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arxiv: 2509.12516 · v2 · submitted 2025-09-15 · 💻 cs.RO

Zero to Autonomy in Real-Time: Online Adaptation of Dynamics in Unstructured Environments

William Ward , Sarah Etter , Jesse Quattrociocchi , Christian Ellis , Adam J. Thorpe , Ufuk Topcu This is my paper

Pith reviewed 2026-05-18 15:37 UTC · model grok-4.3

classification 💻 cs.RO
keywords online adaptationdynamics modelingrecursive least squaresfunction encodersrobot navigationunstructured environmentsreal-time learningodometry
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The pith

Robots adapt to new dynamics in seconds by updating function encoder coefficients with recursive least squares from streaming odometry.

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

The paper shows how autonomous robots can move from no prior knowledge to safe control in unstructured settings where terrain shifts suddenly, such as from dry ground to ice. It introduces an online adaptation technique that combines function encoders with recursive least squares, treating the encoder coefficients as latent states that are updated directly from incoming odometry measurements. This produces constant-time model updates without any gradient-based inner loops, allowing accurate dynamics estimates after only a few seconds of data. Tests on a Van der Pol system, a Unity off-road simulator, and a physical Clearpath Jackal robot demonstrate higher model accuracy and fewer collisions during planning than either static models or meta-learning baselines.

Core claim

Treating function encoder coefficients as latent states and updating them via recursive least squares from streaming odometry yields constant-time coefficient estimation. This produces stable, accurate dynamics models from only a few seconds of data, which in turn improve downstream planning and reduce collisions relative to static and meta-learning baselines across a Van der Pol oscillator, Unity simulator navigation tasks, and real-robot trials on ice.

What carries the argument

Function encoder coefficients treated as latent states and estimated in constant time by recursive least squares updates driven by streaming odometry.

If this is right

  • Constant-time updates remove the need for slow inner-loop optimization, enabling real-time response to dynamics shifts.
  • More accurate online models lead to safer trajectory planning in environments with sudden changes such as ice.
  • Adaptation from seconds of data allows recovery from zero-knowledge states without pre-collected datasets.
  • The same pipeline works across simulated oscillators, high-fidelity simulators, and physical robots.

Where Pith is reading between the lines

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

  • The latent-state treatment of encoder coefficients could be combined with other filtering methods for even faster convergence in noisy conditions.
  • Extending the approach to aerial or legged platforms would test whether the constant-time property holds when dynamics involve more degrees of freedom.
  • Integration with uncertainty-aware planners might further reduce collisions by explicitly accounting for estimation error during the first seconds of adaptation.

Load-bearing premise

Recursive least squares updates applied to function encoder coefficients will produce dynamics models stable and accurate enough to improve planning and reduce collisions when the robot encounters abrupt terrain changes.

What would settle it

Running the Clearpath Jackal on the ice rink terrain and finding no reduction in collisions or model accuracy relative to a static baseline would falsify the claim that the online adaptation improves performance.

Figures

Figures reproduced from arXiv: 2509.12516 by Adam J. Thorpe, Christian Ellis, Jesse Quattrociocchi, Sarah Etter, Ufuk Topcu, William Ward.

Figure 1
Figure 1. Figure 1: Our approach enables rapid adaptation of the dynamics model to [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Adaptation performance on the Van der Pol system as the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: At each time step, we compute the accumulated prediction error over [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FE-RLS adapts to abrupt changes in terrain dynamics, outperforming [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Representative examples of terrains in our dataset. We collect [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: We evaluate model predictions on real-world trajectories from four [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: We demonstrate adaptation on a challenging mixed-terrain envi [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: As the terrain switches between turf and ice, FE-RLS maintains [PITH_FULL_IMAGE:figures/full_fig_p007_9.png] view at source ↗
read the original abstract

Autonomous robots must go from zero prior knowledge to safe control within seconds to operate in unstructured environments. Abrupt terrain changes, such as a sudden transition to ice, create dynamics shifts that can destabilize planners unless the model adapts in real-time. We present a method for online adaptation that combines function encoders with recursive least squares, treating the function encoder coefficients as latent states updated from streaming odometry. This yields constant-time coefficient estimation without gradient-based inner-loop updates, enabling adaptation from only a few seconds of data. We evaluate our approach on a Van der Pol system to highlight algorithmic behavior, in a Unity simulator for high-fidelity off-road navigation, and on a Clearpath Jackal robot, including on a challenging terrain at a local ice rink. Across these settings, our method improves model accuracy and downstream planning, reducing collisions compared to static and meta-learning baselines.

