Robots operating in real world settings must navigate and maintain safety while interacting with many heterogeneous agents and obstacles. Multi-Agent Control Barrier Functions (CBF) have emerged as a computationally efficient tool to guarantee safety in multi-agent environments, but they assume perfect knowledge of both the robot dynamics and other agents' dynamics. While knowledge of the robot's dynamics might be reasonably well known, the heterogeneity of agents in real-world environments means there will always be considerable uncertainty in our prediction of other agents' dynamics. This work aims to learn high-confidence bounds for these dynamic uncertainties using Matrix-Variate Gaussian Process models, and incorporates them into a robust multi-agent CBF framework. We transform the resulting min-max robust CBF into a quadratic program, which can be efficiently solved in real time. We verify via simulation results that the nominal multi-agent CBF is often violated during agent interactions, whereas our robust formulation maintains safety with a much higher probability and adapts to learned uncertainties
Control Barrier Corridors: From Safety Functions to Safe Sets
Department of Mechanical Engineering, Eindhoven University of Technology（埃因霍温理工大学机械工程系）；Department of Electrical and Computer Engineering, University of California San Diego（加州大学圣地亚哥分校电气与计算机工程系）
This paper introduces differentiable higher-order control barrier functions (CBF) that are end-to-end trainable together with learning systems. CBFs are usually overly conservative, while guaranteeing safety. Here, we address their conservativeness by softening their definitions using environmental dependencies without loosing safety guarantees, and embed them into differentiable quadratic programs. These novel safety layers, termed a BarrierNet, can be used in conjunction with any neural network-based controller, and can be trained by gradient descent. BarrierNet allows the safety constraints…
This report aims to compare two safety methods: control barrier function and Hamilton-Jacobi reachability analysis. We will consider the difference with a focus on the following aspects: generality of system dynamics, difficulty of construction and computation cost. A standard Dubins car model will be evaluated numerically to make the comparison more concrete.
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；Massachusetts Institute of Technology（麻省理工学院）
This work applies universal adaptive control to control barrier functions to achieve forward invariance of a safe set despite the presence of unmatched parametric uncertainties. The approach combines two ideas. The first is to construct a family of control barrier functions that ensures the system is safe for all possible models. The second is to use online parameter adaptation to methodically select a control barrier function and corresponding safety controller from the allowable set. While such a combination does not necessarily yield forward invariance without additional requirements on the…
Control barrier functions (CBFs) have become a popular tool to enforce safety of a control system. CBFs are commonly utilized in a quadratic program formulation (CBF-QP) as safety-critical constraints. A class $\mathcal{K}$ function in CBFs usually needs to be tuned manually in order to balance the trade-off between performance and safety for each environment. However, this process is often heuristic and can become intractable for high relative-degree systems. Moreover, it prevents the CBF-QP from generalizing to different environments in the real world. By embedding the optimization procedure…
Birla Institute of Technology and Science (BITS)（比尔拉理工学院）；Georgia Institute of Technology（佐治亚理工学院）
Control barrier functions are mathematical constructs used to guarantee safety for robotic systems. When integrated as constraints in a quadratic programming optimization problem, instantaneous control synthesis with real-time performance demands can be achieved for robotics applications. Prevailing use has assumed full knowledge of the safety barrier functions, however there are cases where the safe regions must be estimated online from sensor measurements. In these cases, the corresponding barrier function must be synthesized online. This paper describes a learning framework for estimating c…
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…
Individual Control Barrier Functions-Guided Diffusion Model for Safe Offline Multi-Agent Reinforcement Learning
Department of Electrical Engineering and Automation, Aalto University（阿尔托大学电气工程与自动化系）；School of Computing and Data Science, Xiamen University Malaysia（厦门大学马来西亚分校计算与数据科学学院）；Department of Computer Science, University of Toronto（多伦多大学计算机科学系）
