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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. 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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3. 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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4. Provable Probabilistic Safety and Feasibility-Assured Control for Autonomous Vehicles using Exponential Control Barrier Functions

   https://doi.org/10.1109/IV51971.2022.9827424  

   Van Koevering, Spencer ; Lyu, Yiwei ; Luo, Wenhao ; Dolan, John M. ( June 2022 , IEEE Intelligent Vehicles Symposium)

   With the increasing need for safe control in the domain of autonomous driving, model-based safety-critical control approaches are widely used, especially Control Barrier Function (CBF) based approaches. Among them, Exponential CBF (eCBF) is particularly popular due to its realistic applicability to high-relative-degree systems. However, for most of the optimization-based controllers utilizing CBF-based constraints, solution feasibility is a common issue raised from potential conflict among different constraints. Moreover, how to incorporate uncertainty into the eCBF-based constraints in high-relative-degree systems to account for safety remains an open challenge. In this paper, we present a novel approach to extend a eCBF-based safe critical controller to a probabilistic setting to handle potential motion uncertainty from system dynamics. More importantly, we leverage an optimization-based technique to provide a solution feasibility guarantee in run time, while ensuring probabilistic safety. Lane changing and intersection handling are demonstrated as two use cases, and experiment results are provided to show the effectiveness of the proposed approach. 

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5. Towards Robust Data-Driven Control Synthesis for Nonlinear Systems with Actuation Uncertainty

   https://doi.org/10.1109/CDC45484.2021.9683511  

   Taylor, Andrew J. ; Dorobantu, Victor D. ; Dean, Sarah ; Recht, Benjamin ; Yue, Yisong ; Ames, Aaron D. ( December 2021 , 2021 60th IEEE Conference on Decision and Control (CDC))

   Modern nonlinear control theory seeks to endow systems with properties such as stability and safety, and has been deployed successfully across various domains. Despite this success, model uncertainty remains a significant challenge in ensuring that model-based controllers transfer to real world systems. This paper develops a data-driven approach to robust control synthesis in the presence of model uncertainty using Control Certificate Functions (CCFs), resulting in a convex optimization based controller for achieving properties like stability and safety. An important benefit of our framework is nuanced data-dependent guarantees, which in principle can yield sample-efficient data collection approaches that need not fully determine the input-to-state relationship. This work serves as a starting point for addressing important questions at the intersection of nonlinear control theory and non-parametric learning, both theoretical and in application. We demonstrate the efficiency of the proposed method with respect to input data in simulation with an inverted pendulum in multiple experimental settings. 

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