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Continuous Approximations of Projected Dynamical Systems via control barrier functions

IEEE TRANSACTIONS ON AUTOMATIC control 2025年第1期70卷 681-688页

作者： Delimpaltadakis, Giannis Cortes, Jorge Heemels, W. P. M. H. Eindhoven Univ Technol Control Syst Technol Sect Mech Engn NL-5600 Eindhoven Netherlands Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA

Projected dynamical systems (PDSs) form a class of discontinuous constrained dynamical systems, and have been used widely to solve optimization problems and variational inequalities. Recently, they have also gained significant attention for control purposes, such as high-performance integrators, saturated control, and feedback optimization. In this work, we establish that locally Lipschitz continuous dynamics, involving control barrier functions (CBFs), namely, CBF-based dynamics, approximate PDSs. Specifically, we prove that trajectories of CBF-based dynamics uniformly converge to trajectories of PDSs, as a CBF-parameter approaches infinity. Toward this, we also prove that CBF-based dynamics are perturbations of PDSs, with quantitative bounds on the perturbation. Our results pave the way to implement discontinuous PDS-based controllers in a continuous fashion, employing CBFs. We demonstrate this on an example on synchronverter control. Moreover, our results can be employed to numerically simulate PDSs, overcoming disadvantages of existing discretization schemes, such as computing projections to possibly nonconvex sets. Finally, this bridge between CBFs and PDSs may yield other potential benefits, including novel insights on stability.

关键词： Trajectory Power system dynamics Optimization Vehicle dynamics Perturbation methods Dynamical systems control systems control barrier functions discontinuous dynamical systems feedback optimization nonsmooth dynamics projected dynamical systems safety-critical control synchronverters

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Deadlock-free, safe, and decentralized multi-robot navigation in social mini-games via discrete-time control barrier functions

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AUTONOMOUS ROBOTS 2025年第2期49卷 1-31页

作者： Chandra, Rohan Zinage, Vrushabh Bakolas, Efstathios Stone, Peter Biswas, Joydeep Univ Virginia Dept Comp Sci Charlottesville VA 22904 USA Univ Texas Austin Dept Aerosp Engn & Engg Mech Austin TX USA Univ Texas Austin Dept Comp Sci Austin TX USA Sony AI New York NY USA

We present an approach to ensure safe and deadlock-free navigation for decentralized multi-robot systems operating in constrained environments, including doorways and intersections. Although many solutions have been proposed that ensure safety and resolve deadlocks, optimally preventing deadlocks in a minimally invasive and decentralized fashion remains an open problem. We first formalize the objective as a non-cooperative, non-communicative, partially observable multi-robot navigation problem in constrained spaces with multiple conflicting agents, which we term as social mini-games. Formally, we solve a discrete-time optimal receding horizon control problem leveraging control barrier functions for safe long-horizon planning. Our approach to ensuring liveness rests on the insight that there exists barrier certificates that allow each robot to preemptively perturb their state in a minimally-invasive fashion onto liveness sets i.e. states where robots are deadlock-free. We evaluate our approach in simulation as well on physical robots using F1/10 robots, a Clearpath Jackal, as well as a Boston Dynamics Spot in a doorway, hallway, and corridor intersection scenario. Compared to both fully decentralized and centralized approaches with and without deadlock resolution capabilities, we demonstrate that our approach results in safer, more efficient, and smoother navigation, based on a comprehensive set of metrics including success rate, collision rate, stop time, change in velocity, path deviation, time-to-goal, and flow rate.

关键词： Social navigation control barrier functions Deadlock prevention Multi-robot systems Multi-agent systems

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Adaptive safety with control barrier functions and triggered Batch Least-Squares Identifier

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AUTOMATICA 2025年 173卷

作者： Shen, Jiajun Wang, Wei Zhou, Jing Lu, Jinhu Beihang Univ Sch Automat Sci & Elect Engn Beijing 100191 Peoples R China Beihang Univ Hangzhou Innovat Inst Hangzhou 310051 Peoples R China Zhongguancun Lab Beijing 100194 Peoples R China Univ Agder Dept Engn Sci N-4898 Grimstad Norway

