This paper examines the problem of achieving "grace" when controlling dynamical systems for safety, which is defined in terms of providing multi-layered safety assurances. Namely, two safety layers are created: a primary layer that represents a desirable degree of safety, and a secondary failsafe layer. Graceful control then involves ensuring that even if the primary layer is breached, the failsafe layer remains forward invariant. The paper pursues this goal by constructing a safety constraint that combines the concepts of zeroing and reciprocal control barrier functions with regard to the primary and secondary safe sets, respectively. This constraint is analogous to a stiffening spring, making it possible to construct energy-based analytical proofs of the resulting graceful safety guarantees. The proposed approach is developed for systems with a relative degree of either 1 or 2, the latter case being particularly useful for mechanical systems. We demonstrate the applicability of the method using a wall collision avoidance example. This demonstration highlights the benefits of the proposed approach compared to traditional benchmarks from the literature.
In this paper, we propose the safety barrier certificates for uncertain multi-robot systems playing red light, green light game. According to the rule of the game, the robots are allowed to move forward after a doll shouts `green light' and must stop when it shouts `red light'. Following this rule, a two-mode nominal controller is designed where one mode is for moving forward and the other one is for slowing down and being motionless. Then, multiple exponential control barrier functions(ECBFs) are developed to handle safety constraints for limited playground, collision avoidance, and saturatio…
Uncertainty Estimators for Robust Backup Control Barrier Functions
California Institute of Technology（加州理工学院）；Illinois Institute of Technology（伊利诺伊理工大学）；Delft University of Technology（代尔夫特理工大学）；Georgia Institute of Technology（佐治亚理工学院）；Cleveland State University（克利夫兰州立大学）；Texas A&M University（德克萨斯农工大学）；The Aerospace Corporation（美国航空航天公司）
This paper presents a framework for designing provably safe feedback controllers for sampled-data control affine systems with measurement and actuation uncertainties. Based on the interval Taylor model of nonlinear functions, a sampled-data control barrier function (CBF) condition is proposed which ensures the forward invariance of a safe set for sampled-data systems. Reachable set overapproximation and Lasserre's hierarchy of polynomial optimization are used for finding the margin term in the sampled-data CBF condition. Sufficient conditions for a safe controller in the presence of measuremen…
Massachusetts Institute of Technology（麻省理工学院）；University of California, San Diego（加利福尼亚大学圣地亚哥分校）
Safety and stability are common requirements for robotic control systems; however, designing safe, stable controllers remains difficult for nonlinear and uncertain models. We develop a model-based learning approach to synthesize robust feedback controllers with safety and stability guarantees. We take inspiration from robust convex optimization and Lyapunov theory to define robust control Lyapunov barrier functions that generalize despite model uncertainty. We demonstrate our approach in simulation on problems including car trajectory tracking, nonlinear control with obstacle avoidance, satell…
Control Lyapunov functions (CLFs) and control barrier functions (CBFs) are widely used tools for synthesizing controllers subject to stability and safety constraints. Paired with online optimization, they provide stabilizing control actions that satisfy input constraints and avoid unsafe regions of state-space. Designing CLFs and CBFs with rigorous performance guarantees is computationally challenging. To certify existence of control actions, current techniques not only design a CLF/CBF, but also a nominal controller. This can make the synthesis task more expensive, and performance estimation …
MIT（麻省理工学院）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；IBM（国际商业机器公司）
In order to be effective partners for humans, robots must become increasingly comfortable with making contact with their environment. Unfortunately, it is hard for robots to distinguish between ``just enough'' and ``too much'' force: some force is required to accomplish the task but too much might damage equipment or injure humans. Traditional approaches to designing compliant force-feedback controllers, such as stiffness control, require difficult hand-tuning of control parameters and make it difficult to build safe, effective robot collaborators. In this paper, we propose a novel yet easy-to…
Georgia Institute of Technology（佐治亚理工学院）；Meiji University（明治大学）
Inspired by the success of control barrier functions (CBFs) in addressing safety, and the rise of data-driven techniques for modeling functions, we propose a non-parametric approach for online synthesis of CBFs using Gaussian Processes (GPs). Mathematical constructs such as CBFs have achieved safety by designing a candidate function a priori. However, designing such a candidate function can be challenging. A practical example of such a setting would be to design a CBF in a disaster recovery scenario where safe and navigable regions need to be determined. The decision boundary for safety in suc…
University of Toronto Institute for Aerospace Studies（多伦多大学航空航天研究所）；Technical University of Munich（慕尼黑工业大学）；University of Toronto Robotics Institute（多伦多大学机器人研究所）；Vector Institute for Artificial Intelligence（矢量人工智能研究所）
In this work, we consider the problem of designing a safety filter for a nonlinear uncertain control system. Our goal is to augment an arbitrary controller with a safety filter such that the overall closed-loop system is guaranteed to stay within a given state constraint set, referred to as being safe. For systems with known dynamics, control barrier functions (CBFs) provide a scalar condition for determining if a system is safe. For uncertain systems, robust or adaptive CBF certification approaches have been proposed. However, these approaches can be conservative or require the system to have…
This paper studies the stabilization and safety problems of nonlinear time-delay systems. Following both Razumikhin and Krasovskii approaches, we propose novel control Lyapunov functions/functionals for the stabilization problem and novel control barrier functions/functionals for the safety problem. The proposed control Lyapunov and barrier functions/functionals extend the existing ones from the delay-free case to the time-delay case, and allow for designing the stabilizing and safety controllers in closed-form. Since analytical solutions to time-delay optimal control problems are hard to be a…
Fixed time convergence guarantees for Higher Order Control Barrier Functions
Department of Engineering Design, Indian Institute of Technology, Madras（工程设计系，印度理工学院，马德拉斯）；Center for Cyber-Physical Systems, Indian Institute of Science (IISc), Bengaluru（网络物理系统中心，印度科学研究院（IISc），班加罗尔）
Optimal Parameter Adaptation for Safety-Critical Control via Safe Barrier Bayesian Optimization
University of Electronic Science and Technology of China（电子科技大学）；University of Exeter（埃克塞特大学）；Australian AI Institute（澳大利亚人工智能研究所）；University of Technology Sydney（悉尼科技大学）；Hunan University（湖南大学）；China University of Mining and Technology（中国矿业大学）；Southeast University（东南大学）
Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificates
Stanford University（斯坦福大学）；The Hebrew University of Jerusalem（耶路撒冷希伯来大学）；IT University of Copenhagen（哥本哈根信息技术大学）；Google（谷歌公司）；GE Aerospace Research（GE航空航天研究院）
