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REVIEW 3 major objections 4 minor 1 cited by

Probabilistic Latent Variable Modeling for Dynamic Friction Identification and Estimation

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper claims that adding a learned two-dimensional latent state to a probabilistic robot dynamics model captures friction memory well enough to beat physics-based and supervised data-driven friction models in open-loop prediction on…

desk verdict A sensible method paper whose central superiority claim rests on a single trajectory; worth a referee's time but not yet decisive evidence. read the letter →

arxiv 2412.15756 v1 pith:HWAY6UXC submitted 2024-12-20 cs.RO cs.LGcs.SYeess.SY

Victor Vantilborgh , Sander De Witte , Frederik Ostyn , Tom Lefebvre , Guillaume Crevecoeur This is my paper · ORCID
classification cs.ROcs.LGcs.SYeess.SY
keywords roboticsdata-drivenmodelingfrictionidentificationprobabilisticstate-spacemodellatentvariablesexpectation-maximizationsequentialMonteCarloneuralnetwork
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper proposes that the hard-to-model memory effects in robot-joint friction can be captured by augmenting a conventional rigid-body dynamics model with a learned latent dynamic state. Both the friction torque and the evolution of this latent state are neural networks, and the whole probabilistic state-space model is fitted directly from noisy joint-position and motor-current measurements using expectation-maximization with sequential Monte Carlo. On an industrial robot, the resulting model predicts open-loop joint motion with lower error and better stability over a full trajectory than Coulomb-viscous, Stribeck, LuGre, GMS, feedforward neural-network, and recurrent neural-network benchmarks. The practical upshot is that accurate dynamic friction identification no longer requires torque sensors or hand-designed friction laws.

What carries the argument

The load-bearing object is a probabilistic state-space model whose state is the standard robot state augmented by a latent friction state, $x_t = (q_t,\dot{q}_t,z_t)$, with the transition given by equation (4). The latent dynamics follow $\dot{z}_t = \eta_\theta(x_t)$ and the friction torque is $\tau_{f,\theta}(x_t)$, both parametrized by neural networks, so the extended state carries the memory that static friction laws lack. Identification is performed by maximizing the marginal likelihood via the EM algorithm, with the E-step smoothing distribution approximated by sequential Monte Carlo (particle filtering using 200 particles), yielding the neural-network weights and base inertial parameters directly from noisy encoder data.

What would settle it

Run the same identification procedure on a second test trajectory whose spectral content and velocity range differ markedly from the training excitation, and refit the model with latent dimension 1, 2, 3, and 4; if the 2D model's open-loop error grows sharply on the new trajectory while higher-dimensional variants hold up, the sufficiency and generality of the two-dimensional Markovian latent state is refuted.

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Extended reading notes

Core claim

The paper's central claim is that representing unmodeled friction dynamics by a low-dimensional latent state, learned jointly with a neural-network friction model inside a probabilistic state-space model, yields a dynamic robot model that beats both physics-based and supervised data-driven benchmarks in open-loop prediction. Concretely, on the KUKA KR6 R700, the proposed latent-variable model reports a mean squared error of 0.024 and a mean absolute error of 0.11 over the first 10 seconds of open-loop prediction, against best baseline LuGre at 0.027 and 0.12; over the complete test trajectory it reports 0.11 and 0.22, against LuGre at 0.66 and 0.42. The supervised neural network and recurrent network baselines become unstable on longer horizons, while the latent-variable model remains accurate, which the paper attributes to the latent state providing the memory required to stay inside the trained dynamics.

Load-bearing premise

The load-bearing premise is that a two-dimensional Markovian latent state, with dynamics learned by a neural network, is identifiable from joint position and motor-current data alone and is sufficient to represent all unmodeled friction dynamics.

Editorial extensions

If this is right

  • Open-loop dynamic simulation of a robot joint can remain accurate over a full trajectory, not just the first seconds, without joint torque sensors.
  • The identified latent state provides a ready-built online state estimator that can be reused for friction compensation and output-torque estimation in control.
  • Because the same maximum-likelihood identification applies to physics-based friction models, the benchmark models could be refitted under the same probabilistic noise model for a more uniform comparison.
  • Since the latent dynamics carry no physical prior, the same formulation can absorb other unmodeled actuator effects such as backlash or elasticity with no change to the model structure.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct check of whether the learned two-dimensional latent state corresponds to a physical quantity (for example, bristle deflection or pre-sliding displacement) would require joint torque sensing, which the current testbed lacks; without such a check, the latent state remains a purely functional quantity.
  • The latent dimension was set to two without a reported model-selection or identifiability analysis, so a reader should treat it as a tuned hyperparameter rather than a discovered property of the friction physics.
  • Particle filtering with 200 particles will likely become expensive as the number of joints grows, so scaling this approach to full six- or seven-degree-of-freedom robots probably needs variational or amortized inference rather than plain sequential Monte Carlo.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes a probabilistic state-space model for robot-joint friction identification, in which the rigid-body dynamics are augmented with a low-dimensional latent state whose transition and friction torque are parameterized by neural networks. The model parameters (inertial parameters, two NN parameter sets, and noise covariances) are estimated by maximizing the marginal likelihood via the EM algorithm with Sequential Monte Carlo approximations. The method is evaluated on a KUKA KR6 R700 by open-loop prediction of joint positions and velocities from measured motor torques, comparing against Coulomb+viscous, Stribeck, LuGre, GMS, fully connected NN, and RNN baselines. The reported results show the LVM achieving lower MSE/MAE than the baselines over a 10 s horizon and over the full 31.4 s validation trajectory.