In this paper, a triggered Batch Least-Squares Identifier (BaLSI) based adaptive safety control scheme is proposed for uncertain systems with potentially conflicting control objectives and safety constraints. A relaxation term is added to the Quadratic Programs (QP) combining the transformed control Lyapunov functions (CLFs) and control barrier functions (CBFs), to mediate the potential conflict. The existing Lyapunov-based adaptive laws designed to guarantee specific properties of the Lyapunov functions, may grow unboundedly under the effects of the relaxation term. The proposed adaptive law is designed by processing system inputs and outputs, to avoid unbounded estimates and overparameterization problems in the existing results. A safety-triggered condition is presented, based on which the forward invariant property of the safe set is shown and Zeno behavior can be excluded. Simulation results are presented to demonstrate the effectiveness of the proposed adaptive control scheme. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： Adaptive control control barrier functions Event-triggered control Quadratic program

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Switched control barrier functions-based safe docking control strategy fora planar floating platform

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control ENGINEERING PRACTICE 2025年 158卷

作者： Saradagi, Akshit Sankaranarayanan, Viswa Narayanan Nikolakopoulos, Avijit Banerjee, Avijit Satpute, Sumeet Nikolakopoulos, George Lulea Univ Technol Dept Comp Elect & Space Engn Robot & Artificial Intelligence Grp SE-97187 Lulea Sweden

In this article, we present and experimentally validate a safe docking control strategy designed for an experimental planar floating platform, called the Slider. Three degrees-of-freedom (DOF) platforms like the Slider are used extensively in space industry and academia to emulate micro-gravity conditions on Earth, for validating in-plane Guidance, Navigation and control (GNC) algorithms. The Slider uses an air cushion (induced by air bearings) to levitate on a smooth flat table, thus emulating the in-plane zero-gravity motion of a spacecraft in orbit. The proposed docking control strategy is applicable in the in-plane approach and docking phases of space docking missions, and is based on the control barrier functions (CBF) approach, where a safe set (a Cardioid), capturing the clearance and direction-of-approach constraints, is rendered positively forward invariant. To enable precise and safe docking in the presence of unmodeled dynamics, disturbances induced by the tether and drifts induced by the non-flat floating surface, we present a switching strategy among the zero and positive level sets of a Cardioid function. In the approach phase, the positive contour of the Cardioid function smoothly steers the Slider platform into the neighborhood of a deadlock point, which is designed to be at a safe distance from the docking port. In the neighborhood of the deadlock point, Slider corrects its proximity and heading until its configuration is well-suited to enter the docking phase. The docking maneuver is initiated by the CBF switching mechanism (positive to zero contour), which expands the safe zone to include the final docking configuration. We present an analysis of the Quadratic program defining the CBF filter, and identify two deadlock points (an asymptotically stable point in the vicinity of the docking port and an unstable point diametrically opposite on the CBF boundary). Both the approach and docking phases are validated through experimentation on the Slider pl

关键词： control barrier functions Autonomous docking Planar floating platforms Safety critical systems Space-emulating test-beds control applications Robotics

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Safe tracking control for free-flying space robots via control barrier functions

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ROBOTICS AND AUTONOMOUS SYSTEMS 2025年 184卷

作者： Shi, Chengrui Meng, Tao Wang, Kun Lei, Jiakun Wang, Weijia Mao, Renhao Zhejiang Univ Sch Aeronaut & Astronaut Hangzhou 310027 Peoples R China Huanjiang Lab Zhuji 311899 Peoples R China Beihang Univ Hangzhou Innovat Inst Hangzhou 310051 Peoples R China Beihang Univ Hangzhou Int Innovat Inst Hangzhou 311115 Peoples R China

Safety is a critical problem for space robots in future complex autonomous On-Orbit Services. In this paper, we propose a real-time and guaranteed method for whole-body safe tracking control of free-flying space robots using High Order control barrier functions (HOCBFs). We start by utilizing capsule-shaped safety envelopes for an accurate approximation of space robots. This is followed by the development of HOCBF-based safety filters to ensure simultaneous collision avoidance and compliance with specified joint limits. To mitigate feasibility issues, we incorporate the optimal decay method into our safety filter design. Furthermore, we introduce a data-driven re-planning mechanism to avoid local minimums of control barrier functions. Such a mechanism primarily operates through anomaly detection of tracking behavior using One-Class Support Vector Machines. Numerical experiments demonstrate that our method effectively ensures safety of space robots under complicated circumstances without compromising the system's ability to achieve its intended goals.

