LBA-CBF: Rapidly Adaptive Safety Filters via Parallel Dynamics Inference

Maitham F. AL-Sunni; Timeea-Andreea Radu; Hassan Almubarak; Henry Z. Liao; Michael Görner; Francesco Maurelli; John M. Dolan

cs.ROOct 6, 2026

LBA-CBF: Rapidly Adaptive Safety Filters via Parallel Dynamics Inference

Authors: Maitham F. AL-Sunni, Timeea-Andreea Radu, Hassan Almubarak, Henry Z. Liao, Michael Görner, Francesco Maurelli, John M. Dolan

Organizations: Department of Electrical & Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, USA · School of Computer Science & Engineering, Constructor University, Bremen, Germany · Control & Instrumentation Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia · Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, USA

Abstract

Control barrier functions (CBFs) certify commands through an assumed dynamics model, so an abrupt, unmeasured regime change can undermine the certificate exactly when safety matters most. We present Look-Back Adaptive Control Barrier Functions (LBA-CBF), which rank a finite bank of candidate dynamics by recent prediction error over a short look-back window and enforce the high-order CBF condition against every model within a tolerance of the best, spanning best-fit adaptation to full-bank robust filtering. The dynamics may depend nonlinearly on the unknown parameters, and no switching model or continuously parameterized estimator is required. We prove that any feasible filtered input satisfies the true CBF condition whenever a safety-representative candidate is retained. In quadrotor simulation with abrupt wind reversals and an unknown payload, LBA-CBF is safe and reaches the goal from all random initial conditions, matching an oracle, while adaptive and robust baselines achieve 0-88% success. Banks of up to 250,000 models run inside the control loop, and Crazyflie 2.1 and F1TENTH experiments demonstrate adaptation to wind, payload release, and varying tire-road friction. Code, videos, and project details are available at: https://lla-control.github.io

Figures & tables

Fig. 1: Overview of the LBA-CBF framework. The look-back stage ranks candidate models by recent prediction error and retains a prediction-plausible set, while the look-ahead computes a control input satisfying the CBF constraints for every retained model.

Fig. 2: Ablation over bank size $M$ and window $W$ . (A) One-step prediction error (star indicates minimum). (B) Control rate vs. $M$ .

Method	Safe [%]	Reached [%]	Success [%]	$\Delta U$
Oracle CBF (truth)	$100$	$100$	$100$	$47.2$
LBA-CBF ( $\eta=0$ )	$100$	$100$	$100$	$42.6$
LBA-CBF ( $\eta=0.01$ )	$100$	$100$	$100$	$32.7$
LBA-CBF ( $\eta=0.05$ )	$100$	$100$	$100$	$31.6$
HO-RaCBF	$88$	$100$	$88$	$395.2$
$\mathcal{L}_{1}$ -AC + CBF	$69$	$92$	$62$	$61.1$

TABLE I: Quadrotor simulation, 26 random initial conditions per method. A success is both safe and reached.

\Delta U

is averaged over the 13 starts on which every method with a nonzero success rate succeeded; n/a otherwise.

\eta

is the plausible-set tolerance.

Fig. 3: Quadrotor simulation: all 26 trajectories per method, ordered as in Table I . The vehicle descends from the grey squares to the goal (star) through five gates of paired obstacles (grey discs, whose edge is $h=0$ ); the wind blows along the red arrows, $+x$ in the shaded bands and $-x$ in the white ones. (A) Oracle , (B) LBA-CBF , (C) HO-RaCBF , (D) $\mathcal{L}_{1}$ -AC , (E) DOB-CBF , (F) R-CBF , (G) Nominal CBF .

Method	Closest distance to an obstacle [ $\mathrm{cm}$ ]
Oracle CBF (truth)	$15.2$
LBA-CBF ( $\eta=0$ )	$16.7$
LBA-CBF ( $\eta=0.01$ )	$21.0$
LBA-CBF ( $\eta=0.05$ )	$26.7$

TABLE II: Effect of the plausible-set tolerance

\eta

: median closest approach to any obstacle over the all runs, each row flown from the same course and start.

Fig. 4: Crazyflie 2.1: LBA-CBF vs. Nominal CBF . (A) hover and (B) flight to a goal, both in wind; (C) hover with a swinging payload. Top: $xy$ trajectories, obstacle (grey disc), wind (red arrows), target (star). Bottom: barrier value $h(t)$ ; $h<0$ is a violation.

Fig. 5: Crazyflie 2.1 hardware setups for Experiments 1–3.

Panel of Figure 8 — Fig. 6: Experiment 1: nominal-model tracking (top left), LBA-CBF tracking (top right), and LBA-CBF ’s friction estimates and $P$ -step prediction error (bottom).

Panel of Figure 9 — Fig. 7: Experiment 2: nominal-model tracking (top left), LBA-CBF tracking (top right), and LBA-CBF ’s friction estimates and $P$ -step prediction error (bottom).

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Control barrier functions (CBF) are a popular safety filter to ensure safety for nonlinear dynamical systems. However, when the system is subject to uncertainties and disturbances, this requires the use of robust variants of CBFs, which can be difficult to construct and can be overly conservative, especially for high-dimensional systems under input constraints. In this work, we propose a new approach to solve these challenges by introducing Least-Effort Adversarial Potentials (LEAP), a certificate that quantifies the robustness of a given state against disturbances in terms of the effort required by the disturbance to cause failure. We show that LEAP is a CBF for the undisturbed system, but can also be used to construct a safety filter that is robust to disturbances whose cumulative effort is bounded. We propose a method for constructing LEAPs with on-policy deep reinforcement learning. Next, we demonstrate LEAPs in simulation on a variety of multi-agent systems with disturbances and uncertainties. Finally, hardware experiments on a quadruped and quadrotors validate that LEAPs are well suited to tackle the disturbances and uncertainties from real-world robotic systems.

Abstract

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