Safety in terms of collision avoidance for multi-robot systems is a difficult challenge under uncertainty, non-determinism and lack of complete information. This paper aims to propose a collision avoidance method that accounts for both measurement uncertainty and motion uncertainty. In particular, we propose Probabilistic Safety Barrier Certificates (PrSBC) using Control Barrier Functions to define the space of admissible control actions that are probabilistically safe with formally provable theoretical guarantee. By formulating the chance constrained safety set into deterministic control cons…
Budapest University of Technology and Economics（布达佩斯技术与经济大学）；California Institute of Technology（加州理工学院）；University of Michigan（密歇根大学）
This work presents a theoretical framework for the safety-critical control of time delay systems. The theory of control barrier functions, that provides formal safety guarantees for delay-free systems, is extended to systems with state delay. The notion of control barrier functionals is introduced to attain formal safety guarantees, by enforcing the forward invariance of safe sets defined in the infinite dimensional state space. The proposed framework is able to handle multiple delays and distributed delays both in the dynamics and in the safety condition, and provides an affine constraint on …
Georgia Institute of Technology（佐治亚理工学院）；University of Waterloo（滑铁卢大学）；Outrider（Outrider公司）；University of California, Irvine（加州大学欧文分校）
Reinforcement Learning (RL) has been shown to be effective in many scenarios. However, it typically requires the exploration of a sufficiently large number of state-action pairs, some of which may be unsafe. Consequently, its application to safety-critical systems remains a challenge. An increasingly common approach to address safety involves the addition of a safety layer that projects the RL actions onto a safe set of actions. In turn, a difficulty for such frameworks is how to effectively couple RL with the safety layer to improve the learning performance. In this paper, we frame safety as …
Safety-critical applications require controllers/policies that can guarantee safety with high confidence. The control barrier function is a useful tool to guarantee safety if we have access to the ground-truth system dynamics. In practice, we have inaccurate knowledge of the system dynamics, which can lead to unsafe behaviors due to unmodeled residual dynamics. Learning the residual dynamics with deterministic machine learning models can prevent the unsafe behavior but can fail when the predictions are imperfect. In this situation, a probabilistic learning method that reasons about the uncerta…
California Institute of Technology（加州理工学院）；Argo AI
Control Barrier Functions (CBFs) have been demonstrated to be a powerful tool for safety-critical controller design for nonlinear systems. Existing design paradigms do not address the gap between theory (controller design with continuous time models) and practice (the discrete time sampled implementation of the resulting controllers); this can lead to poor performance and violations of safety for hardware instantiations. We propose an approach to close this gap by synthesizing sampled-data counterparts to these CBF-based controllers using approximate discrete time models and Sampled-Data Contr…
Safety requirements in dynamical systems are commonly enforced with set invariance constraints over a safe region of the state space. Control barrier functions, which are Lyapunov-like functions for guaranteeing set invariance, are an effective tool to enforce such constraints and guarantee safety when the system is represented as a point in the state space. In this paper, we introduce extent-compatible control barrier functions as a tool to enforce safety for the system including its volume (extent) in the physical world. In order to implement the extent-compatible control barrier functions f…
Arizona State University（亚利桑那州立大学）；Toyota Research Institute of North America（丰田北美研究院）
Sampling-based methods such as Rapidly-exploring Random Trees (RRTs) have been widely used for generating motion paths for autonomous mobile systems. In this work, we extend time-based RRTs with Control Barrier Functions (CBFs) to generate, safe motion plans in dynamic environments with many pedestrians. Our framework is based upon a human motion prediction model which is well suited for indoor narrow environments. We demonstrate our approach on a high-fidelity model of the Toyota Human Support Robot navigating in narrow corridors. We show in three scenarios that our proposed online method can…
We propose new methods to synthesize control barrier function (CBF)-based safe controllers that avoid input saturation, which can cause safety violations. In particular, our method is created for high-dimensional, general nonlinear systems, for which such tools are scarce. We leverage techniques from machine learning, like neural networks and deep learning, to simplify this challenging problem in nonlinear control design. The method consists of a learner-critic architecture, in which the critic gives counterexamples of input saturation and the learner optimizes a neural CBF to eliminate those …