关键词： control barrier functions Safe control Space robot

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Can control barrier functions keep automated vehicles safe in live freeway traffic? 25

Can control barrier functions keep automated vehicles safe i...

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Proceedings of the ACM/IEEE 16th International Conference on Cyber-Physical Systems (with CPS-IoT Week 2025)

作者： George Gunter Matthew Nice Matt Bunting Jonathan Sprinkle Daniel Work Vanderbilt University Nashville TN USA

ISBN: (纸本)9798400714986

This work presents testing of a control barrier Function (CBF) supervised Automated Vehicle (AV) in live freeway traffic. The CBF is designed and implemented using a common dynamical model for AV longitudinal control and a time-gap based safety property combined with CAN bus injection software/hardware. 1.17 hours of car-following data is collected from driving in congested freeway traffic. We analyze the extent to which the CBF controlled AV satisfied three properties: 1) forward-invariance of the safety property, 2) recovery of the safety property, and 3) collision *** main findings are as follows. Forward-invariance was not strictly satisfied across all states. When trajectories begin satisfying the safety property it was violated by a maximum of 3.4[m], and 90% of violations were less than 2[m]. Recovery was also not strictly satisfied across all states. For trajectories which begin outside of the safe set due to merge-in events, if the violation to the safety property was by more than 5[m] the AV was recovering back to the safe set in more than 98% of the time. Finally, the minimum spacing-gap was 11.7[m]. Across the tests the AV remained far from any collisions. We additionally analyze errors between control inputs and achieved outputs and hypothesize that unaccounted for modeling errors may lead to under-braking compared to what the CBF logic specifies, which may contribute to the observed property violations.

关键词： control barrier functions

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control barrier functions for Mechanical Systems: Theory and Application to Robotic Grasping

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IEEE TRANSACTIONS ON control SYSTEMS TECHNOLOGY 2021年第2期29卷 530-545页

作者： Shaw Cortez, Wenceslao Oetomo, Denny Manzie, Chris Choong, Peter Royal Inst Technol KTH Sch EECS S-10044 Stockholm Sweden Univ Melbourne MIDAS Lab Sch Elect Mech & Infrastruct Engn Melbourne Vic 3010 Australia Univ Melbourne Dept Surg St Vincents Hosp Melbourne Fitzroy Vic 3065 Australia

control barrier functions have been demonstrated to be a useful method of ensuring constraint satisfaction for a wide class of controllers. However, the existing results are mostly restricted to continuous-time systems. Mechanical systems, including robots, are typically second-order systems in which the control occurs at the force/torque level. These systems have actuator, velocity, and position constraints (i.e., relative degree two) that are vital for safety and/or task execution. Additionally, mechanical systems are typically controlled digitally as sampled-data systems. The contribution of this article is twofold. The first contribution is the development of novel, robust control barrier functions that ensure constraint satisfaction for sampled-data systems in the presence of model uncertainty and allows for satisfaction of actuator constraints. The second contribution is the application of the proposed method to the challenging problem of robotic grasping in which a robotic hand must ensure that an object remains inside the grasp while manipulating it to the desired reference trajectory. A grasp constraint satisfying controller is proposed that can admit the existing nominal manipulation controllers from the literature while simultaneously ensuring no slip, no overextension (e.g., singular configurations), and no rolling off of the fingertips. Simulation and experimental results validate the proposed control for the robotic hand application.

