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1. Guaranteeing Safety of Learned Perception Modules via Measurement-Robust Control Barrier Functions

   Dean, Sarah; Taylor, Andrew; Cosner, Ryan; Recht, Benjamin; Ames, Aaron (November 2020, 4th Annual Conference on Robotic Learning)

   null (Ed.)

   Modern nonlinear control theory seeks to develop feedback controllers that endow systems with properties such as safety and stability. The guarantees ensured by these controllers often rely on accurate estimates of the system state for determining control actions. In practice, measurement model uncertainty can lead to error in state estimates that degrades these guarantees. In this paper, we seek to unify techniques from control theory and machine learning to synthesize controllers that achieve safety in the presence of measurement model uncertainty. We define the notion of a Measurement-Robust Control Barrier Function (MR-CBF) as a tool for determining safe control inputs when facing measurement model uncertainty. Furthermore, MR-CBFs are used to inform sampling methodologies for learning-based perception systems and quantify tolerable error in the resulting learned models. We demonstrate the efficacy of MR-CBFs in achieving safety with measurement model uncertainty on a simulated Segway system. 

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2. Adaptive Robotic Information Gathering via non-stationary Gaussian processes

   https://doi.org/10.1177/02783649231184498  

   Chen, Weizhe; Khardon, Roni; Liu, Lantao (April 2024, The International Journal of Robotics Research)

   Robotic Information Gathering (RIG) is a foundational research topic that answers how a robot (team) collects informative data to efficiently build an accurate model of an unknown target function under robot embodiment constraints. RIG has many applications, including but not limited to autonomous exploration and mapping, 3D reconstruction or inspection, search and rescue, and environmental monitoring. A RIG system relies on a probabilistic model’s prediction uncertainty to identify critical areas for informative data collection. Gaussian processes (GPs) with stationary kernels have been widely adopted for spatial modeling. However, real-world spatial data is typically non-stationary—different locations do not have the same degree of variability. As a result, the prediction uncertainty does not accurately reveal prediction error, limiting the success of RIG algorithms. We propose a family of non-stationary kernels named Attentive Kernel (AK), which is simple and robust and can extend any existing kernel to a non-stationary one. We evaluate the new kernel in elevation mapping tasks, where AK provides better accuracy and uncertainty quantification over the commonly used stationary kernels and the leading non-stationary kernels. The improved uncertainty quantification guides the downstream informative planner to collect more valuable data around the high-error area, further increasing prediction accuracy. A field experiment demonstrates that the proposed method can guide an Autonomous Surface Vehicle (ASV) to prioritize data collection in locations with significant spatial variations, enabling the model to characterize salient environmental features. 

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3. Safe and Efficient Reinforcement Learning using Disturbance-Observer-Based Control Barrier Functions

   Cheng, Yikun; Zhao, Pan; Hovakimyan, Naira (June 2023, Proceedings of The 5th Annual Learning for Dynamics and Control Conference)

   Matni, Nikolai; Morari, Manfred; Pappas, George J. (Ed.)

   Safe reinforcement learning (RL) with assured satisfaction of hard state constraints during training has recently received a lot of attention. Safety filters, e.g., based on control barrier functions (CBFs), provide a promising way for safe RL via modifying the unsafe actions of an RL agent on the fly. Existing safety filter-based approaches typically involve learning of uncertain dynamics and quantifying the learned model error, which leads to conservative filters before a large amount of data is collected to learn a good model, thereby preventing efficient exploration. This paper presents a method for safe and efficient RL using disturbance observers (DOBs) and control barrier functions (CBFs). Unlike most existing safe RL methods that deal with hard state constraints, our method does not involve model learning, and leverages DOBs to accurately estimate the pointwise value of the uncertainty, which is then incorporated into a robust CBF condition to generate safe actions. The DOB-based CBF can be used as a safety filter with model-free RL algorithms by minimally modifying the actions of an RL agent whenever necessary to ensure safety throughout the learning process. Simulation results on a unicycle and a 2D quadrotor demonstrate that the proposed method outperforms a state-of-the-art safe RL algorithm using CBFs and Gaussian processes-based model learning, in terms of safety violation rate, and sample and computational efficiency. 

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4. Safe and Efficient Reinforcement Learning Using Disturbance-Observer-Based Control Barrier Functions

   Cheng, Yikun; Zhao, Pan; Hovakimyan, Naira (June 2023, Proceedings of Machine Learning Research)

   Safe reinforcement learning (RL) with assured satisfaction of hard state constraints during training has recently received a lot of attention. Safety filters, e.g., based on control barrier functions (CBFs), provide a promising way for safe RL via modifying the unsafe actions of an RL agent on the fly. Existing safety filter-based approaches typically involve learning of uncertain dynamics and quantifying the learned model error, which leads to conservative filters before a large amount of data is collected to learn a good model, thereby preventing efficient exploration. This paper presents a method for safe and efficient RL using disturbance observers (DOBs) and control barrier functions (CBFs). Unlike most existing safe RL methods that deal with hard state constraints, our method does not involve model learning, and leverages DOBs to accurately estimate the pointwise value of the uncertainty, which is then incorporated into a robust CBF condition to generate safe actions. The DOB-based CBF can be used as a safety filter with model-free RL algorithms by minimally modifying the actions of an RL agent whenever necessary to ensure safety throughout the learning process. Simulation results on a unicycle and a 2D quadrotor demonstrate that the proposed method outperforms a state-of-the-art safe RL algorithm using CBFs and Gaussian processes-based model learning, in terms of safety violation rate, and sample and computational efficiency. 

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5. Mean-Field Control Barrier Functions: A Framework for Real-Time Swarm Control

   https://doi.org/10.23919/ACC63710.2025.11107531  

   Fung, Samy Wu; Nurbekyan, Levon (July 2025, IEEE)

   Control Barrier Functions (CBFs) are an effective methodology to ensure safety and performative efficacy in real-time control applications such as power systems, resource allocation, autonomous vehicles, robotics, etc. This approach ensures safety independently of the high-level tasks that may have been pre-planned off-line. For example, CBFs can be used to guarantee that a vehicle will remain in its lane. However, when the number of agents is large, computation of CBFs can suffer from the curse of dimensionality in the multi-agent setting. In this work, we present Mean-field Control Barrier Functions (MF-CBFs), which extends the CBF framework to the mean-field (or swarm control) setting. The core idea is to model a population of agents as probability measures in the state space and build corresponding control barrier functions. Similar to traditional CBFs, we derive safety constraints on the (distributed) controls but now relying on the differential calculus in the space of probability measures. 

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