CNRS（法国国家科学研究中心）；University of Rennes（雷恩大学）；Inria（法国国家信息与自动化研究所）；IRISA（法国信息与随机系统研究所）；University of Innsbruck（因斯布鲁克大学）
This paper presents an approach to deal with safety of dynamical systems in presence of multiple non-convex unsafe sets. While optimal control and model predictive control strategies can be employed in these scenarios, they suffer from high computational complexity in case of general nonlinear systems. Leveraging control barrier functions, on the other hand, results in computationally efficient control algorithms. Nevertheless, when safety guarantees have to be enforced alongside stability objectives, undesired asymptotically stable equilibrium points have been shown to arise. We propose a com…
Safe Human-to-Humanoid Motion Imitation Using Control Barrier Functions
New York University Abu Dhabi (NYUAD)（纽约大学阿布扎比分校）；New York University（纽约大学）；NYUAD Center for Artificial Intelligence and Robotics (CAIR)（纽约大学阿布扎比人工智能与机器人中心）
Contextual Robotics Institute（情境机器人研究所）；University of California San Diego（加州大学圣地亚哥分校）
Control barrier functions are widely used to enforce safety properties in robot motion planning and control. However, the problem of constructing barrier functions online and synthesizing safe controllers that can deal with the associated uncertainty has received little attention. This paper investigates safe navigation in unknown environments, using onboard range sensing to construct control barrier functions online. To represent different objects in the environment, we use the distance measurements to train neural network approximations of the signed distance functions incrementally with rep…
In this article, we present a control strategy for the problem of safe autonomous docking for a planar floating platform (Slider) that emulates the movement of a satellite. Employing the proposed strategy, Slider approaches a docking port with the right orientation, maintaining a safe distance, while always keeping a visual lock on the docking port throughout the docking maneuver. Control barrier functions are designed to impose the safety, direction of approach and visual locking constraints. Three control inputs of the Slider are shared among three barrier functions in enforcing the constrai…
Prior work has looked at applying reinforcement learning and imitation learning approaches to autonomous driving scenarios, but either the safety or the efficiency of the algorithm is compromised. With the use of control barrier functions embedded into the reinforcement learning policy, we arrive at safe policies to optimize the performance of the autonomous driving vehicle. However, control barrier functions need a good approximation of the model of the car. We use probabilistic control barrier functions as an estimate of the model uncertainty. The algorithm is implemented as an online versio…
This paper combines episodic learning and control barrier functions in the setting of bipedal locomotion. The safety guarantees that control barrier functions provide are only valid with perfect model knowledge; however, this assumption cannot be met on hardware platforms. To address this, we utilize the notion of projection-to-state safety paired with a machine learning framework in an attempt to learn the model uncertainty as it affects the barrier functions. The proposed approach is demonstrated both in simulation and on hardware for the AMBER-3M bipedal robot in the context of the stepping…
This paper details the theory and implementation behind practically ensuring safety of remotely piloted racing drones. We demonstrate robust and practical safety guarantees on a 7" racing drone at speeds exceeding 100 km/h, utilizing only online computations on a 10 gram micro-controller. To achieve this goal, we utilize the framework of control barrier functions (CBFs) which give guaranteed safety encoded as forward set invariance. To make this methodology practically applicable, we present an implicitly defined CBF which leverages backup controllers to enable gradient-free evaluations that e…
School of Mechanical Engineering and Automation, Harbin Institute of Technology Shenzhen（哈尔滨工业大学（深圳）机械工程与自动化学院）；Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati（辛辛那提大学航空航天工程与工程力学系）
Multi-Agent Reinforcement Learning (MARL) algorithms show amazing performance in simulation in recent years, but placing MARL in real-world applications may suffer safety problems. MARL with centralized shields was proposed and verified in safety games recently. However, centralized shielding approaches can be infeasible in several real-world multi-agent applications that involve non-cooperative agents or communication delay. Thus, we propose to combine MARL with decentralized Control Barrier Function (CBF) shields based on available local information. We establish a safe MARL framework with d…
