collision-cone cbf synthesis

Designing high-order control barrier functions (CBFs) for complex nonlinear dynamical systems remains challenging, and conventional hyperplane-based approximations of unsafe regions often yield overly conservative control policies. To address this, we propose a unified optimization framework that jointly tunes CBF parameters and control inputs. Our key innovation is the “minimally restrictive hyperplane CBF,” which employs continuous parametrization and co-optimization to guarantee strict safety while maximizing control freedom. The method accommodates both static and dynamic obstacles and explicitly incorporates practical actuation constraints—such as acceleration limits. Evaluated on a double-integrator system, our approach significantly improves trajectory flexibility and obstacle avoidance robustness compared to baseline methods, achieving a superior trade-off between safety and performance.

Real-time collision-free control of general ellipsoidal agents in multi-agent systems remains challenging due to non-convex safety constraints and computational inefficiency. Method: This paper proposes a novel Control Barrier Function (CBF) framework grounded in hyperplane separation and dual cone theory. Its core innovation lies in explicitly embedding the separating hyperplane constraint into the CBF dynamics, enabling a single-layer convex optimization formulation—eliminating the need for conventional multi-stage or iterative optimization schemes. Contribution/Results: Theoretical analysis guarantees strict safety for arbitrarily shaped ellipsoids. Compared to state-of-the-art approaches, the method reduces computational latency significantly, achieving millisecond-level response times and 100% collision avoidance success rates in both high-dynamic simulations and real-world robotic experiments. It thus achieves a unique balance of real-time performance, geometric generality, and provable reliability.

To address real-time safe navigation under crowded and extreme conditions (e.g., space robotics), this paper proposes a Collision-Cone Control Barrier Function (CBF) grounded in the analytical geometry of 3D Gaussian lattices. The method constructs a forward collision cone to derive a continuous, closed-form, first-order CBF, enabling tight sensorimotor coupling. Unlike conventional distance-based CBFs, it triggers avoidance earlier, avoids high-order Lie derivatives, ensures control smoothness, and incurs low computational overhead; moreover, it natively supports Minkowski expansion for physical robot modeling. Evaluated on a synthetic 170k-point scene, the approach reduces planning latency to one-third of the baseline, significantly suppresses trajectory jitter, and maintains safety guarantees. This work establishes an efficient and robust safety-critical navigation paradigm for highly dynamic, resource-constrained environments.

Real-time trajectory generation for obstacle avoidance in dynamic environments suffers from reliance on explicit obstacle boundary representations, low computational efficiency, and suboptimal trajectories. Method: This paper proposes a real-time planning and control framework integrating Model Predictive Control (MPC) with discrete-time high-order Control Barrier Functions (DHOCBFs). It automatically generates convex polyhedral obstacle representations from grid maps—bypassing the need for prior geometric knowledge (e.g., explicit boundary equations)—and directly derives DHOCBFs to ensure safety for both convex and non-convex obstacles. Global optimality is further enforced via optimization-driven path planning. Contribution/Results: Experiments in tightly constrained dynamic scenarios demonstrate significant improvements in computational speed and trajectory feasibility compared to baseline CBF methods, while yielding shorter, safer, and dynamically feasible trajectories.

This work addresses the non-conservative collision avoidance problem between control-affine robotic systems and convex obstacles, formulating a differentiable Control Barrier Function (CBF) based on the minimum distance as the safety metric. The core challenge lies in the fact that the minimum distance is typically defined implicitly via optimization and is generally non-differentiable. To overcome this, we first introduce the class of strongly convex mappings, which rigorously guarantees the continuity and differentiability of the minimum distance. We then design an ordinary differential equation (ODE) derived from the Karush–Kuhn–Tucker (KKT) conditions to enable real-time analytical updates of both the minimum distance and its gradient. The framework supports heterogeneous convex set avoidance—e.g., ellipsoid–polyhedron interactions—and exact convex set algebraic operations without conservative approximations. In simulation, the method enables millisecond-scale quadratic programming (QP) solving for a quadrotor navigating a dense obstacle corridor, significantly improving safety guarantees and avoidance accuracy.

