Control Barrier Functions

Also known as CBF

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Latest papers 148

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

Jul 16, 2026

Safe Execution of RL Policies Via Acceleration-Based CBF-QP Constraint Enforcement for Real-World Robotic Deployments

Reinforcement Learning (RL) has demonstrated remarkable capabilities for solving complex robotic control problems, but its lack of safety guarantees severely limits deployment on hardware. In particular, as legged robots and manipulators often operate near safety-critical boundaries, out-of-distribution states can lead to failure upon deployment. To address this, we introduce Acc-CBF-QP, an acceleration-based Quadratic Program (QP) safety filter using Control Barrier Functions (CBFs) that constrains any RL policy onto a safe set at runtime without modifying training. The method applies to unconstrained and Safe-RL policies, and enforces joint position, velocity, torque, and collision constraints within a unified optimization framework. A key contribution is the formulation of RL+QP tasks that regulate deviation from the RL command when constraints would otherwise be violated. We introduce a TorqueTask, minimizing torque deviation, and a Forward Dynamics Task, minimizing induced acceleration deviation, thus providing principled control over safety-performance trade-offs. Experiments on a 7-DoF Kinova Gen3 manipulator and a 19-DoF Unitree H1 humanoid, both in simulation and on hardware, highlight substantial reductions in constraint violations. On the real H1 hardware, a Safe-RL policy alone yielded 10.04 violations/s, which were reduced by 92% to 0.80 violations/s when augmented with Acc-CBF-QP. On the Kinova Gen3, Acc-CBF-QP fully eliminated violations. Nominal task performance of the RL objective is preserved in violation-free regimes. Under aggressive velocity commands on H1, Acc-CBF-QP improves execution by preventing constraint-induced shutdowns, yielding longer survival times. The full pipeline is open-source.

Bastien Muraccioli, Alice Cariou, Pierre-Alexandre Leziart +4

CNRS–AIST Joint Robotics Laboratory (JRL), IRL3218, AIST, Tsukuba, Japan · Department of Mechanical Engineering, The University of Tokyo, Japan

Robotic Control Control Barrier Functions Robot Safety Safe RL

Jul 15, 2026

Discriminative Barrier Functions for Safe Adversarial Imitation Learning from Observation

Inverse Reinforcement Learning (IRL) algorithms are powerful tools for learning from and generalizing expert demonstrations, but they often rely on unconstrained exploration, rendering them unsafe for real-world deployment. Meanwhile, Control Barrier Functions (CBFs) can guarantee the safety of control systems, but the analytical design of CBFs can be time-consuming and esoteric. In this work, we address these limitations jointly by constraining reward function candidacy during IRL to the space of CBFs, yielding a formulation that exhibits safe online control with continuous experiential improvement. Crucially, this framework enables the data-driven recovery of barrier functions directly from unlabeled expert observations. We demonstrate that the recovered barrier function is robust to unsafe states entirely absent from the expert data. Furthermore, we benchmark our method against standard IRL baselines in a simulated navigation environment, demonstrating improved safety performance. Finally, we investigate the trade-offs of planning-based versus policy-based IRL methods across both simulation and a real world obstacle avoidance task.

Anubhav Vishwakarma, Bhaumik Mehta, Caleb Hsu +3

University of Washington

Reinforcement Learning Control Barrier Functions Adversarial Imitation Learning Imitation Learning Safe RL

Jul 15, 2026

Safe Overtaking for Autonomous Racing Using Hierarchical Optimization and Learning-Based Control

Autonomous racing overtaking requires balancing competitive performance with safety under nonlinear vehicle dynamics and real-time constraints. Model Predictive Control (MPC) combined with Control Barrier Functions (CBFs) provides a principled mechanism for certifying forward invariance of a safe set. However, commonly used fixed-decay discrete-time CBF formulations can become overly conservative in interactive racing scenarios, limiting overtaking performance and requiring manual tuning across track conditions. This paper proposes a hierarchical overtaking framework that explicitly separates maneuver-level decision making from safety-certified trajectory control, reducing conservatism while preserving safety. A high-level Mixed-Integer Quadratic Program (MIQP) resolves the combinatorial passing-side selection problem by selecting a feasible overtaking topology, while a nonlinear Frenet-frame MPC enforces vehicle dynamics and safety through embedded discrete-time CBF constraints. This decomposition isolates the combinatorial complexity of maneuver selection from the continuous trajectory optimization. To further mitigate the sensitivity of fixed-decay barrier constraints, a reinforcement learning policy adapts the discrete-time CBF decay parameter online, enabling context-dependent modulation of safety margins without directly controlling vehicle inputs. Simulation and scaled-hardware experiments show that no single fixed decay parameter achieves uniformly strong performance across tracks, whereas the adaptive strategy attains the highest aggregate success rate and consistently strong safety--performance trade-offs without per-track tuning, improving robustness to environment variation while maintaining safety constraint satisfaction in nominal operation.

Hassan Jardali, Kai Yin, Lantao Liu

Luddy School of Informatics, Computing, and Engineering, Indiana University · Machine Learning Science, Expedia Group, Austin, TX 78758 USA

Nonlinear MPC Control Barrier Functions Autonomous Racing Constrained Optimization Mixed-Integer QP

Jul 1, 2026

FastBridge: Closing the Model-Based Realization Gap in Safety Filters on 3D Gaussian Splatting for Fast Quadrotor Flight

Fast quadrotor flight requires safe obstacle avoidance under tight onboard compute limits. While 3D Gaussian Splatting (3DGS) provides a continuous, geometry-aware scene representation for perception-driven navigation, existing 3DGS safety filters use reduced-order models such as single- and double-integrators that ignore actuator limits and assume commanded accelerations are realized instantaneously. Building on an analytic collision cone barrier for 3DGS, we introduce a nonlinear, actuator-aware safety filter enforced through the full quadrotor dynamics. We derive a high-relative-degree collision cone exponential CBF and a backup CBF that preserves QP feasibility under input constraints using a forward-simulated backup policy. Compared with a state-of-the-art 3DGS safety filter, our approach reduces trajectory jerk by 47% and runs 2.25 times faster. We validate the method in simulation and on hardware for real-time navigation in cluttered, perception-derived environments.