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

2 major / 2 minor

Summary. The manuscript presents a method for online adaptation of robot dynamics models in unstructured environments. It combines function encoders with recursive least squares (RLS), treating the encoder coefficients as latent states that are updated in constant time from streaming odometry. This avoids gradient-based inner-loop optimization and enables adaptation from only a few seconds of data. The approach is evaluated on the Van der Pol oscillator to illustrate behavior, in a Unity simulator for high-fidelity off-road navigation, and on a Clearpath Jackal robot operating on challenging ice-rink terrain. Results claim improved model accuracy, better downstream planning performance, and reduced collisions relative to static and meta-learning baselines.

Significance. If the empirical results hold under the stated conditions, the work provides a computationally lightweight alternative to gradient-based meta-learning for real-time dynamics adaptation. The constant-time RLS update and multi-domain evaluation (simulation to hardware) address a practical gap in deploying robots under abrupt terrain changes. Explicit credit is due for the reproducible experimental protocol across three settings and the avoidance of inner-loop gradients.

major comments (2)
  1. [§4.3] §4.3 (Real-robot experiments on the Jackal): the reported collision reduction on ice is presented as evidence that RLS coefficient updates produce stable, accurate models sufficient for improved planning. However, the manuscript provides no analysis of persistent excitation of the regressor, sensitivity to the forgetting factor, or numerical stability under wheel-slip and abrupt friction changes. Without such checks or an ablation, it is difficult to attribute the performance gain specifically to the adaptation mechanism rather than implementation details or tuning.
  2. [§3] §3 (Method description): the claim that treating function-encoder coefficients as latent states and applying standard RLS yields reliable online adaptation rests on the usual RLS assumptions (persistent excitation, bounded noise). The paper does not supply a convergence bound or stability argument tailored to the robotics setting, which is load-bearing for the central claim that adaptation occurs safely within seconds in unstructured environments.
minor comments (2)
  1. The abstract states improvements 'across these settings' but does not include even a single quantitative summary statistic (e.g., mean collision count or model-error reduction). Adding one or two such numbers would strengthen the summary.
  2. [§3] Notation for the function-encoder basis and the RLS covariance update should be cross-referenced to the equations in §3 to avoid ambiguity when readers compare the method to standard RLS formulations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the presentation of our online adaptation method. We address each major point below and outline targeted revisions.

read point-by-point responses

  1. Referee: [§4.3] §4.3 (Real-robot experiments on the Jackal): the reported collision reduction on ice is presented as evidence that RLS coefficient updates produce stable, accurate models sufficient for improved planning. However, the manuscript provides no analysis of persistent excitation of the regressor, sensitivity to the forgetting factor, or numerical stability under wheel-slip and abrupt friction changes. Without such checks or an ablation, it is difficult to attribute the performance gain specifically to the adaptation mechanism rather than implementation details or tuning.

    Authors: We agree that additional analysis would strengthen attribution of gains to the adaptation mechanism. In revision we will add a discussion of persistent excitation using the Jackal's recorded trajectories, a sensitivity plot for the forgetting factor, and numerical stability observations (e.g., covariance conditioning) during wheel-slip events on ice. An ablation varying the forgetting factor will also be included to demonstrate robustness. revision: yes

  2. Referee: [§3] §3 (Method description): the claim that treating function-encoder coefficients as latent states and applying standard RLS yields reliable online adaptation rests on the usual RLS assumptions (persistent excitation, bounded noise). The paper does not supply a convergence bound or stability argument tailored to the robotics setting, which is load-bearing for the central claim that adaptation occurs safely within seconds in unstructured environments.

    Authors: We acknowledge that a custom convergence bound is absent. The method inherits standard RLS assumptions; we will revise §3 to state these assumptions explicitly and explain their satisfaction via the observed rapid adaptation in the Van der Pol, Unity, and hardware experiments. A brief paragraph will be added linking empirical convergence times to the robotics setting, with a note that a full theoretical analysis remains future work. revision: partial

Circularity Check

0 steps flagged

No circularity: standard RLS update on function-encoder coefficients is independent of target claims

full rationale

The paper's core derivation treats function-encoder coefficients as latent states and applies recursive least squares to streaming odometry for constant-time adaptation. This is a direct, standard application of RLS with no evidence that any prediction or result is obtained by construction from the inputs, no self-definitional loops, and no load-bearing self-citations that reduce the central claim to prior work by the same authors. Empirical evaluations on Van der Pol, Unity, and the Jackal robot compare against static and meta-learning baselines without the adaptation mechanism being tautological. The derivation chain 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 dynamics shifts can be captured by updating function encoder coefficients as latent states via recursive least squares from odometry alone.

axioms (1)
  • domain assumption Function encoder coefficients can be treated as latent states that are updated from streaming odometry without gradient-based inner-loop optimization.
    This is the core modeling choice that enables constant-time adaptation.

pith-pipeline@v0.9.0 · 5691 in / 1162 out tokens · 37971 ms · 2026-05-18T15:37:21.878296+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

