Control Barrier Functions

Also known as CBF

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Latest papers 149

36 papers in the last four weeks, up 260% on the four weeks before. 0.2% of all new papers.

May 19, 2026

Conflict-Aware Active Perception and Control in 3D Gaussian Splatting Fields via Control Barrier Functions

Active perception in uncertain environments requires robots to navigate safely while acquiring informative observations to reduce map uncertainty. These objectives inherently conflict, as informative viewpoints often lie near uncertain regions with higher collision risk. To address this challenge, we develop a conflict-aware active perception and control framework for robotic systems operating in environments represented by 3D Gaussian Splatting (3DGS). Safety is enforced using a Control Barrier Function (CBF) derived from an Average Value-at-Risk AV@R collision-risk metric that accounts for geometric uncertainty and guarantees forward invariance of a safe set. To improve perception, we propose a risk-aware Expected Information Gain (EIG) formulation for selecting the next-best-view and introduce perception barrier functions that align the camera orientation with the local information-ascent direction. To obtain a tractable formulation for these conflicting safety and perception objectives, we propose a unified safety-critical, perception-aware quadratic program that enforces safety as a hard constraint while relaxing perception constraints through slack variables. Simulation results demonstrate that the proposed method improves both safety and information acquisition compared to existing 3DGS-based approaches.

Amirhossein Mollaei Khass, Athanasios Cosse, Vivek Pandey +1

Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA, 18015, USA

Active Perception Next-Best-View Planning Control Barrier Functions Safe Motion Planning

May 19, 2026

k-Inductive Neural Barrier Certificates for Unknown Nonlinear Dynamics

While conventional (k=1) discrete-time barrier certificate conditions impose strict safety constraints by requiring the function to be non-increasing at every step, k-inductive barrier certificates relax this by allowing a temporary increase -- up to k-1 times, each within a threshold

ε

-- while maintaining overall safety, and improving flexibility. This paper leverages neural networks and constructs k-inductive neural barrier certificates (k-NBCs) for (partially) unknown nonlinear systems. While neural networks offer scalability in the design process, they lack formal guarantees, requiring additional approaches such as counterexample-guided inductive synthesis (CEGIS) with satisfiability modulo theories (SMT) for verification. However, the CEGIS-SMT framework requires knowledge of system dynamics, which is unavailable in practical settings. To address this, we leverage the generalization of the Willems et al.'s fundamental lemma, using a single state trajectory, to construct a data-driven representation of (partially) unknown models for SMT verification without sacrificing accuracy. Additionally, CEGIS-SMT further removes the constraint of restricting barrier certificates to specific function classes, such as sum-of-squares, enabling greater flexibility in their design. We validate our approach on three nonlinear case studies with (partially) unknown dynamics.

Ben Wooding, Hongchao Zhang, Taylor T. Johnson +1

Vanderbilt University, Nashville, TN, USA · Newcastle University, Newcastle upon Tyne, UK

Control Barrier Functions Formal Verification

May 16, 2026

Beyond Safety Filtering: Control Barrier Function-Informed Reinforcement Learning for Connected and Automated Vehicles

Reinforcement Learning (RL) uses rewards to guide learning, yet reward design is typically hand-crafted using heuristics that can be difficult to tune. We propose a Control Barrier Function (CBF)-informed reward design for Multi-Agent RL (MARL) that converts CBF constraint values under joint MARL actions into a reward signal that explicitly guides safe learning. We compare against two heuristic reward baselines in a four-way multi-lane intersection with connected and automated vehicles. Results show that our method achieves the highest task performance and is less sensitive to reward hyperparameters, yielding consistently strong performance across the tested hyperparameter range. Code for reproducing the experimental results and a video demonstration are available at https://github.com/bassamlab/SigmaRL.

Jianye Xu, Bassam Alrifaee

Department of Computer Science, RWTH Aachen University, Germany · Department of Aerospace Engineering, University of the Bundeswehr Munich, Germany

Reward Shaping Control Barrier Functions RL for Autonomous Driving Safe RL Multi-Agent Reinforcement Learning

May 15, 2026

Policy Library CBF: Finite-Horizon Safety at Runtime via Parallel Rollouts

Safety-critical autonomy in unstructured environments poses significant challenges for online safety certification under evolving constraints. We propose Policy Library Control Barrier Function~(PL-CBF), a runtime safety filter that evaluates a library of fallback policies via parallel finite-horizon rollouts, selects the least invasive safe mode, and enforces safety by solving a quadratic program that minimally modifies a nominal policy. We provide a theoretical analysis based on a finite-horizon language metric over closed-loop behaviors, characterizing policy-library coverage requirements for certifying finite-horizon safety. Simulations on a planar double-integrator (4 states), highway driving with abrupt friction changes using a realistic nonlinear vehicle model (8 states), and 3D quadrotor navigation in crowded dynamic environments (12 states) demonstrate improved safety coverage over single-policy safety filters while retaining millisecond-level runtime.

