eess.SYAug 20, 2026

Learning-Based Measurement-Robust Control Barrier Functions for Obstacle Avoidance under State Estimation Error

Authors: Nicholas Rober, Yixuan Jia, Jonathan P. How

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Abstract

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.

Figures & tables

Fig. 1 : Our approach (NMR-CBF) enables safe and performant obstacle avoidance despite state estimation error.
Fig. 2 : Results of trajectory rollouts show time to goal, safety rate, and timeout rate for each policy over a range of ε\varepsilon values. DMR-CBF and NMR-CBF are the only approaches that have no collisions and are not overly conservative.
Fig. 3 : Sample trajectories with ε=0.3\varepsilon=0.3 show R-CBF (0.2) and R-CBF-QP starting to fail more frequently.
CategoryApproachε=0.10\varepsilon=0.10ε=0.30\varepsilon=0.30
  TimeTimeoutUnsafeTimeTimeoutUnsafe
Non-robustNominal—0.0100.04.330.081.9
CBF4.500.00.14.500.017.7
Set-basedDuality CBF4.593.00.04.682.00.0
Point-basedR-CBF (0.2)4.500.00.04.510.015.5
R-CBF (1.0)4.540.00.04.540.03.8
TABLE I : Time-to-goal (s) and Timeout  / \,/\, Unsafe outcome rates (%) vs. noise parameter ε\varepsilon on the 12D quadrotor.
MethodPlanar DIQuadrotor
Nominal0.010.01
CBF0.260.47
R-CBF (0.2)0.260.51
R-CBF (1.0)0.310.59
R-CBF-QP0.300.54
Duality CBF2.7345.28
TABLE II : Per-step computation time (ms/step).
Fig. 4 : A Unitree Go2 in an experimental hardware space.
Fig. 5 : Hardware experiment comparing a standard CBF and NMR-CBF navigating obstacle field from similar initial conditions. The CBF does not account for state estimation error (artificially injected bias and odometry drift), resulting in collision with an obstacle. The NMR-CBF accounts for possible state estimation errors to avoid both obstacles.
Fig. 6 : Go2 trajectories with CBF and NMR-CBF safety filters from different initial conditions. For the CBF (top), the state estimates (dotted orange) show the CBF allows the true state (solid orange) to collide with Obstacle 1 (top left) and Obstacle 2 (top right) depending on the initial configuration. The NMR-CBF (bottom) accounts for possible error in the state estimate, keeping the true state safe.
 Collisions 
MethodObstacle 1Obstacle 2Safety rate
CBF127/10
NMR-CBF0010/10
TABLE III : Collisions and safety rate over 10 hardware trials per method. A collision is recorded when the ground-truth robot center crosses the keep-out boundary.

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