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  1. Zero-Shot Function Encoder-Based Differentiable Predictive Control

    eess.SY 2025-11 unverdicted novelty 4.0

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Reference graph

Works this paper leans on

28 extracted references · 28 canonical work pages · cited by 1 Pith paper

  1. [1]

    SE3-Pose-Nets: Structured deep dynamics models for visuomotor control

    Arunkumar Byravan, Felix Leeb, Franziska Meier, and Dieter Fox. SE3-Pose-Nets: Structured deep dynamics models for visuomotor control. InInternational Confer- ence on Robotics and Automation, 2018

    work page 2018

  2. [2]

    Di- rect LiDAR-inertial odometry: Lightweight LIO with continuous-time motion correction.International Con- ference on Robotics and Automation, 2023

    Kenny Chen, Ryan Nemiroff, and Brett T Lopez. Di- rect LiDAR-inertial odometry: Lightweight LIO with continuous-time motion correction.International Con- ference on Robotics and Automation, 2023

    work page 2023

  3. [3]

    Neural ordinary differential equations.Advances in neural information processing systems, 2018

    Ricky TQ Chen, Yulia Rubanova, Jesse Bettencourt, and David K Duvenaud. Neural ordinary differential equations.Advances in neural information processing systems, 2018

    work page 2018

  4. [4]

    Online terrain estimation for autonomous vehicles on deformable terrains.Journal of Terrame- chanics, 91:11–22, 2020

    James Dallas, Kshitij Jain, Zheng Dong, Leonid Sapronov, Michael P Cole, Paramsothy Jayakumar, and Tulga Ersal. Online terrain estimation for autonomous vehicles on deformable terrains.Journal of Terrame- chanics, 91:11–22, 2020

    work page 2020

  5. [5]

    Autonomous drifting with 3 minutes of data via learned tire models

    Franck Djeumou, Jonathan YM Goh, Ufuk Topcu, and Avinash Balachandran. Autonomous drifting with 3 minutes of data via learned tire models. InInternational Conference on Robotics and Automation, 2023

    work page 2023

  6. [6]

    How to learn and generalize from three minutes of data: Physics- constrained and uncertainty-aware neural stochastic dif- ferential equations

    Franck Djeumou, Cyrus Neary, and Ufuk Topcu. How to learn and generalize from three minutes of data: Physics- constrained and uncertainty-aware neural stochastic dif- ferential equations. InConference on Robot Learning, 2023

    work page 2023

  7. [7]

    Vehicle- terrain parameter estimation for small-scale unmanned tracked vehicles

    Albert A Espinoza, Jorge L Torres-Filomeno, Karla M Monta˜nez-S´anchez, and ´Angel J Ortiz-And ´ujar. Vehicle- terrain parameter estimation for small-scale unmanned tracked vehicles. InInternational Symposium on Mea- surement and Control in Robotics, 2019

    work page 2019

  8. [8]

    Model- agnostic meta-learning for fast adaptation of deep net- works

    Chelsea Finn, Pieter Abbeel, and Sergey Levine. Model- agnostic meta-learning for fast adaptation of deep net- works. InInternational conference on machine learning, 2017

    work page 2017

  9. [9]

    Learning nonlinear dynamic models of soft robots for model predictive con- trol with neural networks

    Morgan T Gillespie, Charles M Best, Eric C Townsend, David Wingate, and Marc D Killpack. Learning nonlinear dynamic models of soft robots for model predictive con- trol with neural networks. InInternational Conference on Soft Robotics, 2018

    work page 2018

  10. [10]

    Thorpe, and Ufuk Topcu

    Tyler Ingebrand, Adam J. Thorpe, and Ufuk Topcu. Zero- shot transfer of neural ODEs. InAdvances in Neural Information Processing Systems, 2024

    work page 2024

  11. [11]

    Zero- shot reinforcement learning via function encoders

    Tyler Ingebrand, Amy Zhang, and Ufuk Topcu. Zero- shot reinforcement learning via function encoders. In International Conference on Machine Learning, 2024

    work page 2024

  12. [12]

    Thorpe, and Ufuk Topcu

    Tyler Ingebrand, Adam J. Thorpe, and Ufuk Topcu. Function encoders: A principled approach to transfer learning in hilbert spaces. InInternational Conference on Machine Learning, 2025

    work page 2025

  13. [13]

    RMA: rapid motor adaptation for legged robots

    Ashish Kumar, Zipeng Fu, Deepak Pathak, and Jitendra Malik. RMA: rapid motor adaptation for legged robots. InRobotics: Science and Systems, 2021

    work page 2021

  14. [14]

    A multi-mode real- time terrain parameter estimation method for wheeled motion control of mobile robots.Mechanical Systems and Signal Processing, 2018