Taekyung Kim, Hideki Okamoto, Bardh Hoxha +2

Department of Robotics, 3Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, 48109, USA · Toyota Motor North America, Research & Development, Ann Arbor, MI, 48105, USA

Safety-Critical Control Control Barrier Functions Safety Filtering Runtime Assurance

May 15, 2026

Reactive Robot-Centric Safety for Autonomous Navigation in Constrained and Dynamic Environments

In this work, we address the problem of ensuring real-time safety in autonomous robot navigation, in spatially constrained dynamic environments, by utilizing only onboard sensors. We present a real-time control architecture that integrates a 3D LIDAR perception-based composite control barrier function(CBF)-based safety filter directly into the autonomy pipeline. The proposed perception-driven framework enforces collision avoidance constraints dynamically from onboard point cloud data, thus allowing a large number of constraints to be handled at the control frequency, while remaining minimally invasive to nominal task execution. The safety region is defined as an ellipsoid in the body-frame, consistent with the geometry of the platform, which induces time-varying constraints in the world frame as the robot rotates; this effect is handled through a dedicated formulation of time-varying (CBF) for each LIDAR point. We validate the system through multiple field experiments in underground environments by utilizing a quadruped platform performing a visual inspection task, demonstrating reliable operation in the presence of dynamic obstacles, unsafe high-level references, abrupt localization anomalies, and while traversing through narrow corridors.

Viswa Narayanan Sankaranarayanan, Vignesh K. Viswanathan, Akshit Saradagi +2

Robotics and Artificial Intelligence Group of the Department of Computer Science, Electrical and Space Engineering at Luleå University of Technology, Sweden.

Safety-Critical Control Control Barrier Functions Safe Robot Navigation Robot Safety Dynamic Obstacle Avoidance Robot Collision Avoidance

May 15, 2026

parallelcbf: A composable safety-filter and auditability framework for tensor-parallel reinforcement learning

While Isaac Lab provides massive parallel UAV simulation, OmniSafe and safe-control-gym provide constrained-RL benchmarks, and CBFKit provides control-barrier-function synthesis tooling, no existing framework unifies these capabilities for end-to-end safety-constrained training. ParallelCBF is the first framework to unify (i)~tensor-parallel UAV environments, (ii)~hard-gate CBF safety filters, (iii)sharded BC-to-RL pipelines, and (iv)first-class operational auditability -- pre-registration, watchdog registries, failure forensics, and dataset audits as composable APIs rather than user-implemented scripts. We release ParallelCBF v0.1.0 under Apache2.0 with a four-layer composable API, a CPU PyTorch reference implementation of a dual-barrier (squared / linear-predictive) CBF, property-based safety invariance tests across vectorized batch sizes that complete in 1.67s for the full 39-test suite, and a 31{,}415-episode behavior-cloning collection campaign whose curriculum mix, per-bucket yields, and dataset SHA-256 are auditable through the framework's own ops primitives. We report a representative end-to-end pipeline execution in which the framework's auditability layer halted a downstream training stage that did not meet pre-registered convergence criteria, preventing silent propagation of a degraded checkpoint -- an architectural property we argue is necessary, not merely useful, for reproducible empirical robotics research. The framework is installable via pip install parallelcbf; source and release artifacts are available at https://github.com/xiaoyang-123-cell/ParallelCBF.

Yijun Lu, Zilei Yang, Yuyin Ma

Reinforcement Learning Control Barrier Functions Constrained RL Safety Filtering ML Reproducibility Safe RL

May 8, 2026

Efficient Verification of Neural Control Barrier Functions with Smooth Nonlinear Activations

Formal verification of neural control barrier functions (NCBFs) remains challenging, especially for neural networks with nonlinear activations like

\tanh

. Existing CROWN-based methods rely on conservative linear relaxations for Jacobian bounds, limiting scalability. We propose LightCROWN, which computes tighter Jacobian bounds by exploiting the analytical properties of activation functions. Experiments on nonlinear control systems including the inverted pendulum, Dubins car, and planar quadrotor demonstrate that LightCROWN improves verification success rates up to 100%, while enhancing speed and scalability. Our approach provides a generalizable improvement for CROWN-based frameworks, enabling more efficient verification of complex NCBFs. The code can be found at github.com/Autonomous-Systems-and-Control-Lab/verify-neural-CBF.

Jun Zhang, Haibo Zhang, Chun Liu +2

School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China · Beijing Institute of Control Engineering, Beijing, China · School of Mechatronic Engineering and Automation, Shanghai2026 University, Shanghai, China +1

Neural Network Verification Control Barrier Functions

May 7, 2026

Maximal Controlled Invariant-MPC: Enhancing Feasibility and Reducing Conservatism through Terminal CBF Constraint in Safety-Critical Control

Optimal control for safety-critical systems is often dependent on the conservativeness of constraints. Control Barrier Functions (CBFs) serve as a medium to represent such constraints, but constructing a minimally conservative CBF is a computationally intractable problem. Therefore, approaches that can guarantee safety while reducing conservatism will help improve the optimality of the system under consideration. Here, we present a Model Predictive Control (MPC) formulation using CBF as a terminal constraint, which is proven to improve feasibility and reachable sets with increasing prediction horizon. The constructive nature of the proofs allows for warm-starting the nonlinear optimization problem, thereby reducing the computational time substantially. Simulations are set up for a simple nonholonomic system to numerically validate the results, and it is observed that the number of infeasible points decreased by a factor of 1.7 to 2.7. The increase in reachable state space was demonstrated by the ability of the system to track trajectories that are entirely inside the unsafe region of the control barrier function.