Tscholl Dario, Nakka Yashwanth Kumar, Gunter Brian

Collision Avoidance 3D Gaussian Splatting Control Barrier Functions Safe Robot Navigation Safety Filtering Quadrotor Control

Jul 1, 2026

Robust Operational Space Control with Conformal Disturbance Bounds for Safe Redundant Manipulation

Redundant robotic manipulators operating in constrained and human-interactive environments require accurate task-space tracking together with rigorous safety guarantees under dynamic uncertainties. Classical operational space computed torque controller (OSCTC) relies on accurate dynamic models and degrades in the presence of disturbances. In contrast, the data-driven paradigm of residual learning approximates disturbances as functions learned from full-state measurements, which are often noisy in practice, lack rigorous theoretical guarantees, and introduce additional design complexity. This paper proposes a robust OSCTC framework that integrates an extended state observer (ESO) with conformal prediction to combine model-based robustness and data-driven adaptability. The ESO estimates lumped disturbances directly in operational space without requiring full-state measurements as in residual learning, and a robust control barrier function (CBF) is constructed to enforce safety under uncertainty. However, robust CBFs require a known disturbance-variation bound to guarantee absolute safety, which often leads to conservatism in practice. To address this limitation, we further employ a sliding-window conformal prediction mechanism to estimate the bound online in a distribution-free manner, thereby achieving practical probabilistic safety guarantees. Experiments on a 7-DoF Franka Research 3 manipulator demonstrate millimeter-level tracking accuracy and real-time safe control at 1~kHz under various disturbances.

Wenhua Liu, Fan Zhang, Qin Lin

Department of Engineering Technology and the Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77004, USA.

Robotic Control Control Barrier Functions Robust Control Robotic Manipulation

Jun 27, 2026

HJ-SafeDMP: Hamilton-Jacobi Reachability-Guided Dynamic Movement Primitives for Provably Safe Robot Motion

Robots deployed in safety-critical environments must execute motions that are simultaneously robust to disturbances and provably safe from collisions. Dynamic Movement Primitives (DMPs) offer inherent stability, temporal flexibility, and efficient trajectory generalization from single demonstrations, but they lack formal safety certificates. Conversely, Hamilton-Jacobi (HJ) Reachability analysis provides a principled framework for computing worst-case safety margins and forward-invariant safe sets, but classical grid-based methods suffer from the curse of dimensionality and are impractical for real-time control. This paper introduces HJ-SafeDMP, a framework that integrates DMPs with learned HJ Reachability-based safety value functions to achieve provably safe, robust, and computationally efficient robot motion. We learn a Control Barrier Value Function (CBVF) from offline demonstration data using a model-free, finite-difference HJ recursion and deploy it as a real-time safety filter via a closed-form control law that modulates the DMP output. Unlike optimization-based CBF-QP approaches, our method achieves safety filtering without online quadratic program solves, preserving the computational efficiency of DMPs. We further incorporate an expectile-based offline learning objective that avoids querying out-of-distribution actions, and a conformal prediction calibration step that provides finite-sample probabilistic safety coverage. Experimental evaluation on a 7-DOF robot manipulator demonstrates that HJ-SafeDMP achieves formal safety guarantees with orders-of-magnitude faster execution than optimization-based baselines, while maintaining the robustness and adaptability of DMPs for human-robot interaction.

Siddhanth Ramesh, Ravi Prakash

Cyber-Physical Systems, Indian Institute of Science (IISc), Bengaluru.

Reachability Analysis Control Barrier Functions Robot Motion Generation Robot Safety Safe Motion Planning

Jun 23, 2026

Causality-Based Parametric Control Barrier Function for Safe Multi-Vehicle Interaction

Safe control has been widely studied in various safety-critical applications, for instance, autonomous driving. In order to ensure the autonomous vehicle does not collide with other vehicles, it is essential to obtain an accurate expectation of surrounding vehicles' behavior and react adaptively. Instead of assuming fully cooperative and homogeneous vehicles using the same safety-critical controllers, recent works have been exploring different data-driven approaches to model the neighboring vehicles' underlying controllers with observed data. However, existing works either suffer from 1) the inter-vehicle influence during the multi-vehicle interaction, which makes it hard to determine the causality of surrounding vehicles' behavior in controller modeling, or 2) being dominated by the worst-case analysis, which may lead to overly conservative behavior. In this paper, we extend the prior work on Parametric-Control Barrier Function (Parametric-CBF) to multi-robot interactions with embedded causality inference to explicitly reason over the inter-vehicle influence. Given the learned Causality-based Parametric-CBF, we present an adaptive safety-critical controller that allows the ego vehicle to safely react to surrounding vehicles with the learned expectation. We demonstrate that by leveraging the motion flexibility among multi-vehicle systems, task efficiency can be greatly improved in various interaction-intensive scenarios.

