Control Barrier Functions (CBF) are widely used to enforce the safety-critical constraints on nonlinear systems. Recently, these functions are being incorporated into a path planning framework to design safety-critical path planners. However, these methods fall short of providing a realistic path considering both the algorithm's run-time complexity and enforcement of the safety-critical constraints. This paper proposes a novel motion planning approach using the well-known Rapidly Exploring Random Trees (RRT) algorithm that enforces both CBF and the robot Kinodynamic constraints to generate a safety-critical path. The proposed algorithm also outputs the corresponding control signals that resulted in the obstacle-free path. The approach also allows considering model uncertainties by incorporating the robust CBF constraints into the proposed framework. Thus, the resulting path is free of any obstacles and accounts for the model uncertainty from robot dynamics and perception. Result analysis indicates that the proposed method outperforms various conventional RRT-based path planners, guaranteeing a safety-critical path with minimal computational overhead. We present numerical validation of the algorithm on the Hamster V7 robot car, a micro autonomous Unmanned Ground Vehicle that performs dynamic navigation on an obstacle-ridden path with various uncertainties in perception noises and robot dynamics.
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…
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…
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 …
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…
University of Colorado at Boulder（科罗拉多大学博尔德分校）；Google Inc.（谷歌公司）；SRI International（SRI国际）；Willow Garage, Inc.（Willow Garage公司）
Developing robot agnostic software frameworks involves synthesizing the disparate fields of robotic theory and software engineering while simultaneously accounting for a large variability in hardware designs and control paradigms. As the capabilities of robotic software frameworks increase, the setup difficulty and learning curve for new users also increase. If the entry barriers for configuring and using the software on robots is too high, even the most powerful of frameworks are useless. A growing need exists in robotic software engineering to aid users in getting started with, and customizi…
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…
Arizona State University（亚利桑那州立大学）；Toyota Research Institute of North America（丰田北美研究院）
In this paper, we present a decentralized control approach based on a Nonlinear Model Predictive Control (NMPC) method that employs barrier certificates for safe navigation of multiple nonholonomic wheeled mobile robots in unknown environments with static and/or dynamic obstacles. This method incorporates a Learned Barrier Function (LBF) into the NMPC design in order to guarantee safe robot navigation, i.e., prevent robot collisions with other robots and the obstacles. We refer to our proposed control approach as NMPC-LBF. Since each robot does not have a priori knowledge about the obstacles a…
Enforcing safety in the presence of stochastic uncertainty is a challenging problem. Traditionally, researchers have proposed safety in the statistical mean as a safety measure in this case. However, ensuring safety in the statistical mean is only reasonable if system's safe behavior in the large number of runs is of interest, which precludes the use of mean safety in practical scenarios. In this paper, we propose a risk sensitive notion of safety called conditional-value-at-risk (CVaR) safety, which is concerned with safe performance in the worst case realizations. We introduce CVaR barrier f…
Massachusetts Institute of Technology（麻省理工学院）；Microsoft Research（微软研究院）
Large-scale self-supervised models have recently revolutionized our ability to perform a variety of tasks within the vision and language domains. However, using such models for autonomous systems is challenging because of safety requirements: besides executing correct actions, an autonomous agent must also avoid the high cost and potentially fatal critical mistakes. Traditionally, self-supervised training mainly focuses on imitating previously observed behaviors, and the training demonstrations carry no notion of which behaviors should be explicitly avoided. In this work, we propose Control Ba…
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）
Shanghai Jiao Tong University（上海交通大学）；University of Oxford（牛津大学）；Tencent（腾讯）
Collision avoidance is a widely investigated topic in robotic applications. When applying collision avoidance techniques to a mobile robot, how to deal with the spatial structure of the robot still remains a challenge. In this paper, we design a configuration-aware safe control law by solving a Quadratic Programming (QP) with designed Control Barrier Functions (CBFs) constraints, which can safely navigate a mobile robotic arm to a desired region while avoiding collision with environmental obstacles. The advantage of our approach is that it correctly and in an elegant way incorporates the spati…
Norwegian University of Science and Technology（挪威科技大学）