Tanmay Dokania, Yashwanth Kumar Nakka

Graduate Student, Daniel Guggenheim School of Aerospace Engineering. · Assistant Professor, Director, Aerospace Robotics Lab, Daniel Guggenheim School of Aerospace Engineering.

Dynamical Systems Safety-Critical Control Nonlinear MPC Control Barrier Functions Model Predictive Control Optimal Control

May 6, 2026

A Closed-Form Dual-Barrier CBF Safety Filter for Holonomic Robots on Incrementally Built Occupancy Grid Maps

We present a dual-barrier control barrier function (CBF) safety filter for real-time, safety-critical velocity control of holonomic robots operating in incrementally built occupancy grid maps. As a robot explores an unknown environment, unmapped regions introduce irreducible uncertainty, since obstacle geometry beyond the explored frontier is unknown, making entry into such regions a source of collision risk, especially with front-facing sensors. To address this, we enforce two constraints: avoidance of mapped obstacles and restriction from unexplored regions. Both constraints are derived analytically from the occupancy grid's signed distance field, yielding a closed-form safety filter that requires only a small linear system solve per cycle. On resource-constrained platforms such as the Raspberry Pi, where SLAM and planning already consume significant compute, the low overhead of the proposed filter preserves resources. An adaptive gain schedule relaxes the frontier constraint in information-rich regions and tightens it in well-mapped areas, improving exploration efficiency while maintaining safety. The filter operates in velocity space as a minimally invasive correction and composes with arbitrary nominal controllers, including learning-based methods. Hardware flight experiments on a PX4-controlled quadrotor demonstrate zero collisions across multiple indoor runs.

Himanshu Paudel, Basanta Joshi, Dhirendra Raj Madai +3

Safety-Critical Control Control Barrier Functions Safe Robot Navigation Robot Safety Safety Filtering

May 5, 2026

Differentiable Optimization Layered Safety-Critical Control for Risk-Aware Navigation via Conformal Prediction

Risk-aware navigation in unknown environments is a fundamental challenge for autonomous vehicles operating in complex urban systems. To address this issue, this paper presents a differentiable optimization layered safety-critical control method based on conformal prediction. First, to handle uncertainties arising from sensor noise, the conformal prediction method is employed to generate risk-aware obstacle ellipsoids around an elliptical-shaped robot. Second, two nested differentiable optimization layers are introduced to build the control barrier functions for obstacle avoidance and feasibility guarantee, respectively. Then, a quadratic program based safety-critical control law is proposed to integrate the above control barrier function constraints as well as input constraints. In the end, the effectiveness of the proposed framework is demonstrated through numerical simulations.

Jinyang Dong, Shizhen Wu, Yongchun Fang

Institute of Robotics and Automatic Information Systems, College of Artificial Intelligence, Nankai University, Tianjin 300071, China · Academy for Advanced Interdisciplinary Studies, Nankai University, Tianjin 300071, China · Institute of Intelligence Technology and Robotic Systems, Shenzhen Research Institute of Nankai University, Shenzhen 518083, China

Safety-Critical Control Control Barrier Functions Safe Robot Navigation Robot Safety Differentiable Optimization

May 1, 2026

Online Safety Filter for Deformable Object Manipulation with Horizon Agnostic Neural Operators

Safety critical control of robotic manipulation tasks involving deformable media such as fluids, cloth, and soft objects remains challenging because existing learning based approaches encode safety indirectly through reward shaping, which provides no guarantee of constraint satisfaction at deployment. We present a constraint driven online safety filter for deformable object manipulation that enforces explicit task level safety constraints in real time by minimally modifying any nominal control policy. Our approach combines two key components: a horizon agnostic neural operator that learns the boundary input output mapping of the underlying PDE dynamics and generalizes across variable rollout lengths without retraining, and a boundary control barrier function that certifies safety at the task relevant output level via a lightweight quadratic program. The resulting safety constraint is affine in the boundary input rate, enabling real time online filtering. We evaluate the proposed method on fluid manipulation tasks in FluidLab, where the filter improves safe trajectory rates by up to 22% over unfiltered base policies while also reducing the number of steps required to reach the safe set, demonstrating that constraint driven safety enforcement is both more reliable and more efficient than reward shaping approaches.

Jiaxing Li, Hanjiang Hu, Zhuoyuan Wang +2

Carnegie Mellon University, Pittsburgh, PA, USA

Safety-Critical Control Deformable Object Manipulation Control Barrier Functions Robot Safety Safety Filtering

Apr 26, 2026

CAPSULE: Control-Theoretic Action Perturbations for Safe Uncertainty-Aware Reinforcement Learning

Ensuring safe exploration in high-dimensional systems with unknown dynamics remains a significant challenge. Existing safe reinforcement learning methods often provide safety guarantees only in expectation, which can still lead to safety violations. Control-theoretic approaches, in contrast, offer hard constraint-based safety guarantees but typically assume access to known system dynamics or require accurate estimation of control-affine models. In this paper, we propose a safe reinforcement learning framework that learns a probabilistic control-affine dynamics model in an offline setting. The learned model is leveraged to explicitly construct control barrier functions (CBFs) that incorporate model uncertainty to provide conservative safety constraints. These CBF constraints are enforced through an online constraint-based action correction mechanism, enabling safe exploration without overly restricting task performance. Empirical evaluations on nonlinear, complex continuous-control benchmarks demonstrate that our approach achieves returns comparable to those of existing baselines while significantly reducing safety violations.

