This article presents a systematic method for designing time-varying Control Barrier Functions (CBF) composed of a time-invariant component and multiple time-dependent components, leveraging structural properties of the system dynamics. The method involves the construction of a specific class of time-invariant CBFs that encode the system's dynamic capabilities with respect to a given constraint, and augments them subsequently with appropriately designed time-dependent transformations. While transformations uniformly varying the time-invariant CBF can be applied to arbitrary systems, transformations exploiting structural properties in the dynamics - equivariances in particular - enable the handling of a broader and more expressive class of time-varying constraints. The article shows how to leverage such properties in the design of time-varying CBFs. The proposed method decouples the design of time variations from the computationally expensive construction of the underlying CBFs, thereby providing a computationally attractive method to the design of time-varying CBFs. The method accounts for input constraints and under-actuation, and requires only qualitative knowledge on the time-variation of the constraints making it suitable to the application in uncertain environments.

XX 1 Disturbance Compensation for Safe Kinematic Control of Robotic Systems with Closed Architecture Fan Zhang 1,2, Jinfeng Chen 1, Joseph J. B. Mvogo Ahanda 3, Hanz Richter 4, Ge Lv 5, Bin Hu 1,2, Qin Lin 1,2 Abstract--In commercial robotic systems, it is common to encounter a closed inner-loop (low-level) torque controller that is not user-modifiable. However, the outer-loop controller, which sends kinematic commands such as position or velocity for the inner-loop controller to track, is typically exposed to users. In this work, we focus on the development of an easily integrated add-on at the outer-loop layer by combining disturbance rejection control and robust control barrier function for high-performance tracking and safe control of the whole dynamic system of an industrial manipulator . This is particularly beneficial when 1) the inner-loop controller is imperfect, unmodifiable, and uncertain; and 2) the dynamic model exhibits significant uncertainty. Stability analysis, formal safety guarantee proof, simulations, and hardware experiments with a PUMA robotic manipulator are presented. Our solution demonstrates superior performance in terms of simplicity of implementation, robustness, tracking precision, and safety compared to the state of the art. I. INTRODUCTION Robotic systems often employ hierarchical software design, stacking perception, decision-making, planning, and low-level control. Such modularity is particularly beneficial for troubleshooting and improving the reliability of robotic systems. For example, in the control block, a combination of a kinematic controller (outer-loop controller) and a dynamic controller (inner-loop controller) is commonly seen in various robots. However, because tuning the inner-loop controller requires expert knowledge, this component is typically not exposed to users due to product safety considerations, a practice referred to as closed architecture in the literature [1]-[4]. In other words, users are only allowed to design the kinematic controller, sending position or velocity for the inner-loop controller to track. Additionally, mechanical parts 1 The authors are with the Department of Engineering Technology, University of Houston, USA. Corresponding author: Qin Lin, qlin21@central.uh.edu 2 Fan Zhang is also with the Department of Electrical and Computer Engineering, University of Houston, USA 3 Joseph Jean Baptiste Mvogo Ahanda is with the Department of Biomedical Engineering, The University of Ebolowa, Cameroon 4 Hanz Richter is with the Department of Mechanical Engineering, Cleveland State University, USA 5 Ge Lv is with the Department of Mechanical Engineering, Clemson University, USA. This material is based upon work supported by the National Science Foundation under Grant Nos.

This paper presents a Spatiotemporal Tube (STT)-based control framework for differential-drive mobile robots with dynamic uncertainties and external disturbances, guaranteeing the satisfaction of Temporal Reach-Avoid-Stay (T-RAS) specifications. The approach employs circular STT, characterized by smoothly time-varying center and radius, to define dynamic safe corridors that guide the robot from the start region to the goal while avoiding obstacles. In particular, we first develop a sampling-based synthesis algorithm to construct a feasible STT that satisfies the prescribed timing and safety constraints with formal guarantees. To ensure that the robot remains confined within this tube, we then design analytically a closed-form, approximation-free control law. The resulting controller is computationally efficient, robust to disturbances and {model uncertainties}, and requires no model approximations or online optimization. The proposed framework is validated through simulation studies on a differential-drive robot and benchmarked against state-of-the-art methods, demonstrating superior robustness, accuracy, and computational efficiency.

In this paper, we present a novel theoretical framework for online adaptation of Control Barrier Function (CBF) parameters, i.e., of the class K functions included in the CBF condition, under input constraints. We introduce the concept of locally validated CBF parameters, which are adapted online to guarantee finite-horizon safety, based on conditions derived from Nagumo's theorem and tangent cone analysis. To identify these parameters online, we integrate a learning-based approach with an uncertainty-aware verification process that account for both epistemic and aleatoric uncertainties inherent in neural network predictions. Our method is demonstrated on a VTOL quadplane model during challenging transition and landing maneuvers, showcasing enhanced performance while maintaining safety.

