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arxiv: 2511.19651 · v2 · submitted 2025-11-24 · 💻 cs.RO

Online Learning-Enhanced High Order Adaptive Safety Control

Lishuo Pan , Mattia Catellani , Thales C. Silva , Lorenzo Sabattini , Nora Ayanian This is my paper

Pith reviewed 2026-05-17 05:36 UTC · model grok-4.3

classification 💻 cs.RO
keywords control barrier functionsNeural ODEsadaptive safety controlhigh-order CBFquadrotorwind disturbancesonline learning
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The pith

A hybrid high-order adaptive CBF using Neural ODEs maintains formal safety for quadrotors by learning time-varying perturbations online.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper proposes combining high-order control barrier functions with online learning through Neural ODEs to adapt safety filters in real time when model uncertainties arise. Standard CBFs lose their formal guarantees if dynamics shift due to wind, payloads, or other disturbances, so the method compensates without sacrificing those guarantees. The authors test the hybrid controller on a 38 g nano quadrotor and report that it keeps a safe distance from obstacles despite 18 km/h wind. A sympathetic reader would care because many real robotic systems operate under imperfect or changing models where fixed safety filters fail. The approach therefore aims to bridge model-based safety certificates with practical adaptation.

Core claim

We propose an efficient yet flexible online learning-enhanced high-order adaptive control barrier function using Neural ODEs that improves the safety of a CBF controller on the fly even under complex time-varying model perturbations, as shown by deploying the hybrid controller on a 38 g nano quadrotor that maintains safe distance from an obstacle against 18 km/h wind.

What carries the argument

High-order adaptive control barrier function augmented by Neural ODEs that perform real-time identification and compensation of perturbations while retaining the underlying safety certificates.

If this is right

  • Formal safety certificates of the original high-order CBF remain valid while the system adapts to disturbances.
  • The controller can be deployed on resource-limited aerial platforms without requiring perfect a priori models.
  • Safety is enforced for systems whose dynamics have higher relative degree with respect to the barrier function.
  • Online learning occurs continuously, allowing the safety filter to track slowly or rapidly changing perturbations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same structure might apply to other mobile robots or manipulators that face comparable external disturbances.
  • Faster or more memory-efficient ODE architectures could be substituted if real-time constraints tighten on smaller platforms.
  • Combining the learned perturbation model with offline system identification might reduce the adaptation transient.

Load-bearing premise

The Neural ODE component accurately identifies and compensates for complex time-varying perturbations in real time without causing instability or temporary safety violations during the adaptation process.

What would settle it

Place the 38 g nano quadrotor under controlled 18 km/h wind while running the hybrid adaptive CBF controller and check whether it ever violates the prescribed safe distance from the obstacle or exhibits instability during learning.

Figures

Figures reproduced from arXiv: 2511.19651 by Lishuo Pan, Lorenzo Sabattini, Mattia Catellani, Nora Ayanian, Thales C. Silva.

Figure 1
Figure 1. Figure 1: A 38g nano quadrotor tracks a circular trajectory while keeping a safe distance from the obstacle, against an 18km/h wind. The safety is improved on-the-fly, i.e., the quadrotor moves further away from the obstacle after experiencing the wind once. Recently, studies have shown that aCBFs (specifically, resid￾ual learning approaches) are effective in improving the safety of a system under model perturbation… view at source ↗
Figure 2
Figure 2. Figure 2: The picture depicts the system overview of our NODE-HO-aCBF [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Qualitative result of our algorithms compared to baseline controllers [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Qualitative comparison between baseline HO-aCBF controller with [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The top views (first row) and the side views (second row) of [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Long exposure trajectory of the nano quadrotor, maintain the safety [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: hneg and Avg.sDist. of baselines and our controllers. The top of the bars denotes the median, while the ends of the error bars represent the 25th and 75th percentiles. The statistics are obtained from 10 trials. design, our controller is data-efficient and expressive, making it suitable for adapting complex, time-varying residuals online. We demonstrate its efficacy across three types of residuals in simul… view at source ↗
read the original abstract

Control barrier functions (CBFs) are an effective model-based tool to formally certify the safety of a system. With the growing complexity of modern control problems, CBFs have received increasing attention in both optimization-based and learning-based control communities as a safety filter, owing to their provable guarantees. However, success in transferring these guarantees to real-world systems is critically tied to model accuracy. For example, payloads or wind disturbances can significantly influence the dynamics of an aerial vehicle and invalidate the safety guarantee. In this work, we propose an efficient yet flexible online learning-enhanced high-order adaptive control barrier function using Neural ODEs. Our approach improves the safety of a CBF controller on the fly, even under complex time-varying model perturbations. In particular, we deploy our hybrid adaptive CBF controller on a 38g nano quadrotor, keeping a safe distance from the obstacle, against 18km/h wind.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes an online learning-enhanced high-order adaptive control barrier function (CBF) that incorporates Neural ODEs to compensate for complex time-varying model perturbations such as wind on aerial vehicles. The central claim is that this hybrid controller improves safety on the fly while preserving formal CBF safety certificates, with a hardware demonstration on a 38 g nano quadrotor that maintains safe distance from an obstacle under 18 km/h wind.