Rahul Narava, Siddharth Verma, Ojas Jain +2

Indian Institute of Technology Ropar · CRAN, Université de Lorraine

Control Barrier Functions Constrained RL Safe RL Model-Based RL

Apr 24, 2026

Control Barrier Functions Solved with Hierarchical Quadratic Programming for Safe Physical Human-Robot Interaction

Physical human-robot interaction offers the potential to leverage human intelligence and robot physical capabilities to enable a range of exciting applications, e.g., collaborative robots for rehabilitation. Safety is critical for the successful deployment of this kind of robotic system. In recent years, Control Barrier Function (CBF) has emerged as an effective approach to enforce safety guarantees, which has been widely applied in various applications, from adaptive cruise control to navigation of legged robots. CBFs can be solved in a Quadratic Programming (QP) problem, which can include many CBF-formulated tasks. To manage a large number of safety tasks, a hierarchical CBF has been used to allow hierarchical relaxation of safety tasks to ensure the feasibility of a solution in the presence of conflicting tasks. In this work, we propose to use a CBF-based Hierarchical Quadratic Programming (HQP) framework in physical human-robot interaction to allow us to design both performance tasks (e.g., preserve the desired behavior at the human-robot interaction point) and safety tasks at any level of a hierarchy to balance the safety and the performance in a more flexible way. Extensive experiments were carried out on a real redundant robot to validate the effectiveness, flexibility, and generality of this approach.

Rui Luo, Jonas Mariager Jakobsen, Wesley Roozing +2

Robotic Control Control Barrier Functions Constrained Optimization Human-Robot Interaction

Apr 23, 2026

Full-Body Dynamic Safety for Robot Manipulators: 3D Poisson Safety Functions for CBF-Based Safety Filters

Collision avoidance for robotic manipulators requires enforcing full-body safety constraints in high-dimensional configuration spaces. Control Barrier Function (CBF) based safety filters have proven effective in enabling safe behaviors, but enforcing the high number of constraints needed for safe manipulation leads to theoretic and computational challenges. This work presents a framework for full-body collision avoidance for manipulators in dynamic environments by leveraging 3D Poisson Safety Functions (PSFs). In particular, given environmental occupancy data, we sample the manipulator surface at a prescribed resolution and shrink free space via a Pontryagin difference according to this resolution. On this buffered domain, we synthesize a globally smooth CBF by solving Poisson's equation, yielding a single safety function for the entire environment. This safety function, evaluated at each sampled point, yields task-space CBF constraints enforced by a real-time safety filter via a multi-constraint quadratic program. We prove that keeping the sample points safe in the buffered region guarantees collision avoidance for the entire continuous robot surface. The framework is validated on a 7-degree-of-freedom manipulator in dynamic environments.

Meg Wilkinson, Gilbert Bahati, Ryan M. Bena +3

Computing and Mathematical Sciences, California Institute of Technology. · Mechanical and Civil Engineering, California Institute of Technology.

Control Barrier Functions Robot Safety Safety Filtering Dynamic Obstacle Avoidance Robot Collision Avoidance

Apr 22, 2026

Stochastic Barrier Certificates in the Presence of Dynamic Obstacles

Safety of stochastic dynamic systems in environments with dynamic obstacles is studied in this paper through the lens of stochastic barrier functions. We introduce both time-invariant and time-varying barrier certificates for discrete-time, continuous-space systems subject to uncertainty, which provide certified lower bounds on the probability of remaining within a safe set over a finite horizon. These certificates explicitly account for time-varying unsafe regions induced by obstacle dynamics. By leveraging Bellman's optimality perspective, the time-varying formulation directly captures temporal structure and yields less conservative bounds than state-of-the-art approaches. By restricting certificates to polynomial functions, we show that time-varying barrier synthesis can be formulated as a convex sum-of-squares program, enabling tractable optimization. Empirical evaluations on nonlinear systems with dynamic obstacles show that time-varying certificates consistently achieve tight guarantees, demonstrating improved accuracy and scalability over state-of-the-art methods.

Rayan Mazouz, Luca Laurenti, Morteza Lahijanian

Dept. of Aerospace Eng. Sciences at University of Colorado Boulder, USA · Delft University of Technology, The Netherlands

Control Barrier Functions Dynamic Obstacle Avoidance

Apr 14, 2026

Boundary Sampling to Learn Predictive Safety Filters via Pontryagin's Maximum Principle

Safety filters provide a practical approach for enforcing safety constraints in autonomous systems. While learning-based tools scale to high-dimensional systems, their performance depends on informative data that includes states likely to lead to constraint violation, which can be difficult to efficiently sample in complex, high-dimensional systems. In this work, we characterize trajectories that barely avoid safety violations using the Pontryagin Maximum Principle. These boundary trajectories are used to guide data collection for learned Hamilton-Jacobi Reachability, concentrating learning efforts near safety-critical states to improve efficiency. The learned Control Barrier Value Function is then used directly for safety filtering. Simulations and experimental validation on a shared-control automotive racing application demonstrate PMP sampling improves learning efficiency, yielding faster convergence, reduced failure rates, and improved safe set reconstruction, with wall times around 3ms.