Yiwei Lyu, Caleb Chang, John M. Dolan

Department of Computer Science and Engineering, Texas A&M University, College Station, TX, 77845 USA · School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, 30332 USA · Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, 15213 USA

Collision Avoidance Safety-Critical Control Control Barrier Functions Autonomous Driving Multi-Agent Control

Jun 19, 2026

Conflict-Aware Switching for CBF-CLF-Based Multi-Goal Navigation

Quadratic programs (QPs) using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs) are widely used for safe control in reach-and-avoid navigation. However, the inherently conflicting nature of CBF and CLF constraints can lead to performance degradation, including slowdowns and deadlocks. This issue is exacerbated in multi-goal scenarios, where multiple nominal control objectives must be satisfied under shared safety constraints. Existing approaches for preemptive safety are often computationally expensive or overly conservative, while methods that relax or switch between nominal objectives are not well-suited for sequential goal-to-goal navigation. To address these limitations, we propose a conflict-aware switching strategy that detects high-conflict conditions and switches between available nominal control objectives to reduce constraint conflict. We apply this approach to multi-agent, multi-goal reach-and-avoid scenarios under CBF-CLF-QP control. Compared to a baseline sequential goal traversal strategy, our method reduces both completion time and timeout rates, demonstrating improved performance in satisfying all nominal control objectives while respecting safety constraints.

Rohan Walia, Kevin Leahy

Robotics Engineering Department, Worcester Polytechnic Institute, Worcester, MA 01609, USA

Robot Navigation Control Barrier Functions Multi-Agent Control Safe Robot Navigation

Jun 16, 2026

Memory-Efficient Meta-Reinforcement Learning for Adaptive Safety-Critical Control in Adversarial Spacecraft Proximity Operations

Autonomous spacecraft rendezvous and proximity operations (RPO) require controllers that guarantee safety under thrust constraints while minimizing fuel expenditure. Input-constrained control barrier functions (ICCBFs) provide a control method for nonlinear systems with actuation constraints that construct a forward-invariant safe set. Previous work has shown that learning class-

\mathcal{K}

functions defining the ICCBF recursion via meta reinforcement learning (meta-RL) yields a robust, non-greedy approach to safety-critical control in RPO. This paper extends that framework further by investigating the performance of three recurrent network architectures (Long Short Term Memory (LSTM), Gated Recurrent Unit (GRU), Selective State Space Model (Mamba)) and two training algorithms (Proximal Policy Optimization (PPO) and Soft Actor Critic (SAC)) to identify the best setup for tuning ICCBF class-K functions via meta-RL. In addition to cooperative test cases, performance is evaluated in the presence of adversarial behavior where the target spacecraft behaves in a way that worsens the safety of the chaser spacecraft. Results indicate that state space models such as Mamba when used with PPO achieve superior task completion, safety, and fuel-savings compared to other architectures, across all cooperative and uncooperative scenarios tested.

Alejandro Posadas-Nava, Richard Linares, Minduli Wijayatunga

Researcher, AeroAstro, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139-4307. · Associate Professor and Rockwell International Career Development Professor, AeroAstro, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139-4307. · Assistant Professor, Department of Aerospace Engineering, University of Illinois, Urbana-Champaign, 104 S Wright St, Urbana, IL 61801.

Spacecraft Rendezvous and Proximity Operations Control Barrier Functions Meta-Reinforcement Learning Safe RL State Space Models

Jun 13, 2026

Robust Conformal CBF and CLF Controllers via Iterative Policy Updates

Conformal prediction (CP) has been used to obtain probabilistic bounds on the error between a learned dynamics model and the true but unknown system. Such CP bounds can then be embedded into robust control Lyapunov function (CLF) and control barrier function (CBF) frameworks. However, such an approach does not retain stability/safety guarantees because of the distribution shift between the closed-loop trajectory distribution under the deployed CLF/CBF policy and the trajectory distribution from which the CP bound and its guarantees were derived. To address this issue, we propose an episodic framework that iteratively updates the robust conformal CLF/CBF policy while maintaining stability/safety guarantees across episodes. We achieve this by (1) using adversarially robust conformal prediction, and (2) quantifying a distribution shift budget that allows us to control how much the model error can increase across policy updates. This distribution shift budget is derived via a closed-loop trajectory sensitivity analysis, yielding an implicit and an explicit update rule for the CP bound. We analyze convergence of our algorithm, which we demonstrate on three case studies. To the best of our knowledge, these are the first results that provide stability/safety guarantees for robust conformal CBF/CLF policies.

Omid Mirzaeedodangeh, Eliot Shekhtman, Nikolai Matni +1

1Automatic Control Laboratory, ETH Zürich, Switzerland. · 2Computer and Information Science, University of Pennsylvania, USA. · 3Electrical and Systems Engineering, University of Pennsylvania, USA.

Distribution Shift Robustness Lyapunov-Based Control Control Barrier Functions Conformal Prediction Robust Control

Jun 11, 2026

Embedding ISO 10218 Safety Compliance in Robots via Control Barrier Functions for Human-Robot Collaboration

Human-Robot Collaboration (HRC) requires strict adherence to safety standards, such as ISO 10218, to prevent harmful interactions. Standard Speed and Separation Monitoring (SSM) filters calculate safe robotic speeds based on conservative assumptions, such as constant human velocity, which prevents accurate predictions of minimum separation distances and causes unnecessary operational halts. This paper proposes a Control Barrier Function (CBF) that explicitly incorporates human acceleration data to analytically forward-predict the minimum human-robot separation distance during a worst-case robotic stopping trajectory. To guarantee safety at the control level, this predictive CBF is integrated as an inequality constraint within a Sequential Quadratic Programming (SQP) framework. Specifically, two methods are proposed: Method I, a CBF-constrained PD safety filter; and Method II, a task-scaling SQP controller that enforces a spatial tube constraint. Simulated and real-world experiments on a UR10e robot evaluate the two proposed methods against a standard industrial SSM module baseline. Results demonstrate that Method II dynamically modulates execution speed and confines spatial deviations. Compared to Method I, Method II achieves a 63% reduction in mean trajectory error and avoids excessive evasive manoeuvres, ensuring high task throughput while complying with ISO 10218 SSM guidelines.