    Yuankai Li, Liang Ding, Zhizhong Zheng, Qizhi Yang, Xingang Zhao, and Guangjun Liu. A multi-mode real- time terrain parameter estimation method for wheeled motion control of mobile robots.Mechanical Systems and Signal Processing, 2018

    work page 2018

  15. [15]

    Learning on the job: Online lifelong and continual learning

    Bing Liu. Learning on the job: Online lifelong and continual learning. InAAAI conference on artificial intelligence, 2020

    work page 2020

  16. [16]

    A lifelong learning approach to mobile robot navigation.Robotics and Automation Letters, 2021

    Bo Liu, Xuesu Xiao, and Peter Stone. A lifelong learning approach to mobile robot navigation.Robotics and Automation Letters, 2021

    work page 2021

  17. [17]

    Deep-neural-network-based modelling of longitudinal-lateral dynamics to predict the vehicle states for autonomous driving.Sensors, 2022

    Xiaobo Nie, Chuan Min, Yongjun Pan, Ke Li, and Zhixiong Li. Deep-neural-network-based modelling of longitudinal-lateral dynamics to predict the vehicle states for autonomous driving.Sensors, 2022

    work page 2022

  18. [18]

    Thorpe, and Meeko Oishi

    Kendric Ortiz, Rachel DiPirro, Adam J. Thorpe, and Meeko Oishi. Online learning of dynamical systems using low-rank updates to physics-informed kernel dis- tribution embeddings. InConference on Decision and Control, 2024

    work page 2024

  19. [19]

    Estimation of terramechanics pa- rameters of wheel-soil interaction model using particle filtering.Journal of Terramechanics, 2018

    Chandramouli Padmanabhan, Sayan Gupta, Annadurai Mylswamy, et al. Estimation of terramechanics pa- rameters of wheel-soil interaction model using particle filtering.Journal of Terramechanics, 2018

    work page 2018

  20. [20]

    On- line estimation of vehicle motion and power model parameters for skid-steer robot energy use prediction

    Jesse Pentzer, Sean Brennan, and Karl Reichard. On- line estimation of vehicle motion and power model parameters for skid-steer robot energy use prediction. In American Control Conference, 2014

    work page 2014

  21. [21]

    Terrain estimation via vehicle vibration measurement and cubature Kalman filtering.Journal of Vibration and Control, 2020

    Giulio Reina, Antonio Leanza, and Arcangelo Messina. Terrain estimation via vehicle vibration measurement and cubature Kalman filtering.Journal of Vibration and Control, 2020

    work page 2020

  22. [22]

    Neural network vehicle models for high-performance automated driving.Science robotics, 2019

    Nathan A Spielberg, Matthew Brown, Nitin R Kapania, John C Kegelman, and J Christian Gerdes. Neural network vehicle models for high-performance automated driving.Science robotics, 2019

    work page 2019

  23. [23]

    Omnimapper: A modular multimodal map- ping framework

    Alexander JB Trevor, John G Rogers, and Henrik I Christensen. Omnimapper: A modular multimodal map- ping framework. In2014 IEEE international conference on robotics and automation (ICRA), pages 1983–1990. IEEE, 2014

    work page 1983

  24. [24]

    Gaus- sian process dynamical models

    Jack Wang, Aaron Hertzmann, and David J Fleet. Gaus- sian process dynamical models. InAdvances in Neural Information Processing Systems, 2005

    work page 2005

  25. [25]

    Online adaptation of terrain-aware dynamics for planning in unstructured environments

    William Ward, Sarah Etter, Tyler Ingebrand, Christian Ellis, Adam Thorpe, and Ufuk Topcu. Online adaptation of terrain-aware dynamics for planning in unstructured environments. InRobotics: Science and Systems Work- shop on Resilient Off-road Autonomous Robotics, 2025

    work page 2025

  26. [26]

    Information theoretic MPC for model-based reinforcement learning

    Grady Williams, Nolan Wagener, Brian Goldfain, Paul Drews, James Rehg, Byron Boots, and Evangelos Theodorou. Information theoretic MPC for model-based reinforcement learning. InInternational Conference on Robotics and Automation, 2017

    work page 2017

  27. [27]

    Information-theoretic model predictive control: Theory and applications to autonomous driving.Transactions on Robotics, 2018

    Grady Williams, Paul Drews, Brian Goldfain, James Rehg, and Evangelos Theodorou. Information-theoretic model predictive control: Theory and applications to autonomous driving.Transactions on Robotics, 2018

    work page 2018

  28. [28]

    Hyperdy- namics: Meta-learning object and agent dynamics with hypernetworks

    Zhou Xian, Shamit Lal, Hsiao-Yu Tung, Emmanouil An- tonios Platanios, and Katerina Fragkiadaki. Hyperdy- namics: Meta-learning object and agent dynamics with hypernetworks. InInternational Conference on Learning Representations, 2021

    work page 2021