James Dallas, Thomas Lew, John Talbot +3

Toyota Research Institute, Los Altos, CA 94022, USA. · Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, USA.

Safety Filtering Control Barrier Functions Reachability Analysis Adaptive Sampling

Apr 14, 2026

Capability-Aware Heterogeneous Control Barrier Functions for Decentralized Multi-Robot Safe Navigation

Safe navigation for multi-robot systems requires enforcing safety without sacrificing task efficiency under decentralized decision-making. Existing decentralized methods often assume robot homogeneity, making shared safety requirements non-uniformly interpreted across heterogeneous agents with structurally different dynamics, which could lead to avoidance obligations not physically realizable for some robots and thus cause safety violations or deadlock. In this paper, we propose Capability-Aware Heterogeneous Control Barrier Function (CA-HCBF), a decentralized framework for consistent safety enforcement and capability-aware coordination in heterogeneous robot teams. We derive a canonical second-order control-affine representation that unifies holonomic and nonholonomic robots under acceleration-level control via canonical transformation and backstepping, preserving forward invariance of the safe set while avoiding relative-degree mismatch across heterogeneous dynamics. We further introduce a support-function-based directional capability metric that quantifies each robot's ability to follow its motion intent, deriving a pairwise responsibility allocation that distributes the safety burden proportionally to each robot's motion capability. A feasibility-aware clipping mechanism further constrains the allocation to each agent's physically achievable range, mitigating infeasible constraint assignments common in dense decentralized CBF settings. Simulations with up to 30 heterogeneous robots and a physical multi-robot demonstration show improved safety and task efficiency over baselines, validating real-world applicability across robots with distinct kinematic constraints.

Joonkyung Kim, Yanze Zhang, Wenhao Luo +1

Department of Computer Science and Engineering, Texas A&M University · Department of Computer Science, University of Illinois Chicago

Safe Robot Navigation Control Barrier Functions Multi-Agent Control Multi-Robot Coordination Robot Collision Avoidance

Apr 14, 2026

Synthesis and Deployment of Maximal Robust Control Barrier Functions through Adversarial Reinforcement Learning

Robust control barrier functions (CBFs) provide a principled mechanism for smooth safety enforcement under worst-case disturbances. However, existing approaches typically rely on explicit, closed-form structure in the dynamics (e.g., control-affine) and uncertainty models. This has led to limited scalability and generality, with most robust CBFs certifying only conservative subsets of the maximal robust safe set. In this paper, we introduce a new robust CBF framework for general nonlinear systems under bounded uncertainty. We first show that the safety value function solving the dynamic programming Isaacs equation is a valid robust discrete-time CBF that enforces safety on the maximal robust safe set. We then adopt the key reinforcement learning (RL) notion of quality function (or Q-function), which removes the need for explicit dynamics by lifting the barrier certificate into state-action space and yields a novel robust Q-CBF constraint for safety filtering. Combined with adversarial RL, this enables the synthesis and deployment of robust Q-CBFs on general nonlinear systems with black-box dynamics and unknown uncertainty structure. We validate the framework on a canonical inverted pendulum benchmark and a 36-D quadruped simulator, achieving substantially less conservative safe sets than barrier-based baselines on the pendulum and reliable safety enforcement even under adversarial uncertainty realizations on the quadruped.

Donggeon David Oh, Duy P. Nguyen, Haimin Hu +1

Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ 08540, USA · Department of Computer Science, Johns Hopkins University, Baltimore, MD 21218, USA

Control Barrier Functions

Apr 10, 2026

SafeMind: A Risk-Aware Differentiable Control Framework for Adaptive and Safe Quadruped Locomotion

Learning-based quadruped controllers achieve impressive agility but typically lack formal safety guarantees under model uncertainty, perception noise, and unstructured contact conditions. We introduce SafeMind, a differentiable stochastic safety-control framework that unifies probabilistic Control Barrier Functions with semantic context understanding and meta-adaptive risk calibration. SafeMind explicitly models epistemic and aleatoric uncertainty through a variance-aware barrier constraint embedded in a differentiable quadratic program, thereby preserving gradient flow for end-to-end training. A semantics-to-constraint encoder modulates safety margins using perceptual or language cues, while a meta-adaptive learner continuously adjusts risk sensitivity across environments. We provide theoretical conditions for probabilistic forward invariance, feasibility, and stability under stochastic dynamics. SafeMind is deployed on Unitree A1 and ANYmal C at 200~Hz and validated across 12 terrain types, dynamic obstacles, morphology perturbations, and semantically defined tasks. Experiments show that SafeMind reduces safety violations by 3--10x and energy consumption by 10--15% relative to state-of-the-art CBF, MPC, and hybrid RL baselines, while maintaining real-time control performance.

