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.

Abstract--This study proposes a hybrid safety verification framework for closed-loop multi-agent systems under bounded stochastic disturbances. The proposed approach augments control barrier functions with a novel ψ-weighted formulation that encodes directional control alignment between agents into the safety constraints. Deterministic admissibility is combined with empirical validation via Monte Carlo rollouts, and a PAC-style guarantee is derived based on margin-aware safety violations to provide a probabilistic safety certificate. The results from the experiments conducted under different bounded stochastic disturbances validate the feasibility of the proposed approach. Safety within multi-agent systems is essential for real-world applications such as autonomous driving [1], [2] and robotic swarm deployments in agriculture [3], [4], manufacturing [5], [6], and search and rescue operations [7], where agents must navigate safely through their environment.

We consider nonconvex obstacle avoidance where a robot described by nonlinear dynamics and a nonconvex shape has to avoid nonconvex obstacles. Obstacle avoidance is a fundamental problem in robotics and well studied in control. However, existing solutions are computationally expensive (e.g., model predictive controllers), neglect nonlinear dynamics (e.g., graph-based planners), use diffeomorphic transformations into convex domains (e.g., for star shapes), or are conservative due to convex overapproximations. The key challenge here is that the computation of the distance between the shapes of the robot and the obstacles is a nonconvex problem. We propose efficient computation of this distance via sampling-based distance functions. We quantify the sampling error and show that, for certain systems, such sampling-based distance functions are valid nonsmooth control barrier functions. We also study how to deal with disturbances on the robot dynamics in our setting. Finally, we illustrate our method on a robot navigation task involving an omnidirectional robot and nonconvex obstacles. We also analyze performance and computational efficiency of our controller as a function of the number of samples.

In this article, we present a centralized approach for the control of multiple unmanned aerial vehicles (UAVs) for landing on moving unmanned ground vehicles (UGVs) using control barrier functions (CBFs). The proposed control framework employs two kinds of CBFs to impose safety constraints on the UAVs' motion. The first class of CBFs (LCBF) is a three-dimensional exponentially decaying function centered above the landing platform, designed to safely and precisely land UAVs on the UGVs. The second set is a spherical CBF (SCBF), defined between every pair of UAVs, which avoids collisions between them. The LCBF is time-varying and adapts to the motions of the UGVs. In the proposed CBF approach, the control input from the UAV's nominal tracking controller designed to reach the landing platform is filtered to choose a minimally-deviating control input that ensures safety (as defined by the CBFs). As the control inputs of every UAV are shared in establishing multiple CBF constraints, we prove that the control inputs are shared without conflict in rendering the safe sets forward invariant. The performance of the control framework is validated through a simulated scenario involving three UAVs landing on three moving targets.

This paper presents an approach for navigation and control in unmapped environments under input and state constraints using a composite control barrier function (CBF). We consider the scenario where real-time perception feedback (e.g., LiDAR) is used online to construct a local CBF that models local state constraints (e.g., local safety constraints such as obstacles) in the a priori unmapped environment. The approach employs a soft-maximum function to synthesize a single time-varying CBF from the N most recently obtained local CBFs. Next, the input constraints are transformed into controller-state constraints through the use of control dynamics. Then, we use a soft-minimum function to compose the input constraints with the time-varying CBF that models the a priori unmapped environment. This composition yields a single relaxed CBF, which is used in a constrained optimization to obtain an optimal control that satisfies the state and input constraints. The approach is validated through simulations of a nonholonomic ground robot that is equipped with LiDAR and navigates an unmapped environment. The robot successfully navigates the environment while avoiding the a priori unmapped obstacles and satisfying both speed and input constraints.

This paper proposes a safe reinforcement learning filter (SRLF) to realize multicopter collision-free trajectory tracking with input disturbance. A novel robust control barrier function (RCBF) with its analysis techniques is introduced to avoid collisions with unknown disturbances during tracking. To ensure the system state remains within the safe set, the RCBF gain is designed in control action. A safety filter is introduced to transform unsafe reinforcement learning (RL) control inputs into safe ones, allowing RL training to proceed without explicitly considering safety constraints. The SRLF obtains rigorous guaranteed safe control action by solving a quadratic programming (QP) problem that incorporates forward invariance of RCBF and input saturation constraints. Both simulation and real-world experiments on multicopters demonstrate the effectiveness and excellent performance of SRLF in achieving collision-free tracking under input disturbances and saturation.

