SC3BF: Shifted Collision Cone Control Barrier Function for Dynamic Obstacle Avoidance

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.

Control Barrier Functions (CBFs) can provide provable safety guarantees for dynamic systems. However, finding a valid CBF for a system of interest is often non-trivial, especially for systems with low computational resources, higher-order dynamics, and moving close to obstacles of complex shape. A common solution to this problem is to use a purely distance-based CBF. In this paper, we study Hyperplane CBFs (H-CBFs), where a hyperplane separates the agent from the obstacle. First, we note that the common distance-based CBF is a special case of an H-CBF where the hyperplane is a supporting hyperplane of the obstacle that is orthogonal to a line between the agent and the closest point of the obstacle. We then show that a less conservative CBF can be found by optimising over the orientation of the supporting hyperplane, in order to find the Least Restrictive Hyperplane CBF. This enables us to maintain the safety guarantees while allowing controls that are closer to the desired ones, especially when moving fast and passing close to obstacles. We illustrate the approach on a double integrator dynamical system with acceleration constraints, moving through a group of arbitrarily shaped static and moving obstacles, and show that the proposed approach reduces the average gap between desired and safe controls by an order of magnitude.

As the number of autonomous robots continues to grow, safety becomes increasingly important. Control barrier functions (CBFs) provide a theoretically grounded framework for ensuring safety, but existing design methods often face limitations in effectiveness, scalability, or interpretability, and may result in overly conservative safe sets. In this paper, we propose \emph{VertexCBF}, a framework for learning neural CBFs in a scalable, systematic, and explainable way. We approximate the stationary Hamilton--Jacobi value function using a neural network trained via a combination of physics-informed and sparsely supervised learning. By exploiting control-affine dynamics and a convex polytope control set, under which the Hamiltonian is maximized at the control vertices, we efficiently generate supervision points via GPU-parallel vertex-restricted tree search, while a residual architecture guarantees that the learned CBF is never larger than the specified constraint function. We evaluate the method on 15 systems and compare it against relevant baselines, showing that it reliably recovers large safe sets where the baselines are conservative or fail completely. In addition, we perform a hardware experiment in which a mobile robot safely avoids pedestrians using a neural CBF trained with our method.