Zukun Zhang, Kai Shu, Mingqiao Mo

The University of Hong Kong, Pokfulam, Hong Kong, China · Alibaba, Beijing, China · University of Chinese Academy of Sciences, No.1 Yanqihu East Rd, Huairou District, Beijing, China

Robotic Control Robot Safety Quadruped Locomotion Control Barrier Functions

Apr 6, 2026

FORMULA: FORmation MPC with neUral barrier Learning for safety Assurance

Multi-robot systems (MRS) are essential for large-scale applications such as disaster response, material transport, and warehouse logistics, yet ensuring robust, safety-aware formation control in cluttered and dynamic environments remains a major challenge. Existing model predictive control (MPC) approaches suffer from limitations in scalability and provable safety, while control barrier functions (CBFs), though principled for safety enforcement, are difficult to handcraft for large-scale nonlinear systems. This paper presents FORMULA, a safe distributed, learning-enhanced predictive control framework that integrates MPC with Control Lyapunov Functions (CLFs) for stability and neural network-based CBFs for decentralized safety, eliminating manual safety constraint design. This scheme maintains formation integrity during obstacle avoidance, resolves deadlocks in dense configurations, and reduces online computational load. Simulation results demonstrate that FORMULA enables scalable, safety-aware, formation-preserving navigation for multi-robot teams in complex environments.

Qintong Xie, Weishu Zhan, Peter Chin

Thayer School of Engineering, Dartmouth College, NH 03784. · Department of Computer Science, The University of Manchester, Manchester M13 9PL, United Kingdom.

Multi-Robot Formation Control Model Predictive Control Multi-Robot Motion Planning Control Barrier Functions

Apr 5, 2026

Optimization-Free Constrained Control with Guaranteed Recursive Feasibility: A CBF-Based Reference Governor Approach

This letter presents a constrained control framework that integrates Explicit Reference Governors (ERG) with Control Barrier Functions (CBF) to ensure recursive feasibility without online optimization. We formulate the reference update as a virtual control input for an augmented system, governed by a smooth barrier function constructed from the softmin aggregation of Dynamic Safety Margins (DSMs). Unlike standard CBF formulations, the proposed method guarantees the feasibility of safety constraints by design, exploiting the forward invariance properties of the underlying Lyapunov level sets. This allows for the derivation of an explicit, closed-form reference update law that strictly enforces safety while minimizing deviation from a nominal reference trajectory. Theoretical results confirm asymptotic convergence, and numerical simulations demonstrate that the proposed method achieves performance comparable to traditional ERG frameworks.

Satoshi Nakano, Emanuele Garone, Gennaro Notomista

Department of Engineering, Nagoya Institute of Technology, 466-8555 Aichi, Japan · Department of Control Engineering and System Analysis, Universite Libre de Bruxelles, 1050 Brussels, Belgium · Department of Electrical and Computer Engineering, University of Waterloo, ON N2L 3G1, Canada

Control Barrier Functions

Apr 2, 2026

Backup-Based Safety Filters: A Comparative Review of Backup CBF, Model Predictive Shielding, and gatekeeper

This paper revisits three backup-based safety filters -- Backup Control Barrier Functions (Backup CBF), Model Predictive Shielding (MPS), and gatekeeper -- through a unified comparative framework. Using a common safety-filter abstraction and shared notation, we make explicit both their common backup-policy structure and their key algorithmic differences. We compare the three methods through their filter-inactive sets, i.e., the states where the nominal policy is left unchanged. In particular, we show that MPS is a special case of gatekeeper, and we further relate gatekeeper to the interior of the Backup CBF inactive set within the implicit safe set. This unified view also highlights a key source of conservatism in backup-based safety filters: safety is often evaluated through the feasibility of a backup maneuver, rather than through the nominal policy's continued safe execution. The paper is intended as a compact tutorial and review that clarifies the theoretical connections and differences among these methods.

Taekyung Kim, Aswin D. Menon, Akshunn Trivedi +1

Department of Robotics, University of Michigan, Ann Arbor, MI, 48109, USA · Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, 48109, USA

Safety Filtering Control Barrier Functions

Mar 31, 2026

Long-Horizon Geometry-Aware Navigation among Polytopes via MILP-MPC and Minkowski-Based CBFs

Autonomous navigation in complex, non-convex environments remains challenging when robot dynamics, control limits, and exact robot geometry must all be taken into account. In this paper, we propose a hierarchical planning and control framework that bridges long-horizon guidance and geometry-aware safety guarantees for a polytopic robot navigating among polytopic obstacles. At the high level, Mixed-Integer Linear Programming (MILP) is embedded within a Model Predictive Control (MPC) framework to generate a nominal trajectory around polytopic obstacles while modeling the robot as a point mass for computational tractability. At the low level, we employ a control barrier function (CBF) based on the exact signed distance in the Minkowski-difference space as a safety filter to explicitly enforce the geometric constraints of the robot shape, and further extend its formulation to a high-order CBF (HOCBF). We demonstrate the proposed framework in U-shaped and maze-like environments under single- and double-integrator dynamics. The results show that the proposed architecture mitigates the topology-induced local-minimum behavior of purely reactive CBF-based navigation while enabling safe, real-time, geometry-aware navigation.

