OcclusionCBF: Backup Control Barrier Functions for Safe Navigation Among Hidden Dynamic Obstacles
Authors: Taekyung Kim, Hun Kuk Park, Renya Wada, Nikolay Atanasov, Shumon Koga, Dimitra Panagou
Organizations: Department of Robotics, University of Michigan, Ann Arbor, MI 48109, USA · Department of Computer Science and Systems Engineering, Kobe University, Hyogo, Japan · Department of Electrical and Computer Engineering, University of California, San Diego, CA 92093, USA · Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109, USA
Robots navigating under occlusion may enter states from which no admissible input can avoid a dynamic obstacle once it becomes visible. We present OcclusionCBF, a safety filter that extends backup control barrier functions to reachable-occupancy predictions for potentially hidden dynamic obstacles in occluded regions. The method certifies a prescribed backup rollout against collision-inflated occupancy and a verified terminal set, yielding affine constraints for minimally invasive quadratic-program filtering. We establish recursive feasibility of the resulting safety filter, and collision avoidance for every hidden-obstacle motion covered by the occupancy prediction. Randomized benchmarks, MetaUrban simulations, and hardware experiments demonstrate improved task success over reactive and occlusion-aware predictive baselines with millisecond-scale computation.
Figures & tables
Fig. 1: Illustrative comparison of safety filtering with and without occlusion awareness for a double-integrator robot at a blind crossing. (a) A conventional CBF-QP considers only detected vehicles and follows the nominal command while the approaching vehicle remains occluded, reaching a state with insufficient control authority to avoid collision after detection. (b) OcclusionCBF propagates the admissible motion of potentially hidden vehicles, certifies a backup rollout against the resulting reachable occupancy, and minimally modifies the nominal input to slow down and increase clearance before entering the crossing.
Fig. 2: Geometric interpretation for one occluded region. (a) The occluded region is enclosed by O(j)(t) and inflated by rcol to H(j)(t,0) ; hjC(y,t,0) is constructed from its facet margins. (b) The occupancy expands with the look-ahead time s while the backup rollout remains outside it and reaches S0(t+T) with terminal clearance ρT .
Fig. 3: Representative successful OCBF-QP trial for the double integrator with Nobs=50 . The global view shows the completed waypoint route, while the local views show representative occlusion interactions and backup rollouts.
Fig. 4: Benchmark results over 100 paired trials for the double integrator (top) and unicycle (bottom) as Nobs increases. OCBF-QP attains the highest hard-constrained success rate at every tested density.
Fig. 5: High-fidelity simulation and hardware evaluations. (a) MetaUrban demonstrations for the unicycle (left) and double-integrator quadruped (right), with robot-view snapshots above and trajectories below. (b) Hardware blind crossing: the occlusion-agnostic CBF-QP collides after late detection, whereas OcclusionCBF intervenes before detection and reaches the goal.
Method
Unicycle ( Nobs )
Double integrator ( Nobs )
10
20
30
10
30
50
Control-Tree MPC [ 9 ]
48.3
54.2
58.9
106.7
110.7
117.0
Single-Hypothesis MPC
7.3
8.1
8.7
13.0
13.8
15.4
OA-MPC [ 2 ]
69.2
101.5
117.5
93.8
151.4
186.9
OACP [ 3 ]
80.5
76.9
78.5
87.4
89.4
88.8
CBF-QP [ 11 ]
0.7
0.7
0.8
0.6
0.7
0.8
TABLE I: Average controller computation time per update ( ms ).
Safety filters are an effective tool for enforcing constraints in safety-critical systems, but most existing methods assume perfect state information, which is rarely available in practice. Recent work has begun to close this gap by developing filtering mechanisms that are robust to state estimation error, but these methods can still exhibit safety violations or overly conservative behavior as estimation error grows. Focusing on obstacle avoidance, we develop two new control barrier function (CBF) formulations: drift-measurement-robust (DMR)-CBFs and neural measurement-robust (NMR)-CBFs. The DMR-CBF augments the standard CBF condition with an inner optimization over the worst-case uncertainty in the drift dynamics, improving robustness to estimation error. This DMR-CBF then supervises a pretraining phase for the NMR-CBF, which replaces the inner optimization with a learned term. The NMR-CBF is subsequently finetuned through differentiable trajectory rollouts, yielding a filter that achieves empirical safety comparable to the DMR-CBF while reducing both conservativeness and computational cost. We provide theoretical analysis of the DMR-CBF along with numerical results on a planar double integrator and a 12D quadrotor, where both proposed approaches prevent collisions while other robust methods either fail or are overly conservative. Finally, we deployed the NMR-CBF on a Unitree Go2, enabling successful navigation of an obstacle field under odometry errors that caused a standard CBF to collide.
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 of autonomous robots remains one of the core challenges in the field, especially in dynamic and uncertain environments. One prevalent approach is safety filtering based on control barrier functions (CBFs), which are easy to deploy but difficult to design. Motivated by the shortcomings of existing learning- and model-based methods, we propose a simple yet effective neural CBF design method for safe robot navigation in dynamic environments. We employ the idea of a composite CBF, where multiple neural CBFs are combined into a single CBF. Individual CBFs are trained using data generated offline via the Hamilton-Jacobi reachability framework to approximate the optimal safe set for single moving obstacles. Additionally, we use a residual neural architecture, ensuring that the estimated safe set does not intersect with the corresponding failure set. The method is extensively evaluated in simulation experiments for a ground robot and a quadrotor, comparing it against several baseline methods. The proposed method improves success rates by up to 18% over the strongest baseline, while maintaining comparable or lower path lengths and motion times. The method is also demonstrated in hardware experiments for both types of robots.
Bojan Derajić, Sebastian Bernhard, Wolfgang Hönig
Technical University of Berlin, Germany · AUMOVIO, Germany · Robotics Institute Germany (RIG), Germany