Applications that require multi-robot systems to operate independently for extended periods of time in unknown or unstructured environments face a broad set of challenges, such as hardware degradation, changing weather patterns, or unfamiliar terrain. To operate effectively under these changing conditions, algorithms developed for long-term autonomy applications require a stronger focus on robustness. Consequently, this work considers the ability to satisfy the operation-critical constraints of a disturbed system in a modular fashion, which means compatibility with different system objectives and disturbance representations. Toward this end, this paper introduces a controller-synthesis approach to constraint satisfaction for disturbed control-affine dynamical systems by utilizing Control Barrier Functions (CBFs). The aforementioned framework is constructed by modelling the disturbance as a union of convex hulls and leveraging previous work on CBFs for differential inclusions. This method of disturbance modeling grants compatibility with different disturbance-estimation methods. For example, this work demonstrates how a disturbance learned via a Gaussian process may be utilized in the proposed framework. These estimated disturbances are incorporated into the proposed controller-synthesis framework which is then tested on a fleet of robots in different scenarios.
This paper presents a formal framework for collision avoidance in multi-robot systems, wherein an existing controller is modified in a minimally invasive fashion to ensure safety. We build this framework through the use of control barrier functions (CBFs) which guarantee forward invariance of a safe set; these yield safety barrier certificates in the context of heterogeneous robot dynamics subject to acceleration bounds. Moreover, safety barrier certificates are extended to a distributed control framework, wherein neighboring agent dynamics are unknown, through local parameter identification. …
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 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…
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…
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…
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…
This paper proposes embedded Gaussian Process Barrier States (GP-BaS), a methodology to safely control unmodeled dynamics of nonlinear system using Bayesian learning. Gaussian Processes (GPs) are used to model the dynamics of the safety-critical system, which is subsequently used in the GP-BaS model. We derive the barrier state dynamics utilizing the GP posterior, which is used to construct a safety embedded Gaussian process dynamical model (GPDM). We show that the safety-critical system can be controlled to remain inside the safe region as long as we can design a controller that renders the B…
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…
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…
The optimal performance of robotic systems is usually achieved near the limit of state and input bounds. Model predictive control (MPC) is a prevalent strategy to handle these operational constraints, however, safety still remains an open challenge for MPC as it needs to guarantee that the system stays within an invariant set. In order to obtain safe optimal performance in the context of set invariance, we present a safety-critical model predictive control strategy utilizing discrete-time control barrier functions (CBFs), which guarantees system safety and accomplishes optimal performance via …
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…
Performing swift and agile maneuvers is essential for the safe operation of autonomous mobile robots. Moreover, the presence of time-delay restricts the response time of the system and hinders the safety performance. Thus, this paper proposes a modular and scalable safety-control design that utilizes the Smith predictor and barrier certificates to safely and consistently avoid obstacles with different footprints. The proposed solution includes a two-layer predictor to compensate for the time-delay in the servo-system and angle control loops. The proposed predictor configuration dramatically im…
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）
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…
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…
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 …
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 …
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…
Institute for Robotics and Intelligent Machines (IRIM)（机器人与智能机器研究所（IRIM））；Georgia Institute of Technology（佐治亚理工学院）；School of Aerospace Engineering（航空航天工程学院）；Stanford University（斯坦福大学）
This paper introduces a new formulation for stochastic optimal control and stochastic dynamic optimization that ensures safety with respect to state and control constraints. The proposed methodology brings together concepts such as Forward-Backward Stochastic Differential Equations, Stochastic Barrier Functions, Differentiable Convex Optimization and Deep Learning. Using the aforementioned concepts, a Neural Network architecture is designed for safe trajectory optimization in which learning can be performed in an end-to-end fashion. Simulations are performed on three systems to show the effica…
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…
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）
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…
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…
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 …
Reinforcement Learning for Safe Robot Control using Control Lyapunov Barrier Functions
Delft University of Technology（代尔夫特理工大学）；Harbin Institute of Technology（哈尔滨工业大学）；Huawei Technologies（华为技术有限公司）；University College London（伦敦大学学院）；University of Manchester（曼彻斯特大学）
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…
Path-tracking control of self-driving vehicles can benefit from deep learning for tackling longstanding challenges such as nonlinearity and uncertainty. However, deep neural controllers lack safety guarantees, restricting their practical use. We propose a new approach of learning almost-barrier functions, which approximately characterizes the forward invariant set for the system under neural controllers, to quantitatively analyze the safety of deep neural controllers for path-tracking. We design sampling-based learning procedures for constructing candidate neural barrier functions, and certifi…
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）
Safety is a fundamental requirement in any human-robot collaboration scenario. To ensure the safety of users for such scenarios, we propose a novel Virtual Barrier system facilitated by an augmented reality interface. Our system provides two kinds of Virtual Barriers to ensure safety: 1) a Virtual Person Barrier which encapsulates and follows the user to protect them from colliding with the robot, and 2) Virtual Obstacle Barriers which users can spawn to protect objects or regions that the robot should not enter. To enable effective human-robot collaboration, our system includes an intuitive r…
A multi-agent partially observable Markov decision process (MPOMDP) is a modeling paradigm used for high-level planning of heterogeneous autonomous agents subject to uncertainty and partial observation. Despite their modeling efficiency, MPOMDPs have not received significant attention in safety-critical settings. In this paper, we use barrier functions to design policies for MPOMDPs that ensure safety. Notably, our method does not rely on discretization of the belief space, or finite memory. To this end, we formulate sufficient and necessary conditions for the safety of a given set based on di…
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…