Yi-Hsuan Chen, Salman Ghori, Ania Adil +2

Dept. of Aerospace Engineering, University of Maryland, College Park, MD, USA. · Computer, Electrical and Mathematical Science & Engineering Division (CEMSE), KAUST, Saudi Arabia. · Dept. Electrical and Computer Engineering and Dept. Computer Science, University of Maryland, College Park, MD, USA.

Safe Robot Navigation Motion Planning Constrained Motion Planning Control Barrier Functions Model Predictive Control

Mar 31, 2026

Distributed Predictive Control Barrier Functions: Towards Scalable Safety Certification in Modular Multi-Agent Systems

We consider safety-critical multi-agent systems with distributed control architectures and potentially varying network topologies. While learning-based distributed control enables scalability and high performance, a lack of formal safety guarantees in the face of unforeseen disturbances and unsafe network topology changes may lead to system failure. To address this challenge, we introduce structured control barrier functions (s-CBFs) as a multi-agent safety framework. The s-CBFs are augmented to a distributed predictive control barrier function (D-PCBF), a predictive, optimization-based safety layer that uses model predictions to guarantee recoverable safety at all times. The proposed approach enables a permissive yet formal plug-and-play protocol, allowing agents to join or leave the network while ensuring safety recovery if a change in network topology requires temporarily unsafe behavior. We validate the formulation through simulations and real-time experiments of a miniature race-car platoon.

Jonas Ohnemus, Alexandre Didier, Ahmed Aboudonia +2

Institute for Dynamic Systems and Control, ETH Zurich, 8092 Zurich, Switzerland · University of California Berkeley, 94720 CA, USA

Safety-Critical Control Control Barrier Functions Multi-Agent Control

Mar 29, 2026

Safety Guardrails in the Sky: Realizing Control Barrier Functions on the VISTA F-16 Jet

The advancement of autonomous systems -- from legged robots to self-driving vehicles and aircraft -- necessitates executing increasingly high-performance and dynamic motions without ever putting the system or its environment in harm's way. In this paper, we introduce Guardrails -- a novel runtime assurance mechanism that guarantees dynamic safety for autonomous systems, allowing them to safely evolve on the edge of their operational domains. Rooted in the theory of control barrier functions, Guardrails offers a control strategy that carefully blends commands from a human or AI operator with safe control actions to guarantee safe behavior. To demonstrate its capabilities, we implemented Guardrails on an F-16 fighter jet and conducted flight tests where Guardrails supervised a human pilot to enforce g-limits, altitude bounds, geofence constraints, and combinations thereof. Throughout extensive flight testing, Guardrails successfully ensured safety, keeping the pilot in control when safe to do so and minimally modifying unsafe pilot inputs otherwise.

Andrew W. Singletary, Max H. Cohen, Tamas G. Molnar +1

Safety-Critical Control Runtime Assurance Control Barrier Functions Feedback Control

Mar 24, 2026

Task-Space Singularity Avoidance for Control Affine Systems Using Control Barrier Functions

Singularities in robotic and dynamical systems arise when the mapping from control inputs to task-space motion loses rank, leading to an inability to determine inputs. This limits the system's ability to generate forces and torques in desired directions and prevents accurate trajectory tracking. This paper presents a control barrier function (CBF) framework for avoiding such singularities in control-affine systems. Singular configurations are identified through the eigenvalues of a state-dependent input-output mapping matrix, and barrier functions are constructed to maintain a safety margin from rank-deficient regions. Conditions for theoretical guarantees on safety are provided as a function of actuator dynamics. Simulations on a planar 2-link manipulator and a magnetically actuated needle demonstrate smooth trajectory tracking while avoiding singular configurations and reducing control input spikes by up to 100x compared to the nominal controller.

Kimia Forghani, Suraj Raval, Lamar Mair +2

Department of Mechanical Engineering, University of Maryland, College Park, MD 20742 · Division of Magnetic Manipulation and Particle Research, Weinberg Medical Physics, Inc., North Bethesda, MD 20852 · Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218

Safety-Critical Control Control Barrier Functions

Mar 22, 2026

Dynamic Control Barrier Function Regulation with Vision-Language Models for Safe, Adaptive, and Realtime Visual Navigation

Robots operating in dynamic, unstructured environments must balance safety and efficiency under potentially limited sensing. While control barrier functions (CBFs) provide principled collision avoidance via safety filtering, their behavior is often governed by fixed parameters that can be overly conservative in benign scenes or overly permissive near hazards. We present AlphaAdj, a vision-to-control navigation framework that uses egocentric RGB input to adapt the conservativeness of a CBF safety filter in real time. A vision-language model(VLM) produces a bounded scalar risk estimate from the current camera view, which we map to dynamically update a CBF parameter that modulates how strongly safety constraints are enforced. To address asynchronous inference and non-trivial VLM latency in practice, we combine a geometric, speed-aware dynamic cap and a staleness-gated fusion policy with lightweight implementation choices that reduce end-to-end inference overhead. We evaluate AlphaAdj across multiple static and dynamic obstacle scenarios in a variety of environments, comparing against fixed-parameter and uncapped ablations. Results show that AlphaAdj maintains collision-free navigation while improving efficiency (in terms of path length and time to goal) by up to 18.5% relative to fixed settings and improving robustness and success rate relative to an uncapped baseline.