Federico Parma, Cesare Tonola, Nicola Pedrocchi +1

Dept. of Electrical and Information Engineering, Polytechnic of Bari, Italy · Dipartimento di Ingegneria Meccanica e Industriale, University of Brescia, Italy · Institute of Intelligent Industrial Technologies and Systems, National Research Council of Italy, STIIMA-CNR, Milan, Italy

Control Barrier Functions Robotics Robot Safety Human-Robot Collaboration

Jun 10, 2026

Individual Control Barrier Functions-Guided Diffusion Model for Safe Offline Multi-Agent Reinforcement Learning

Offline reinforcement learning allows control policies to be learned directly from data without online interaction, making it suitable for safety-critical tasks. Recent studies have applied diffusion models to offline reinforcement learning to leverage their strong capacity for modeling complex data distributions. However, existing approaches primarily focus on single-agent settings, leaving the safety challenges in multi-agent environments largely unexplored. In this work, we propose a safe offline multi-agent reinforcement learning algorithm that embeds neural individual control barrier functions into the diffusion model to enhance safety during trajectory generation, with control policies recovered through inverse dynamics. We evaluate our algorithm across diverse benchmarks, demonstrating substantial safety improvements while maintaining competitive rewards.

Qingyun Guo, Junyi Shi, Jianuo Huang +1

Department of Electrical Engineering and Automation, Aalto University, Espoo, Finland · School of Computing and Data Science, Xiamen University Malaysia, Sepang, Malaysia · Department of Computer Science, University of Toronto, Toronto, Canada

Control Barrier Functions Offline RL Safe RL Multi-Agent Reinforcement Learning Offline MARL

Jun 8, 2026

Who Earns the Safety? Intervention-Aware Quantum Predictive Control with Safety Attribution

Hard safety filters are increasingly placed downstream of learned controllers to guarantee constraint satisfaction at run time. Yet a filtered controller that never violates a constraint may still have learned nothing about safety: the filter can silently repair an incompetent upstream policy, so that post-filter success measures the filter, not the policy. We argue that safe policy learning should ask who earns the safety - the policy or its protective layers - and we make this question measurable. We introduce Intervention-Aware Variational Quantum Differentiable Predictive Control (IA-VQC-DPC), which (i) trains a compact variational quantum circuit (VQC) policy under a primal-dual intervention budget that penalizes reliance on a differentiable Control-Barrier-Function (CBF) projection, and (ii) is evaluated with a safety-attribution protocol that decomposes the executed-trajectory correction into a CBF term and a deployment runtime-guard term, and stress-tests the policy with guard-off evaluation. On closed-loop, high-fidelity BOPTEST building-control emulators (5 seeds, 60 episodes per method), intervention-aware training significantly lowers the quantum policy's raw pre-filter violation and total safety-layer reliance (both p < 10^-4) with no significant energy regression; at an equal approximately 400-parameter budget the quantum policy is significantly safer and more comfortable than a matched classical policy. Guard-off evaluation confirms the improvement is policy-level and exposes a valuable negative result: a learned differentiable energy head is only safe when paired with a distribution-aware runtime guard. The attribution protocol is general beyond quantum policies and buildings.

Yifan Wang

Department of Mechanical Engineering, McGill University Montréal, QC H3A 2T7, Canada

Safety-Critical Control Control Barrier Functions Building Energy Management Safety Filtering Model Predictive Control Variational Quantum Circuits

Jun 8, 2026

Safe Polytope-in-Polytope Motion Planning and Control with Control Barrier Functions

Autonomous mobile robots operating in tight environments require motion planning frameworks that account for the physical footprint of the robot. Simplifying the geometry to a point or a circle is conservative and discards information needed to successfully and safely traverse narrow passages. This work proposes a safe local motion planning and control method that guarantees that a polytopic robot footprint stays inside a continuously updated convex free-space region. The containment condition is formulated as a set of discrete-time control barrier function constraints within a model predictive controller. The number of safety constraints depends on the complexity of the local free-space geometry and the robot shape, instead of the number of obstacles. The proposed free-space formulation does not need any obstacle detection or segmentation. A comparative analysis against a polytope-based obstacle avoidance formulation confirms favorable scaling up to a reduction of 91

\times

in computation time as the number of obstacles increases. The approach is validated in simulation with an autonomous surface vehicle and on hardware with a non-holonomic mobile robot, using both occupancy grids and LiDAR sensing. The experiments demonstrate safe real-time motion planning and control at 10~Hz on an onboard embedded computer, including reactive avoidance of dynamic obstacles.

Alejandro Gonzalez-Garcia, Dries Dirckx, Jan Swevers +1

Constrained Motion Planning Control Barrier Functions Robot Safety Model Predictive Control Safe Motion Planning Motion Planning+2

Jun 3, 2026

Scenario Generation for Risk-Aware Reinforcement Learning with Probably Approximately Safe Guarantees

Guaranteeing safety is critical to the deployment of reinforcement learning (RL) agents in the real-world, especially as policies learned using deep RL may demonstrate susceptibility to transition perturbations that result in unknown or unsafe behaviour. A method of policy verification is to construct probabilistic barrier-certificates by sampling policy trajectories with respect to safety constraints, thereby demarcating known safe behaviour from unknown behaviour. Obtaining tight upper and lower bounds on the probability of violation of these constraints may be difficult if the policy is susceptible to transition uncertainty or perturbation that places the agent in insufficiently explored states. To address this, we approximate the distribution of the encountered state-space using a variational autoencoder (VAE) and construct upper and lower-bound barrier-certificates using latent characteristics of states to optimize for regions of known, safe behaviour with high confidence. We frame this in our work as a dual optimization problem where the lower-bound barrier-certificate presents a more conservative estimate of the safe region than the upper-bound barrier-certificate. Sampling states that lie within the set difference of the two during training, i.e. the non-robust region, allows us to tighten the upper and lower bounds to provide sharper probabilistic guarantees on safety. Within our study, we describe the guarantees placed and demonstrate the tightness of our bounds experimentally.