With the increasing emphasis on the safe autonomy for robots, model-based safe control approaches such as Control Barrier Functions have been extensively studied to ensure guaranteed safety during inter-robot interactions. In this paper, we introduce the Parametric Control Barrier Function (Parametric-CBF), a novel variant of the traditional Control Barrier Function to extend its expressivity in describing different safe behaviors among heterogeneous robots. Instead of assuming cooperative and homogeneous robots using the same safe controllers, the ego robot is able to model the neighboring ro…
In this draft article, we consider the problem of achieving safe control of a dynamic system for which the safety index or (control barrier function (loosely)) has relative degree equal to two. We consider parameter affine nonlinear dynamic systems and assume that the parametric uncertainty is uniform and known a-priori or being updated online through an estimator/parameter adaptation law. Under this uncertainty, the usual CBF-QP safe control approach takes the form of a robust optimization problem. Both the right hand side and left hand side of the inequality constraints depend on the unknown…
A Safety-Aware Shared Autonomy Framework with BarrierIK Using Control Barrier Functions
Technical University of Darmstadt（德累斯顿技术大学）；German Research Center for Artificial Intelligence (DFKI)（德国人工智能研究中心）；Robotics Institute Germany (RIG)（德国机器人研究所）；Centre for Cognitive Science（认知科学中心）；Honda Research Institute Europe GmbH（本田欧洲研究机构）
Maintaining safety under adaptation has long been considered to be an important capability for autonomous systems. As these systems estimate and change the ego-model of the system dynamics, questions regarding how to develop safety guarantees for such systems continue to be of interest. We propose a novel robust safe control methodology that uses set-based safety constraints to make a robotic system with dynamical uncertainties safely adapt and operate in its environment. The method consists of designing a scalar energy function (safety index) for an adaptive system with parametric uncertainty…
Microsoft Corporation（微软公司）；Technion - Israel Institute of Technology（以色列理工学院）
Recent advances in Deep Machine Learning have shown promise in solving complex perception and control loops via methods such as reinforcement and imitation learning. However, guaranteeing safety for such learned deep policies has been a challenge due to issues such as partial observability and difficulties in characterizing the behavior of the neural networks. While a lot of emphasis in safe learning has been placed during training, it is non-trivial to guarantee safety at deployment or test time. This paper extends how under mild assumptions, Safety Barrier Certificates can be used to guarant…
Training-time safety violations have been a major concern when we deploy reinforcement learning algorithms in the real world. This paper explores the possibility of safe RL algorithms with zero training-time safety violations in the challenging setting where we are only given a safe but trivial-reward initial policy without any prior knowledge of the dynamics model and additional offline data. We propose an algorithm, Co-trained Barrier Certificate for Safe RL (CRABS), which iteratively learns barrier certificates, dynamics models, and policies. The barrier certificates, learned via adversaria…
Input-to-State Safe Backstepping: Robust Safety-Critical Control with Unmatched Uncertainties
Department of Electrical and Computer Engineering, North Carolina State University（电气与计算机工程系，北卡罗来纳州立大学）；Department of Mechanical and Civil Engineering, California Institute of Technology（机械与土木工程系，加州理工学院）
School of Electrical and Computer Engineering（电气与计算机工程学院）；King Fahd University of Petroleum & Minerals（法赫德国王石油与矿产大学）；School of Computer Science（计算机科学学院）；George W. Woodruff School of Mechanical Engineering（乔治·W·伍德拉夫机械工程学院）；Daniel Guggenheim School of Aerospace Engineering（丹尼尔·古根海姆航空航天工程学院）
Certified safe control is a growing challenge in robotics, especially when performance and safety objectives must be concurrently achieved. In this work, we extend the barrier state (BaS) concept, recently proposed for safe stabilization of continuous time systems, to safety embedded trajectory optimization for discrete time systems using discrete barrier states (DBaS). The constructed DBaS is embedded into the discrete model of the safety-critical system integrating safety objectives into the system's dynamics and performance objectives. Thereby, the control policy is directly supplied by saf…