Jeffrey Chen, Rohan Chandra

Authors are with the Department of Computer Science, University of Virginia.

Safe Robot Navigation Control Barrier Functions Adaptive Control Dynamic Obstacle Avoidance

Mar 19, 2026

A Closed-Form CLF-CBF Controller for Whole-Body Continuum Soft Robot Collision Avoidance

Safe operation is essential for deploying robots in human-centered 3D environments. Soft continuum manipulators provide passive safety through mechanical compliance, but still require active control to achieve reliable collision avoidance. Existing approaches, such as sampling-based planning, are often computationally expensive and lack formal safety guarantees, which limits their use for real-time whole-body avoidance. This paper presents a closed-form Control Lyapunov Function--Control Barrier Function (CLF--CBF) controller for real-time 3D obstacle avoidance in soft continuum manipulators without online optimization. By analytically embedding safety constraints into the control input, the proposed method ensures stability and safety under the stated modeling assumptions, while avoiding feasibility issues commonly encountered in online optimization-based methods. The resulting controller is up to

10\times

faster than standard CLF--CBF quadratic-programming approaches and up to

100\times

faster than traditional sampling-based planners. Simulation and hardware experiments on a tendon-driven soft manipulator demonstrate accurate 3D trajectory tracking and robust obstacle avoidance in cluttered environments. These results show that the proposed framework provides a scalable and provably safe control strategy for soft robots operating in dynamic, safety-critical settings.

Kiwan Wong, Maximillian Stölzle, Wei Xiao +1

Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA · Robotics Engineering Department, Worcester Polytechnic Institute, Worcester, MA 01609, USA

Continuum Robot Control Robot Collision Avoidance Soft Robotics Control Barrier Functions Lyapunov-Based Control

Mar 19, 2026

Safety-Guaranteed Imitation Learning from Nonlinear Model Predictive Control for Spacecraft Close Proximity Operations

This paper presents a safety-guaranteed, runtime-efficient imitation learning framework for spacecraft close proximity control. We leverage Control Barrier Functions (CBFs) for safety certificates and Control Lyapunov Functions (CLFs) for stability as unified design principles across data generation, training, and deployment. First, a nonlinear Model Predictive Control (NMPC) expert enforces CBF constraints to provide safe reference trajectories. Second, we train a neural policy with a novel CBF-CLF-informed loss and DAgger-like rollouts with curriculum weighting, promoting data-efficiency and reducing future safety filter interventions. Third, at deployment a lightweight one-step CBF-CLF quadratic program minimally adjusts the learned control input to satisfy hard safety constraints while encouraging stability. We validate the approach for ESA-compliant close proximity operations, including fly-around with a spherical keep-out zone and final approach inside a conical approach corridor, using the Basilisk high-fidelity simulator with nonlinear dynamics and perturbations. Numerical experiments indicate stable convergence to decision points and strict adherence to safety under the filter, with task performance comparable to the NMPC expert while significantly reducing online computation. A runtime analysis demonstrates real-time feasibility on a commercial off-the-shelf processor, supporting onboard deployment for safety-critical on-orbit servicing.

Alexander Meinert, Niklas Baldauf, Peter Stadler +1

Space Applications Group, e:fs TechHub GmbH, Gaimersheim, Germany. · Faculty of Electrical Engineering and Information Technology, Ingolstadt University of Applied Sciences, Germany.

Imitation Learning Safety-Critical Control Spacecraft Rendezvous and Proximity Operations Control Barrier Functions

Mar 13, 2026

Verification and Forward Invariance of Control Barrier Functions for Differential-Algebraic Systems

Differential-algebraic equations (DAEs) arise in power networks, chemical processes, and multibody systems, where algebraic constraints encode physical conservation laws. The safety of such systems is critical, yet safe control is challenging because algebraic constraints restrict allowable state trajectories. Control barrier functions (CBFs) provide computationally efficient safety filters for ordinary differential equation (ODE) systems. However, existing CBF methods are not directly applicable to DAEs due to potential conflicts between the CBF condition and the constraint manifold. This paper introduces DAE-aware CBFs that incorporate the differential-algebraic structure through projected vector fields. We derive conditions that ensure forward invariance of safe sets while preserving algebraic constraints and extend the framework to higher-index DAEs. A systematic verification framework is developed, establishing necessary and sufficient conditions for geometric correctness and feasibility of DAE-aware CBFs. For polynomial systems, sum-of-squares certificates are provided, while for nonpolynomial and neural network candidates, satisfiability modulo theories are used for falsification. The approach is validated on wind turbine and flexible-link manipulator systems.

Hongchao Zhang, Mohamad H. Kazma, Meiyi Ma +2

Department of Computer Science, Vanderbilt University, Nashville, TN 37235 USA. · Department of Civil and Environmental Engineering, Vanderbilt University, Nashville, TN 37235 USA.

Control Barrier Functions Dynamical Systems Formal Verification