Mohit Prashant, Arvind Easwaran

Nanyang Technological University

Control Barrier Functions Risk-Sensitive RL Safe RL Robust RL

Jun 1, 2026

Embedding Semantic Risk into Distance Fields and CBFs for Online Monocular Safe Control

We propose an online monocular perception-to-control framework that embeds semantic risk into the distance field used by Control Barrier Function (CBF)-based safe navigation and teleoperation. Many perception-based safety filters assign the same distance-based safety margin to all mapped obstacles or use semantics only as a downstream controller adjustment, rather than encoding semantic risk in the spatial representation. Our framework instead reasons online about obstacle geometry and class-dependent risk by embedding semantic information directly into the Euclidean Signed Distance Field (ESDF). This design encodes semantic risk before control optimization, so high-risk objects exert a larger spatial influence in the safety field while retaining efficient ESDF queries at runtime. Specifically, a foundation-model-based SLAM front end reconstructs dense 3-D geometry from monocular RGB video, while per-frame semantic segmentation provides pixel-level class labels that are fused into the reconstructed geometry. The resulting geometric-semantic representation is then converted into an ESDF, where semantic labels identify safety-relevant regions and impose class-dependent inflation before field computation. The semantic-aware ESDF provides the local distance values and spatial derivatives required by the CBF controller, while class-dependent gains further regulate the controller response. Extensive simulation and hardware experiments demonstrate online operation at 10--20 Hz and semantic-aware safe behavior in both teleoperation and autonomous navigation.

Dawei Zhang, Nuo Chen, Shuo Liu +2

Division of Systems Engineering, Boston University, United States · Department of Electrical and Computer Engineering at Texas A&M University, United States · Department of Mechanical Engineering, Boston University, United States

Signed Distance Functions Control Barrier Functions Safe Robot Navigation

Jun 1, 2026

Spatio-Temporal Reconnection for Multi-Robot Networks using Adaptive Prescribed-Time CBFs

In multi-robot systems, maintaining persistent communication graph connectivity is often overly restrictive, especially when robots have limited communication ranges but operate in large environments. Instead, allowing robots to temporarily disconnect and later reconnect is often more desirable for efficient task execution while still ensuring timely information sharing across the team. In this paper, we propose an adaptive prescribed-time control barrier function (adaptive PT-CBF) framework that enables robots to temporarily disconnect and re-enter the communication range within an adjustable and feasible prescribed time. Moreover, we introduce a reconnection triggering mechanism that jointly considers task execution and reconnection urgency, thereby providing a principled way to decide when reconnection should occur. Theoretical analysis justifies convergence to the satisfying reconnection within a prescribed finite time. Experimental results validate the performance of our proposed adaptive PT-CBF with improved task efficiency and satisfying reconnections.

Hao Liu, Yupeng Yang, Yanze Zhang +1

Department of Computer Science, University of Illinois Chicago, Chicago, IL 60607, USA · Department of Computer Science, University of North Carolina at Charlotte, Charlotte, NC 28223, USA

Multi-Robot Systems Control Barrier Functions Multi-Robot Coordination Feedback Control Multi-Agent Communication

May 31, 2026

Robust Integrated Planning and Control for Quadrotors in Dynamic Environments via NMPC with CBF Penalties

This paper presents a new robust integrated planning and control (IPC) strategy for multirotor uncrewed aerial vehicles. We propose a nonlinear model predictive control (NMPC) formulation that embeds control barrier functions (CBFs) as exponential penalties, improving feasibility while ensuring smooth obstacle avoidance under tight input bounds. The penalty weights provide a practical tuning knob to trade off tracking accuracy against avoidance aggressiveness. We enhance the system robustness by employing a high-gain disturbance observer (HGDO) to estimate and compensate for external disturbances. We also incorporate a Kalman filter (KF) for computationally efficient, real-time prediction of obstacle motion, enabling avoidance of moving obstacles. Comparative studies against both conventional NMPC and NMPC with hard CBF constraints, validated in Gazebo and hardware experiments, demonstrate superior feasibility, safety, and robustness. To the best of our knowledge, this is the first hardware-validated NMPC-CBF IPC framework, offering a practical step toward safe quadrotor deployment in dynamic environments.

Zeinab Shayan, Mohammadreza Izadi, Reza Faieghi

Autonomous Vehicles Laboratory, Department of Aerospace Engineering, Toronto Metropolitan University, Toronto, Canada.

