertainties; and (2) adding a safety layer on top of the nominal (learned locomotion) controller that leverages this model via a stochastic discrete-time CBF formulation enforcing safety constraints in probability. The result is a minimally-invasive safety layer that can be added to the existing autonomy stack to give probabilistic guarantees of safety that balance risk and performance. In hardware experiments on an Unitree G1 humanoid, SHIELD enables safe navigation (obstacle avoidance) through varied indoor and outdoor environments using a nominal (unknown) RL controller and onboard perception.

A key source of brittleness for robotic systems is the presence of model uncertainty and external disturbances. Most existing approaches to robust control either seek to bound the worst-case disturbance (which results in conservative behavior), or to learn a deterministic dynamics model (which is unable to capture uncertain dynamics or disturbances). This work proposes a different approach: training a state-conditioned generative model to represent the distribution of error residuals between the nominal dynamics and the actual system. In particular we introduce the Online Risk-Informed Optimization controller (ORIO), which uses Discrete-Time Control Barrier Functions, combined with a learned, generative disturbance model, to ensure the safety of the system up to some level of risk. We demonstrate our approach in simulations and hardware, and show that our method can learn a disturbance model that is accurate enough to enable risk-sensitive control of a quadrotor flying aggressively with an unmodelled slung load. We use a conditional variational autoencoder (CVAE) to learn a state-conditioned dynamics residual distribution, and find that the resulting controller can run at 100Hz on an embedded computer and exhibits less conservative behavior while retaining theoretical safety properties.

Drivers have a responsibility to exercise reasonable care to avoid collision with other road users. This assumed responsibility allows interacting agents to maintain safety without explicit coordination. Thus to enable safe autonomous vehicle (AV) interactions, AVs must understand what their responsibilities are to maintain safety and how they affect the safety of nearby agents. In this work we seek to understand how responsibility is shared in multi-agent settings where an autonomous agent is interacting with human counterparts. We introduce Responsibility-Aware Control Barrier Functions (RA-CBFs) and present a method to learn responsibility allocations from data. By combining safety-critical control and learning- based techniques, RA-CBFs allow us to account for scene- dependent responsibility allocations and synthesize safe and efficient driving behaviors without making worst-case assumptions that typically result in overly-conservative behaviors. We test our framework using real-world driving data and demonstrate its efficacy as a tool for both safe control and forensic analysis of unsafe driving.

Autonomous vehicles must often contend with conflicting planning requirements, e.g., safety and comfort could be at odds with each other if avoiding a collision calls for slamming the brakes. To resolve such conflicts, assigning importance ranking to rules (i.e., imposing a rule hierarchy) has been proposed, which, in turn, induces rankings on trajectories based on the importance of the rules they satisfy. On one hand, imposing rule hierarchies can enhance interpretability, but introduce combinatorial complexity to planning; while on the other hand, differentiable reward structures can be leveraged by modern gradient-based optimization tools, but are less interpretable and unintuitive to tune. In this paper, we present an approach to equivalently express rule hierar-chies as differentiable reward structures amenable to modern gradient-based optimizers, thereby, achieving the best of both worlds. We achieve this by formulating rank-preserving reward functions that are monotonic in the rank of the trajectories induced by the rule hierarchy; i.e., higher ranked trajectories receive higher reward. Equipped with a rule hierarchy and its corresponding rank-preserving reward function, we develop a two-stage planner that can efficiently resolve conflicting planning requirements. We demonstrate that our approach can generate motion plans in ~7-10 Hz for various challenging road navigation and intersection negotiation scenarios.

With the increasing prevalence of complex vision-based sensing methods for use in obstacle identification and state estimation, characterizing environment-dependent measurement errors has become a difficult and essential part of modern robotics. This paper presents a self-supervised learning approach to safety-critical control. In particular, the uncertainty associated with stereo vision is estimated, and adapted online to new visual environments, wherein this estimate is leveraged in a safety-critical controller in a robust fashion. To this end, we propose an algorithm that exploits the structure of stereo-vision to learn an uncertainty estimate without the need for ground-truth data. We then robustify existing Control Barrier Function-based controllers to provide safety in the presence of this uncertainty estimate. We demonstrate the efficacy of our method on a quadrupedal robot in a variety of environments. When not using our method safety is violated. With offline training alone we observe the robot is safe, but overly-conservative. With our online method the quadruped remains safe and conservatism is reduced.

The increasing complexity of modern robotic systems and the environments they operate in necessitates the formal consideration of safety in the presence of imperfect measurements. In this paper we propose a rigorous framework for safety-critical control of systems with erroneous state estimates. We develop this framework by leveraging Control Barrier Functions (CBFs) and unifying the method of Backup Sets for synthesizing control invariant sets with robustness requirements—the end result is the synthesis of Measurement-Robust Control Barrier Functions (MR-CBFs). This provides theoretical guarantees on safe behavior in the presence of imperfect measurements and improved robustness over standard CBF approaches. We demonstrate the efficacy of this framework both in simulation and experimentally on a Segway platform using an onboard stereo-vision camera for state estimation.