This paper presents a novel task-priority control framework for redundant robotic systems based on a hierarchy of control Lyapunov function (CLF) and control barrier function (CBF) based quadratic programs (QPs). The proposed method guarantees strict priority among different groups of tasks such as safety-related, operational and optimization tasks. Moreover, a soft priority measure in the form of penalty parameters can be employed to prioritize tasks at the same priority level. As opposed to kinematic control schemes, the proposed framework is a holistic approach to control of redundant robot…
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…
Digital Twin technology is playing a pivotal role in the modern industrial evolution. Especially, with the technological progress in the Internet-of-Things (IoT) and the increasing trend in autonomy, multi-sensor equipped robotics can create practical digital twin, which is particularly useful in the industrial applications for operations, maintenance and safety. Herein, we demonstrate a real-world digital twin of a safety-critical robotics applications with a Franka-Emika-Panda robotic arm. We develop and showcase an edge-assisted collaborative digital twin for dynamic obstacle avoidance whic…
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…
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…
University of Southern California（南加州大学）；University of California, Berkeley（加州大学伯克利分校）
We present a novel method of optimal robust control through quadratic programs that offers tracking stability while subject to input and state-based constraints as well as safety-critical constraints for nonlinear dynamical robotic systems in the presence of model uncertainty. The proposed method formulates robust control Lyapunov and barrier functions to provide guarantees of stability and safety in the presence of model uncertainty. We evaluate our proposed control design on dynamic walking of a five-link planar bipedal robot subject to contact force constraints as well as safety-critical pr…
Institute for Robotics and Intelligent Machines, Georgia Institute of Technology（佐治亚理工学院机器人与智能机器研究所）
The Robotarium, a remotely accessible swarm-robotics testbed, has provided free, open access to robotics and controls research for hundreds of users in thousands of experiments. This high level of usage requires autonomy in the system, which mainly corresponds to constraint satisfaction in the context of users' submissions. In other words, in case that the users' inputs to the robots may lead to collisions, these inputs must be altered to avoid these collisions automatically. However, these alterations must be minimal so as to preserve the users' objective in the experiment. Toward this end, t…
Safety-aware Goal-oriented Semantic Sensing, Communication, and Control for Robotics
Department of Engineering, King’s College London（工程系，伦敦国王学院）；Department of Intelligent Systems, KTH Royal Institute of Technology（智能系统系，皇家理工学院）；Department of Automation Technology, ABB Corporate Research Sweden（自动化技术系，ABB瑞典公司）；Institute for Digital Communications, FriedrichAlexander-Universität Erlangen-Nürnberg（数字通信研究所，埃尔兰根-纽伦堡弗里德里希-亚历山大大学）
Robust Adaptive Safe Robotic Grasping with Tactile Sensing
Maersk Mc-Kinney Moller Institute, University of Southern Denmark（马士基麦金尼默勒研究所，丹麦南方大学）；Departments of Mechanical and Civil Engineering and Computing and Mathematical Sciences , California Institute of Technology（机械与土木工程系和计算与数学科学系，加州理工学院）
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…
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…
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…
This paper presents a framework for the safety-critical control of robotic systems, when safety is defined on safe regions in the configuration space. To maintain safety, we synthesize a safe velocity based on control barrier function theory without relying on a -- potentially complicated -- high-fidelity dynamical model of the robot. Then, we track the safe velocity with a tracking controller. This culminates in model-free safety critical control. We prove theoretical safety guarantees for the proposed method. Finally, we demonstrate that this approach is application-agnostic. We execute an o…
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…
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…
University of Bristol（布里斯托大学）；Bristol Robotics Laboratory（布里斯托机器人实验室）；Avian Technologies Ltd（Avian Technologies有限公司）
The success of the human-robot co-worker team in a flexible manufacturing environment where robots learn from demonstration heavily relies on the correct and safe operation of the robot. How this can be achieved is a challenge that requires addressing both technical as well as human-centric research questions. In this paper we discuss the state of the art in safety assurance, existing as well as emerging standards in this area, and the need for new approaches to safety assurance in the context of learning machines. We then focus on robotic learning from demonstration, the challenges these tech…
Robotic Shepherding in Cluttered and Unknown Environments using Control Barrier Functions
Center for Artificial Intelligence and Robotics, New York University Abu Dhabi（人工智能与机器人中心，纽约大学阿布扎比分校）；New York University（纽约大学）；New York University, Brooklyn（纽约大学布鲁克林分校）
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…