Nonlinear MPC Control Barrier Functions Robust Control Quadrotor Control Dynamic Obstacle Avoidance

May 29, 2026

Predicted-Flow Control Barrier Functions for Real-Time Safe Optimal Control

Control barrier functions (CBFs) provide real-time safety guarantees through pointwise conditions on the state. However, synthesizing a valid CBF is difficult and the resulting controllers are myopic. To address myopia, this article introduces predicted-flow control barrier functions (P-CBFs), which generalize the CBF from a function of the current state to a functional of a predicted flow under a parametrized control plan over a finite prediction horizon. For safety, a P-CBF can certify that the predicted flow is in a safe set over the entire prediction horizon. However, candidate P-CBFs suffer from the same challenge as candidate CBFs, namely, control constraints make it difficult to guarantee that the P-CBF is valid. This article resolves this challenge by introducing a terminal candidate P-CBF requiring that the predicted flow end in a backup safe set at the terminal time, and a planning-time shift that modulates the prediction horizon, providing an additional degree of freedom to ensure feasibility. The real-time control and the evolution of the control-plan parameter and planning-time shift are determined jointly by a single convex optimization that is guaranteed to be feasible and renders the associated safe set forward invariant. The resulting safe optimal flow control provides a safety certificate over the entire prediction horizon and unifies finite-horizon integral-cost optimization with safety certification. This optimization reduces to a quadratic program (QP) if the control constraints are a convex polytope. The QP implementation, termed FlowBarrier, is validated on a nonholonomic ground robot navigating a dense environment. FlowBarrier is compared to nonlinear model predictive control and two CBF-based safety filter methods across 100 trials, where FlowBarrier achieves the highest goal-reaching rate, zero safety violations, and the lowest computation time.

Amirsaeid Safari, Jesse B. Hoagg

Department of Mechanical and Aerospace Engineering, University of Kentucky, Lexington, KY 40506 USA

Safety-Critical Control Control Barrier Functions Safe Motion Planning Optimal Control

May 29, 2026

Geometry-Aware Control Barrier Functions for Collision Avoidance via Bernstein Polynomial Approximations

Safe navigation often relies on well-defined conditions based on the shape of robots and obstacles, and can be challenging when they have irregular geometries. While Control Barrier Functions (CBFs) offer an efficient mechanism to enforce safe set forward invariance, common shape surrogates (e.g., spheres or super-ellipsoids) either are overly conservative in unstructured scenes or require many local primitives, which inflates constraint counts and degrades real-time performance. In this paper, we introduce a novel geometry-aware Control Barrier Function (CBF) based on Bernstein-Polynomial Signed Distance Fields (BP-SDFs). It provides a unified way to represent the obstacles and robots, so as to represent the barrier function with a unified minimum distance. Benefiting from the differentiability of the Bernstein polynomials, one can easily enforce the control constraints in a closed loop. We validate the method's efficiency and performance to guarantee safety in single-robot navigation and heterogeneous multi-robot collision avoidance via simulations under different environments.

Siwon Jo, Yanze Zhang, Yupeng Yang +1

GRASP Laboratory, University of Pennsylvania, Philadelphia, PA, USA · Department of Computer Science, University of Illinois Chicago, Chicago, IL, USA · Department of Computer Science, University of North Carolina at Charlotte, Charlotte, NC, USA

Multi-Robot Motion Planning Signed Distance Functions Control Barrier Functions Safe Robot Navigation Robot Safety Robot Collision Avoidance

May 27, 2026

Safety-Critical Adaptive Impedance Control via Nonsmooth Control Barrier Functions under State and Input Constraints

Safe physical interaction is critical for deploying robotic manipulators in human-robot interaction and contact-rich tasks, where uncertainty, external forces, and actuator limitations can compromise both performance and safety. We propose an online adaptive impedance control framework that enforces joint-state safety while achieving compliant interaction under uncertain dynamics. The approach combines a quadratic-program-based safety filter with a novel composed position-velocity non-smooth control barrier function (NCBF), enabling joint position and velocity constraints to be enforced through a unified relative-degree-one barrier. Unknown dynamics are compensated online using an interval type-2 fuzzy logic system, while actuator torque limits are handled through soft constraints with exact penalty recovery of feasible solutions. A disturbance-observer-enhanced safety mechanism improves robustness against modelling errors and external interaction forces. Using composite Lyapunov analysis, we prove forward invariance of the safe set and the uniform ultimately boundedness of the impedance-tracking error. Simulations on a 7-DOF manipulator with severe parametric uncertainty and external interaction wrenches demonstrate safe constraint satisfaction and robust impedance tracking.

Faisal Lawan, Xiaoran Han, Joaquin Carrasco +2

Department of Electrical and Electronic Engineering, The University of Manchester, M13 9PL, United Kingdom

Control Barrier Functions Robust Control Impedance Control Adaptive Control

May 26, 2026

Credibility-Aware Learning and Control for Safe USV Navigation under Perception Uncertainty

Safe navigation for Unmanned Surface Vehicles (USVs) under the International Regulations for Preventing Collisions at Sea (COLREGs) remains challenging in dynamic maritime environments, especially when perception uncertainty is miscalibrated. Errors in state estimation can produce unreliable belief states that mislead value learning, while logic based on discrete traffic rules can cause abrupt action corrections. To address these challenges, we integrate Credibility-Weighted Value Learning (CWVL) with Covariance- and Recovery-Aware Control Barrier Function Quadratic Programming (CoReCBF-QP). CWVL derives a dynamic trust factor from the discrepancy between the covariance estimated by the filter and empirical error statistics. This factor modulates the critic's heteroscedastic loss and limits overfitting to miscalibrated observations. CoReCBF expands the collision geometry according to uncertainty and incorporates terms for braking and turning recovery. The resulting hyperbolic safety boundary preserves feasible avoidance velocities and supplies the QP safety constraint. A continuous COLREGs-aware reference in the objective promotes starboard maneuvers in Rule 14 head-on and Rule 15 give-way crossing encounters. Simulations show improved robustness in collision avoidance and COLREGs event compliance, achieving an 82.0% success rate with ten target ships beyond the training range.

