Safe control in unknown environments is a key challenge in mobile robotics. Control Barrier Functions (CBFs) provide a principled framework for guaranteeing safety constraint satisfaction. State-of-the-art CBF approaches assume either known environments with predefined obstacles, or rely only on obstacles currently within the robot's Field of View (FoV). However, practical robots in a priori unknown environments can observe their surroundings only partially, and therefore can violate safety due to limited FoV, sensor range, or occlusion. This paper incorporates the memory of previously observed obstacles of arbitrary shape that have left the robot's FoV into CBF-based safe control. In particular, we couple the Signed Distance Function (SDF)-based CBF formulation to an occupancy grid map built online during the system's operation. Furthermore, the lack of steering authority induced by the SDF gradient degeneracy when facing obstacles head-on is addressed by constructing a Gaussian pyramid of the SDF, yielding a multi-level CBF. The efficacy of the proposed approach is evaluated against memory unaware baselines in the CARLA simulator. Moreover, we demonstrate the generalizability of the proposed approach in real deployments on a small warehouse robot and a large, articulated frame steering autonomous wheel loader.
We present a dual-barrier control barrier function (CBF) safety filter for real-time, safety-critical velocity control of holonomic robots operating in incrementally built occupancy grid maps. As a robot explores an unknown environment, unmapped regions introduce irreducible uncertainty, since obstacle geometry beyond the explored frontier is unknown, making entry into such regions a source of collision risk, especially with front-facing sensors. To address this, we enforce two constraints: avoidance of mapped obstacles and restriction from unexplored regions. Both constraints are derived analytically from the occupancy grid's signed distance field, yielding a closed-form safety filter that requires only a small linear system solve per cycle. On resource-constrained platforms such as the Raspberry Pi, where SLAM and planning already consume significant compute, the low overhead of the proposed filter preserves resources. An adaptive gain schedule relaxes the frontier constraint in information-rich regions and tightens it in well-mapped areas, improving exploration efficiency while maintaining safety. The filter operates in velocity space as a minimally invasive correction and composes with arbitrary nominal controllers, including learning-based methods. Hardware flight experiments on a PX4-controlled quadrotor demonstrate zero collisions across multiple indoor runs.
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.
Safely navigating polytopic environments while respecting the dynamics, control, and exact geometry of the underlying system is a challenge in robotics. Control barrier functions (CBFs) synthesize safe control policies by rendering the safe set forward invariant, but many existing CBF-based methods approximate polytopes using conservative smooth shapes, such as spheres or ellipsoids, to obtain explicit differentiable distance functions. In this article, we propose an exact Signed Distance Function (SDF) formulation for a {\it polytopic} robot and {\it polytopic} obstacles and integrate it with nonsmooth CBFs. Leveraging Minkowski operations, the proposed method computes the exact SDF via companion convex programs in both the collision-free (positive-sign) and in-collision (negative-sign) cases. Furthermore, by exploiting the convenient geometric properties of 2D Minkowski operations and the optimality conditions of the two companion convex programs, we derive a unified analytical expression for the gradient of the exact SDF via sensitivity analysis. The exact rotational gradient further reveals a previously masked class of local minima induced by the coupling between geometry and nonholonomic kinematics. We demonstrate the effectiveness of the proposed framework through a pure-translation case and three scenarios with unicycle models involving recovery from an unsafe initialization and single- and multiple-obstacle avoidance. Comparisons with baseline methods highlight how the proposed framework enables non-conservative maneuvers and safety recovery.