关键词： Robots Mechanical systems control systems Grasping Sampled data systems Uncertainty Sensors Constraint satisfaction control barrier functions control systems-control design control systems-robot control engineering-general-mechanical systems robots-manipulators robotic grasping

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control barrier functions for Cyber-Physical Systems and Applications to NMPC

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IEEE ROBOTICS AND AUTOMATION LETTERS 2021年第4期6卷 8623-8630页

作者： Schilliger, Jan Lew, Thomas Richards, Spencer M. Hanggi, Severin Pavone, Marco Onder, Christopher Swiss Fed Inst Technol Inst Dynam Syst & Control IDSC CH-8092 Zurich Switzerland Stanford Univ Dept Aeronaut & Astronaut Stanford CA 94305 USA

Tractable safety-ensuring algorithms for cyber-physical systems are important in critical applications. Approaches based on control barrier functions assume continuous enforcement, which is not possible in an online fashion. This letter presents two tractable algorithms to ensure forward invariance of discrete-time controlled cyber-physical systems. Both approaches are based on control barrier functions to provide strict mathematical safety guarantees. The first algorithm exploits Lipschitz continuity and formulates the safety condition as a robust program which is subsequently relaxed to a set of affine conditions. The second algorithm is inspired by tube-NMPC and uses an affine control barrier Function formulation in conjunction with an auxiliary controller to guarantee safety of the system. We combine an approximate NMPC controller with the second algorithm to guarantee strict safety despite approximated constraints and show its effectiveness experimentally on a mini-Segway.

关键词： Safety control systems Dynamical systems Cyber-physical systems Approximation algorithms Trajectory Stability analysis Optimization and optimal control robot safety control barrier functions nonlinear model predictive control

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Safe-by-construction autonomous vehicle overtaking using control barrier functions and model predictive control

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2024年第7期55卷 1283-1303页

作者： Yuan, Dingran Yu, Xinyi Li, Shaoyuan Yin, Xiang Shanghai Jiao Tong Univ Dept Automat Shanghai 200240 Peoples R China Univ Southern Calif Dept Comp Sci Los Angeles CA USA

Ensuring safety for vehicle overtaking systems is one of the most fundamental and challenging tasks in autonomous driving. This task is particularly intricate when the vehicle must not only overtake its front vehicle safely but also consider the presence of potential opposing vehicles in the opposite lane that it will temporarily occupy. In order to tackle the overtaking task in such challenging scenarios, we introduce a novel integrated framework tailored for vehicle overtaking manoeuvres. Our approach integrates the theories of varying-level control barrier functions (CBF) and time-optimal model predictive control (MPC). The main feature of our proposed overtaking strategy is that it is safe-by-construction, which enables rigorous mathematical proof and validation of the safety guarantees. We show that the proposed framework is applicable when the opposing vehicle is either fully autonomous or driven by human drivers. To demonstrate our framework, we perform a set of simulations for overtaking scenarios under different settings. The simulation results show the superiority of our framework in the sense that it ensures collision-free and achieves better safety performance compared with the standard MPC-based approach without safety guarantees.

关键词： Overtaking manoeuvres formal methods control barrier functions autonomous driving

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Hybrid control barrier functions for Continuous-Time Systems

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IEEE TRANSACTIONS ON AUTOMATIC control 2024年第10期69卷 6605-6619页

作者： Marley, Mathias Skjetne, Roger Teel, Andrew R. Norwegian Univ Sci & Technol Ctr Autonomous Marine Operat & Syst Dept Marine Technol N-7491 Trondheim Norway Univ Calif Santa Barbara Dept Elect & Comp Engn Santa Barbara CA 93106 USA

control barrier functions (CBFs) enable constraint satisfaction in controlled dynamical systems, by mapping state constraints into state-dependent input constraints. This article investigates the use of hybrid CBF formulations for constraint satisfaction in continuous-time systems. Augmenting CBFs with logic variables enables solving control problems that are not solvable by continuous, or even discontinuous, control. Examples include robust deadlock resolution for vehicles moving in the presence of bounded obstacles, and robust obstacle avoidance for nonholonomic vehicles required to maintain a nonzero forward speed. A recursive procedure for constructing hybrid high-order CBFs is proposed, thereby extending hybrid CBFs to systems with high-order safety constraints. The theoretical results are illustrated by several examples.

关键词： Safety System recovery Collision avoidance Vectors Switches Task analysis Robustness control barrier functions hybrid feedback control obstacle avoidance safety uniform global asymptotic stability

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