Yuhang Zhang, Shuqi Chai, Yukang Zhang +5

School of Information Engineering, Henan University of Science and Technology, Luoyang 471023, China · Shenzhen Research Institute of Big Data, Shenzhen 518172, China · Chinese University of Hong Kong, Shenzhen, Shenzhen 518172, China +5

Collision Avoidance Robot Navigation Control Barrier Functions Safe RL Robust RL Robot Collision Avoidance

May 26, 2026

Robust Koopman Control Barrier Filters for Safe Actor-Critic Reinforcement Learning

Safe reinforcement learning (RL) for robotic systems requires policies that improve task performance while satisfying state and input constraints during both training and deployment. Control barrier functions (CBFs) provide a principled mechanism for enforcing forward invariance through minimally invasive safety filters, but their use in model-free RL is limited by the need for accurate dynamics and hand-designed barrier certificates. We propose Robust Koopman-CBF SAC, a safety-filtered actor--critic framework that learns a finite-dimensional Koopman predictor from data, constructs affine CBF constraints in the lifted space, and enforces them through a quadratic-program safety layer. To account for finite-dimensional Koopman approximation error, the CBF condition is tightened using a projected residual margin estimated from held-out rollout data. The critic is trained on the executed safe action, while the actor is regularized toward the Koopman-CBF feasible set, reducing dependence on the filter over training. Across safe-control benchmarks, the method achieves zero constraint violations on CartPole stabilization and tracking while matching or exceeding unconstrained SAC returns. On high-dimensional Safety Gymnasium locomotion tasks, the method reduces violations in some settings but also exposes important limitations of first-order velocity barriers and linear EDMD models, motivating high-order and multi-step Koopman-CBF extensions. These results suggest that robust Koopman-CBF filters are a promising bridge between model-free RL and certifiable safety, while clarifying the structural conditions under which such filters remain effective.

Dhruv S. Kushwaha, Zoleikha A. Biron

Koopman Operator Learning Control Barrier Functions Safety Filtering Safe RL Robust RL

May 25, 2026

Safety-Critical Whole-Body Control for Humanoid Robots via Input-to-State Safe Control Barrier Functions

Safety-critical control is essential for humanoid robots operating in complex human-centered environments, where physical safety constraints such as joint limits, self-collision avoidance, obstacle avoidance, and workspace boundaries must be satisfied during real-robot operation. However, existing approaches remain limited because kinematic safety guarantees can be degraded in the presence of unknown disturbances, such as model uncertainties, trajectory-tracking errors, and external perturbations. This paper presents a hierarchical safety-critical whole-body control framework for humanoid robots based on input-to-state safe control barrier functions (ISSf-CBFs). The proposed architecture integrates a kinematic-level whole-body controller (KinWBC), an ISSf-CBF safety filter, and a dynamic-level whole-body controller (DynWBC). KinWBC generates nominal joint-motion references from prioritized tasks; the ISSf-CBF filter minimally modifies these references to satisfy kinematic safety constraints under bounded disturbances; and DynWBC tracks the filtered references while enforcing full-body dynamic feasibility and contact stability. Safety constraints are imposed on a whole-body kinematic model, and the ISSf-CBF parameters are conservatively tuned so that the resulting kinematic safety guarantees can be transferred to full-order humanoid dynamics under unknown disturbances. Simulation and real-robot experiments demonstrate that the proposed framework improves safety margins under model mismatch and reliably enforces multiple safety constraints in real time during locomotion, teleoperation, and single-leg balancing with hand control. Project website: https://kwlee365.github.io/SafeWBC-Website/

Kwanwoo Lee, Sanghyuk Park, Gyeongjae Park +2

Department of Intelligence and Information, Seoul National University, Republic of Korea · Robotics Lab, Hyundai Motor Group, Republic of Korea · Advanced Institute of Convergence Technology, Republic of Korea +1

Safety-Critical Control Control Barrier Functions Humanoid Robot Control Robust Control Whole-Body Control Robot Safety

May 24, 2026

Latent Q-Barrier Shielding for Safe In-Context Reinforcement Learning

Safe in-context reinforcement learning (ICRL) adapts online from interaction history without test-time parameter updates while controlling episode cost under a safety budget. Under out-of-distribution (OOD) deployment shifts, pretraining-only safe ICRL can give poor reward-safety tradeoffs because the remaining budget affects behavior only through frozen policy conditioning, not an explicit action-level check against predicted future cost. We propose a latent Q-Barrier shield that learns a context representation, latent dynamics, and an ensemble cost critic before deployment. Without parameter updates, the shield infers context from history and filters or softly reweights candidate actions using the remaining budget and predicted future cost. We prove a conditional, error-decomposed barrier-margin result: a Q-Barrier-satisfying action leaves the next latent-budget state with an approximately budget-safe continuation under the learned critic, up to Bellman and latent-prediction errors. Across five safe ICRL benchmarks, the shield improves deployment-time reward-safety tradeoffs over a strong safe-ICRL baseline: after a short context window, it achieves higher return in four of five benchmarks while matching or lowering average episode cost in all five.

Minjae Kwon, Amir Moeini, Shangtong Zhang +1

University of Virginia

Reinforcement Learning Control Barrier Functions In-Context RL Safe RL

May 21, 2026

Kernel-Based Safe Exploration in Deep Reinforcement Learning

Safety has been a major concern when deploying deep reinforcement learning algorithms in the real world. A promising direction that ensures that the learned policy does not visit unsafe regions is to learn a barrier function along with the policy. A barrier is a function from states to reals that assigns low values to the initial states, high values to the unsafe states, and decreases in expectation on each transition; such a function can be used to bound the probability of reaching unsafe states. Previous attempts learned a barrier function directly from exploration data, but this required either large amounts of data or restrictions on the system dynamics. In this paper, we show how kernel embeddings can be used to learn barrier functions during deep reinforcement learning for stochastic systems with unknown dynamics. Our algorithm, kernel-based safe exploration (KBSE), learns an optimal policy and a barrier simultaneously during exploration. The barriers are computed iteratively, represented as conditional mean embeddings, and provide better probabilistic safety guarantees with more exploration. The exploration algorithm uses the learned barrier functions to identify safety violations. In the case of violation, it intervenes to modify the unsafe action to a safe action, thereby ensuring that the exploration is restricted to actions that bound the probability of reaching unsafe states. We evaluate KBSE on several complex continuous control benchmarks. Experimental results establish our new algorithm to be suitable for synthesizing control policies that are probabilistically safe without degradation in reward accumulation.