Abstract-- Control Barrier Functions (CBFs) have emerged as efficient tools to address the safe navigation problem for robot applications. However, synthesizing informative and obstacle motion-aware CBFs online using real-time sensor data remains challenging, particularly in unknown and dynamic scenarios. Motived by this challenge, this paper aims to propose a novel Gaussian Process-based formulation of CBF, termed the Dynamic Log Gaussian Process Control Barrier Function (DLGP-CBF), to enable real-time construction of CBF which are both spatially informative and responsive to obstacle motion. Firstly, the DLGP-CBF leverages a logarithmic transformation of GP regression to generate smooth and informative barrier values and gradients, even in sparse-data regions. Secondly, by explicitly modeling the DLGP-CBF as a function of obstacle positions, the derived safety constraint integrates predicted obstacle velocities, allowing the controller to proactively respond to dynamic obstacles' motion. Simulation results demonstrate significant improvements in obstacle avoidance performance, including increased safety margins, smoother trajectories, and enhanced responsiveness compared to baseline methods.

We study the prescribed-time reach-avoid (PT-RA) control problem for nonlinear systems with unknown dynamics operating in environments with moving obstacles. Unlike robust or learning based Control Barrier Function (CBF) methods, the proposed framework requires neither online model learning nor uncertainty bound estimation. A CBF-based Quadratic Program (CBF-QP) is solved on a simple virtual system to generate a safe reference satisfying PT-RA conditions with respect to time-varying, tightened obstacle and goal sets. The true system is confined to a Virtual Confinement Zone (VCZ) around this reference using an approximation-free feedback law. This construction guarantees real-time safety and prescribed-time target reachability under unknown dynamics and dynamic constraints without explicit model identification or offline precomputation. Simulation results illustrate reliable dynamic obstacle avoidance and timely convergence to the target set.

Haptic shared control (HSC) is effective in teleoperation when full autonomy is limited by uncertainty or sensing constraints. However, autonomous control performance achieved by maximizing HSC strength is limited because the dynamics of the joystick and human arm affect the robot's behavior. We propose a cooperative framework coupling a joystick-independent autonomous controller with HSC. A control barrier function ignores joystick inputs within a safe region determined by the human operator in real-time, while HSC is engaged otherwise. A pilot experiment on simulated tasks with tele-operated underwater robot in virtual environment demonstrated improved accuracy and reduced required time over conventional HSC.

Latent safety filters extend Hamilton-Jacobi (HJ) reachability to operate on latent state representations and dynamics learned directly from high-dimensional observations, enabling safe visuo-motor control under hard-to-model constraints. However, existing methods implement "least-restrictive" filtering that discretely switch between nominal and safety policies, potentially undermining the task performance that makes modern visuomotor policies valuable. While reach-ability value functions can, in principle, be adapted to be control barrier functions (CBFs) for smooth optimization-based filtering, we theoretically and empirically show that current latent-space learning methods produce fundamentally incompatible value functions. We identify two sources of incompatibility: First, in HJ reachability, failures are encoded via a "margin function" in latent space, whose sign indicates whether or not a latent is in the constraint set. However, representing the margin function as a classifier yields saturated value functions that exhibit discontinuous jumps. We prove that the value function's Lipschitz constant scales linearly with the margin function's Lipschitz constant, revealing that smooth CBFs require smooth margins. Second, reinforcement learning (RL) approximations trained solely on safety policy data yield inaccurate value estimates for nominal policy actions, precisely where CBF filtering needs them. We propose the LatentCBF, which addresses both challenges through gradient penalties that lead to smooth margin functions without additional labeling, and a value-training procedure that mixes data from both nominal and safety policy distributions. Experiments on simulated benchmarks and hardware with a vision-based manipulation policy demonstrate that LatentCBF enables smooth safety filtering while doubling the task-completion rate over prior switching methods.

Neural Control Barrier Functions (NCBFs) have shown significant promise in enforcing safety constraints on nonlinear autonomous systems.

Runtime geofencing for ground vehicles is rapidly emerging as a critical technology for enforcing Operational Design Domains (ODDs). However, existing solutions struggle to reconcile high-fidelity learning with the structural requirements of verifiable control. We address this by introducing PCARNN-DCBF, a novel pipeline integrating a Physics-encoded Control-Affine Residual Neural Network with a preview-based Discrete Control Barrier Function. Unlike generic learned models, PCARNN explicitly preserves the control-affine structure of vehicle dynamics, ensuring the linearity required for reliable optimization. This enables the DCBF to enforce polygonal keep-in constraints via a real-time Quadratic Program (QP) that handles high relative degree and mitigates actuator saturation. Experiments in CARLA across electric and combustion platforms demonstrate that this structure-preserving approach significantly outperforms analytical and unstructured neural baselines.