Safe control is of great importance in online decision making for robot learning through filtering out unsafe explorative actions [1, 2, 3, 4], guaranteeing safety during sim-to-real transfer in a hierarchical manner [5]. As an effective tool of safe control, control barrier functions (CBFs) have been studied for years on both verification and synthesis [6, 7, 8, 9, 10]. A valid CBF guarantees safety by ensuring the function values non-positive for any states along the safe trajectory, implicitly enforcing the non-trivial forward invariance that feasible control inputs always exist to maintain the following non-positive energy values once the state is safe. To ensure forward invariance, polynomial-based CBFs have been proposed based on hand-crafted parametric functions [11, 12, 13], which can be verified through algebraic geometry techniques like sum-of-squares (SOS) optimization [14, 15, 16]. However, polynomial-based CBFs cannot encode complicated safety constraints [17], and the generic parameterization of non-conservative safe control for various nonlinear dynamics and nonconvex safety specifications is needed. Neural network parameterized CBFs (neural CBFs) have shown promising results due to their powerful expressiveness in modeling complex dynamics with bounded control inputs [18, 19, 20, 21, 22]. But it is challenging to guarantee that the learned neural CBF is valid because of its poor mathematical interpretability. One way to ensure the safety/stability of the dynamic system is to learn neural barrier/Lyapunov certificates [23, 24, 25, 26, 27, 28], but it may be too conservative and cause false negatives if the formal verification only relies on a specific control policy [17, 29]. Recent works to directly verify the forward invariance of learned neural CBFs are based on SMT-based counterexample falsification [30, 31], mixed integer programming [32], Lipschitz neural networks [33], and CROWN-based linear bound propagation [34, 35, 36].

We consider a nonlinear control system modeled as an ordinary differential equation subject to disturbance, with a state feedback controller parameterized as a feedforward neural network. We propose a framework for training controllers with certified robust forward invariant polytopes, where any trajectory initialized inside the polytope remains within the polytope, regardless of the disturbance. First, we parameterize a family of lifted control systems in a higher dimensional space, where the original neural controlled system evolves on an invariant subspace of each lifted system. We use interval analysis and neural network verifiers to further construct a family of lifted embedding systems, carefully capturing the knowledge of this invariant subspace. If the vector field of any lifted embedding system satisfies a sign constraint at a single point, then a certain convex polytope of the original system is robustly forward invariant. Treating the neural network controller and the lifted system parameters as variables, we propose an algorithm to train controllers with certified forward invariant polytopes in the closed-loop control system. Through two examples, we demonstrate how the simplicity of the sign constraint allows our approach to scale with system dimension to over $50$ states, and outperform state-of-the-art Lyapunov-based sampling approaches in runtime.

Useful robot control algorithms should not only achieve performance objectives but also adhere to hard safety constraints. Control Barrier Functions (CBFs) have been developed to provably ensure system safety through forward invariance. However, they often unnecessarily sacrifice performance for safety since they are purely reactive. Receding horizon control (RHC), on the other hand, consider planned trajectories to account for the future evolution of a system. This work provides a new perspective on safety-critical control by introducing Forward Invariance in Trajectory Spaces (FITS). We lift the problem of safe RHC into the trajectory space and describe the evolution of planned trajectories as a controlled dynamical system. Safety constraints defined over states can be converted into sets in the trajectory space which we render forward invariant via a CBF framework. We derive an efficient quadratic program (QP) to synthesize trajectories that provably satisfy safety constraints. Our experiments support that FITS improves the adherence to safety specifications without sacrificing performance over alternative CBF and NMPC methods.

Deep reinforcement learning (DRL) has demonstrated impressive performance in many continuous control tasks. However, one major stumbling block to the real-world application of DRL is the lack of safety guarantees. Although DRL agents can statisfy the system safety in expectation through reward shaping, it is quite challenging to design the DRL agent to consistently meet hard constraints (e.g., safety specification) at every time step. On the other hand, existing works in the field of safe control provide guarantees on the persistent satisfaction of hard safety constraints. However, the explicit analytical system dynamics models are required in order to synthesize the safe control, and the dynamics models are typically not accessible in DRL settings. In this paper, we present a model-free safe control algorithm, implicit safe set algorithm, for synthesizing safeguards for DRL agents that will assure provable safety throughout training. The proposed algorithm synthesizes a safety index (also called the barrier certificate) and a subsequent safe control law only by querying a black-box dynamic function (e.g., a digital twin simulator). Moreover, we theoretically prove that the implicit safe set algorithm guarantees finite time convergence to the safe set and forward invariance for both continuous-time and discrete-time systems. We validate the proposed implicit safe set algorithm on the state-of-the-art safety benchmark Safety Gym, where the proposed method achieves zero safety violations and gains 95% 9% cumulative reward compared to state-of-the-art safe DRL methods.