Rupak Majumdar, Nikhil Singh, Sadegh Soudjani

Max Planck Institute for Software Systems, Germany

Control Barrier Functions RL Exploration Safe RL

May 20, 2026

Safe and Steerable Geometric Motion Policies for Robotic Dexterous Manipulation

Robotic dexterous manipulation requires continuously reconciling objectives and constraints defined on heterogeneous geometric spaces: a robot controlled on a

\mathbb{R}^7

configuration manifold may need to track end effector poses on

\mathrm{SE}(3)

while satisfying obstacle avoidance margins in

\mathbb{R}

. We present Safe Pullback Bundle Dynamical Systems (SafePBDS), a geometrically consistent framework that computes optimal, certifiably safe configuration manifold accelerations from objectives and safety requirements on arbitrary task manifolds. SafePBDS builds on prior work that combines predefined task manifold dynamical systems to produce autonomous motion. Its first innovation is a pullback control barrier function construction, which converts task manifold safety conditions into linear constraints on configuration manifold accelerations. The second innovation is a task manifold action interface that allows a high-level policy to inject low dimensional residual motions; zero input recovers the autonomous behavior, while safety is preserved under arbitrary inputs. This lets high-level policies efficiently steer exploration while leaving precise motion to the autonomous behavior. We validate SafePBDS in simulation and on a 23-DOF Franka Panda-Allegro Hand platform. On dexterous grasping, SafePBDS achieves a

92.5\%

success rate across 20 household objects and 120 trials. Using the action interface, the method can exclude any one of the four fingers during grasping via a one-dimensional action, achieving

94.4\%

3-finger grasp success across 3 objects and 36 trials. The efficient planning and safety guarantee of SafePBDS also enables the first model-based, fully actuated palm-down in-hand reorientation, exceeding

360^\circ

of yaw rotation in both directions under varying object weight and wrist motion. Demo video and details: https://tml.stanford.edu/safe-pbds

Albert Wu, Riccardo Bonalli, Thomas Lew +1

Computer Science Department, Stanford University, Stanford, CA 94305, USA. · Laboratory of Signals and Systems, University of Paris-Saclay, CNRS, CentraleSup´elec, France. · Toyota Research Institute, Los Altos, CA 94022, USA.

Robotic Control Constrained Motion Planning Robotic Grasping Dexterous Manipulation In-Hand Manipulation Control Barrier Functions+3

May 20, 2026

DiffCVaR: Reinforcement Learning for Risk Adaptation via Differentiable CVaR Barrier Functions

Planning through crowded environments under uncertain obstacle motions remains difficult, as stochastic interactions often induce overly conservative behavior or reduced efficiency. To address this challenge, we propose an end-to-end risk adaptation framework for crowd navigation under obstacle-motion uncertainty modeled by a Gaussian mixture model. The framework combines reinforcement learning~(RL) with a differentiable quadratic-program safety layer based on Conditional Value-at-Risk~(CVaR) barrier functions, jointly learning nominal control input, risk level, and safety margin and enforcing explicit probabilistic safety constraints. This design enables context-aware adaptation, promoting efficient behavior while invoking caution only when necessary. We conduct extensive evaluations in dynamic, uncertain, and crowded environments across varying obstacle densities and robot models, and further assess generalization under three out-of-distribution cases. Comparisons across optimization-based, RL-based, and integrated RL and optimization methods are provided, and the proposed method is shown to deliver the strongest overall performance in safety, efficiency, and generalization under uncertainty.

Xinyi Wang, Taekyung Kim, Bardh Hoxha +2

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

Control Barrier Functions Risk-Sensitive RL Safe RL Conditional Value-at-Risk Robot Collision Avoidance

May 20, 2026

Safety-Critical Control for Smoothed Implicit Contact Dynamics

Smoothed implicit contact dynamics enables gradient-based planning and control for contact-rich tasks without predefined mode sequences. However, safety-critical control remains challenging because implicit contact dynamics makes safety-filter design nontrivial. The smoothing parameter

κ

relaxes contact complementarity constraints, which makes the dynamics smooth but affects the contact force. This paper provides a safety-filtering framework for smoothed implicit contact dynamics. We first derive a discrete-time control barrier function (CBF) constraint using a first-order Taylor approximation of the implicitly defined contact force. We show that, although reducing

κ

can improve local force-approximation accuracy, the resulting closed-loop force-constraint violations can vary non-monotonically with

κ

. Motivated by this observation, we introduce boundary-focused rollouts that screen candidate

κ

values by comparing the predicted safety margin with the observed one-step under-prediction. We then robustly tighten the predicted CBF constraint with a fixed margin to account for residual force under-prediction. Simulations on four contact-rich systems show that the proposed method eliminates force violations observed under a standard CBF. Project website https://contact-cbf.github.io/

Haegu Lee, Yitaek Kim, Christoffer Sloth

The Maersk Mc-Kinney Moller Institute, University of Southern Denmark, Denmark

Dynamical Systems Contact-Rich Robotic Manipulation Safety-Critical Control Control Barrier Functions Safety Filtering

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