This work addresses the gap between theoretical safety guarantees and practical feasibility of Control Barrier Functions (CBFs) in real-world systems subject to input constraints, where implicit assumptions often render CBFs ineffective. By systematically distinguishing between candidate and valid CBFs, the study uncovers the true source of safety in passive systems and extends safety verification to non-passive systems. Integrating system dynamics, explicit input constraint modeling, and class-K function analysis, the authors establish precise conditions under which CBFs yield valid safety assurances in low-dimensional systems and derive actionable design principles for safe controllers. An accompanying interactive web platform visually illustrates the core mechanisms and common pitfalls, offering practitioners an intuitive guide for reliable deployment.

This work addresses the myopic nature of traditional Control Barrier Functions (CBFs) and their difficulty in simultaneously satisfying safety requirements and control constraints. The authors propose Predictive Flow Control Barrier Functions (P-CBF), which extend safety verification over the entire predicted trajectory by integrating a terminal backup safe set with a planning time-shift mechanism to jointly optimize both the control policy parameters and real-time inputs. By employing an adjustable prediction horizon, the method enables end-to-end trajectory safety certification while unifying finite-horizon cost optimization with safety guarantees. Under convex polyhedral control constraints, the resulting problem reduces to a quadratic program (QP), amenable to efficient real-time solution. Experimental results on nonholonomic ground robots in dense navigation scenarios demonstrate that the proposed FlowBarrier approach achieves the highest goal-reaching success rate, zero safety violations, and the lowest computation time across 100 trials.

This work addresses the challenge of maintaining safety in complex dynamic environments where traditional control barrier functions (CBFs) struggle to adapt in real time to sudden obstacles or environmental disturbances. The authors propose an online optimization framework that integrates Hamilton-Jacobi (HJ) reachability analysis with a warm-start mechanism to locally and incrementally refine unsafe or approximate CBFs, thereby adaptively updating the safety value function. This approach achieves, for the first time, online local reconstruction of safety certificates grounded in HJ reachability, ensuring monotonic improvement of safety during adaptation while supporting seamless deployment from simulation to physical hardware. Experimental validation on ground vehicles and quadrotor drones demonstrates the framework’s effectiveness in handling unexpected obstacles and unmodeled wind disturbances, offering both real-time performance and formal safety guarantees.

This work addresses autonomous obstacle avoidance in dynamic environments where perception is limited to local sensing. The authors propose an end-to-end hierarchical safety filtering framework that introduces the Poisson Safety Function (PSF) as a Control Barrier Function (CBF). Safety constraints are sequentially enforced at two stages—predicted trajectory and real-time velocity—to provide formal safety guarantees for full-order robotic systems. By integrating local point cloud mapping, multi-stage safety filtering, and full-order control, the approach significantly enhances both obstacle avoidance performance and robustness. Extensive experiments across multiple legged robot platforms and real-world dynamic scenarios demonstrate the method’s generality and superiority. Pareto analysis further confirms that it outperforms conventional single-stage safety filters by achieving a better trade-off between safety and motion performance.

This work addresses the inherent collision risk faced by forward-sensing robots operating in unknown environments, where unexplored regions lack geometric information. The authors propose a safety filter based on a dual-constrained Control Barrier Function (CBF) that guarantees safe motion for omnidirectional robots on incrementally built occupancy grid maps, simultaneously avoiding known obstacles and limiting entry into unexplored areas. The key innovation lies in the first closed-form derivation of a dual-constrained CBF directly from the signed distance field of occupancy grids. Integrated with adaptive gain scheduling and a minimal intervention strategy in velocity space, the approach is compatible with arbitrary nominal controllers—including learning-based methods—while remaining computationally efficient enough to run on resource-constrained platforms such as Raspberry Pi. Real-world experiments with a PX4 quadrotor demonstrated zero collisions across multiple indoor missions.