Significance. If the safety certificates are rigorously preserved during online adaptation, the work would contribute to bridging model-based safety filters with data-driven compensation for uncertain dynamics in robotics. The hardware deployment on a resource-constrained nano quadrotor provides a concrete test case, though stronger quantitative validation would be needed to establish practical impact beyond the specific experiment.

major comments (3)
  1. [Abstract] Abstract: The claim of successful hardware deployment is stated without quantitative metrics, error analysis, or an explicit derivation showing how the Neural ODE adaptation preserves the high-order CBF safety certificates (i.e., non-negativity of the CBF and its Lie derivatives) under the stated perturbations. This is load-bearing for the central claim of formal safety under learning.
  2. [Safety analysis] Safety analysis section (likely §4 or equivalent): The hybrid Neural-ODE + high-order adaptive CBF controller is asserted to maintain formal safety certificates while the Neural ODE identifies time-varying disturbances in real time. No explicit Lyapunov or invariance analysis is provided that bounds the transient learning error relative to the CBF relative degree and the 38 g quadrotor’s actuator limits, leaving open the possibility of temporary violations during the initial adaptation window under 18 km/h wind.
  3. [Method] Method/derivation (likely §3, Eq. for adaptive CBF): The reduction of the safety guarantee to the fitted Neural ODE parameters is not shown explicitly; without this step it is unclear whether the adaptation is defined in a manner that could be post-hoc fitted to satisfy the CBF conditions by construction rather than through independent verification.
minor comments (2)
  1. [Preliminaries] Notation for the high-order CBF Lie derivatives and the Neural ODE state augmentation should be clarified with explicit definitions to avoid ambiguity when combining the two frameworks.
  2. [Experiments] Figure captions for the hardware experiment should include quantitative performance metrics (e.g., minimum distance achieved, adaptation convergence time) rather than qualitative descriptions only.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The comments highlight important aspects of quantitative validation and the explicit linkage between the Neural ODE adaptation and the high-order CBF safety certificates. We address each major comment below and have revised the manuscript accordingly to improve clarity and rigor.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim of successful hardware deployment is stated without quantitative metrics, error analysis, or an explicit derivation showing how the Neural ODE adaptation preserves the high-order CBF safety certificates (i.e., non-negativity of the CBF and its Lie derivatives) under the stated perturbations. This is load-bearing for the central claim of formal safety under learning.

    Authors: We agree that the abstract would be strengthened by including key quantitative metrics and a reference to the safety preservation argument. In the revised manuscript, we have updated the abstract to report specific hardware results, including the minimum observed distance to the obstacle (maintained above the safety threshold) and the adaptation convergence time under 18 km/h wind. The explicit derivation showing that the Neural ODE adaptation preserves non-negativity of the CBF and its Lie derivatives is given in Section 4; we have added a cross-reference to this section in the abstract. revision: yes

  2. Referee: [Safety analysis] Safety analysis section (likely §4 or equivalent): The hybrid Neural-ODE + high-order adaptive CBF controller is asserted to maintain formal safety certificates while the Neural ODE identifies time-varying disturbances in real time. No explicit Lyapunov or invariance analysis is provided that bounds the transient learning error relative to the CBF relative degree and the 38 g quadrotor’s actuator limits, leaving open the possibility of temporary violations during the initial adaptation window under 18 km/h wind.

    Authors: This observation is fair. While the high-order CBF construction provides invariance once the adaptation has converged, the original manuscript did not include an explicit bound on the transient Neural ODE error relative to actuator limits. We have added a Lyapunov-based analysis in the safety section that derives an upper bound on the learning error during the initial adaptation phase, showing that this bound remains compatible with the relative degree and the 38 g quadrotor’s actuator saturation under the reported wind speed, thereby precluding temporary safety violations. revision: yes

  3. Referee: [Method] Method/derivation (likely §3, Eq. for adaptive CBF): The reduction of the safety guarantee to the fitted Neural ODE parameters is not shown explicitly; without this step it is unclear whether the adaptation is defined in a manner that could be post-hoc fitted to satisfy the CBF conditions by construction rather than through independent verification.

    Authors: We appreciate the request for an explicit reduction. In the revised Section 3 we have inserted a dedicated derivation step that reduces the high-order CBF safety condition directly to the online-adapted Neural ODE parameters. The adaptive law is constructed so that the CBF constraint is satisfied by design at every time step, independent of any post-hoc fitting; the Neural ODE output is substituted into the Lie derivative terms to enforce this property. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation rests on standard CBF theory plus independent Neural ODE adaptation

full rationale

The paper's core claim combines established high-order CBF safety certificates with Neural ODE online learning for disturbance compensation. No step reduces a formal guarantee to a fitted parameter by construction, nor does any load-bearing premise collapse to a self-citation or ansatz smuggled from prior author work. The hardware demonstration on the nano quadrotor is presented as empirical validation rather than a definitional prediction. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that CBF safety certificates remain valid when the dynamics are corrected by an online learner, plus the implicit assumption that Neural ODEs can be trained stably in closed loop without violating safety during learning.

axioms (1)
  • domain assumption Control barrier functions provide formal safety guarantees provided the system dynamics model is sufficiently accurate.
    Invoked implicitly when claiming that online adaptation restores the guarantee under perturbations.

pith-pipeline@v0.9.0 · 5462 in / 1263 out tokens · 74689 ms · 2026-05-17T05:36:58.969113+00:00 · methodology

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Reference graph

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