Significance. If the results hold, the contribution is valuable: it offers a principled probabilistic framework for learning unobserved friction dynamics without torque sensors, integrates latent dynamics and neural friction models into the standard rigid-body model, and evaluates on a genuine held-out trajectory rather than on the training data. The full-trajectory open-loop result (MSE 0.11 vs 0.66 for LuGre) is suggestive of a real stability advantage. However, the paper's central claim of outperforming all benchmarks rests on a single validation run with no error bars and on an undocumented choice of latent dimension, so the significance is presently conditional on the empirical evaluation being strengthened.

major comments (3)
  1. [Section V-B, Table I] The central claim that 'the proposed data-driven latent variable model outperforms all benchmark models in both accuracy and robustness' is supported only by point estimates in Table I from a single held-out validation trajectory. The paper reports no repeated trials, no standard errors or confidence intervals, and no per-joint breakdown; the 10 s MSE margin over LuGre (0.024 vs 0.027) is small enough that it could be reversed by EM/particle-filter randomness, network initialization, or dataset realization. The full-trajectory margin (0.11 vs 0.66) is encouraging but is still a single observation. Please add multiple validation trajectories or repeated identifications, or at minimum report variability across joints and over repeated runs, before claiming superiority.
  2. [Section V-A] The statement that 'the optimal dimension of the latent state z, was determined to be 2' is given without reporting the selection procedure, a sensitivity analysis, or an identifiability discussion. Because the latent state is the mechanism by which the model absorbs unmodeled friction dynamics, an overparameterized or underparameterized latent dimension could directly affect the open-loop prediction scores and generalizability. Please document how the dimension was chosen (e.g., cross-validated likelihood, held-out score, or comparison across dimensions) and report the sensitivity of Table I to the latent dimension and to the number of particles (200).
  3. [Section V-B, Table I] Table I omits the Simple and RNN entries for the complete trajectory because their predictions 'exploded', which makes the comparison incomplete and the robustness claim hard to quantify. Please report the actual error values even if they are very large, define a divergence criterion, and indicate at what time the divergence occurred; without this information the reader cannot distinguish a systematic robustness advantage of the LVM from a single uncontrolled divergence event.
minor comments (4)
  1. [Section V-C] Since no ground-truth friction torque is available, the identified friction characteristics can only illustrate what the model learned; please reframe the text explicitly as an illustration rather than as confirmation that the model captures real friction phenomena, or add an independent quantitative check.
  2. [Throughout] Please proofread carefully: there are many typographical errors, including 'Quantative' and 'en' in Table I, 'adress', 'Lugre' for 'LuGre', 'frecuency', 'camparison', 'subtilities', 'te note', 'preculding', 'analysys', 'emprical', 'incoporates', 'arbritrary', 'succesfully', 'intrinscally', and 'velocties'. The notation '9q' and '9xt' should be typeset as \dot{q} and \dot{x}_t throughout.
  3. [Section IV-A] The paper does not state whether code or data will be made available. For a data-driven method evaluated on a proprietary robot platform, a public release of the dataset or code, or at least a detailed experiment protocol, would substantially improve reproducibility.
  4. [Section V-B] The term 'robustness' is used without a definition; please specify the metric or criterion (e.g., stability over the full trajectory, error growth rate, or worst-case error) so that the claim can be evaluated quantitatively.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the main claim rests on open-loop prediction against a held-out validation trajectory, and the qualitative friction analysis is explicitly not treated as ground truth.

full rationale

The paper's central comparison is a genuine held-out evaluation. Section IV-A states that the training dataset consists of three trajectories and that 'The validation dataset consist of a fourth trajectory of the same length,' and Section V-B reports open-loop simulations in which measured motor torques are applied and predicted joint positions and velocities are compared with measured values. The LVM parameters are learned by EM/SMC from the training trajectories, so the Table I numbers are not produced by fitting the validation trajectory. The only potentially self-referential passage is Section V-C, where the identified friction characteristic of the LVM is interpreted as showing stiction, Stribeck, and hysteresis; however, the paper explicitly says that 'Due to the lack of joint torque sensors in the KUKA KR6 R700, no direct ground truth for the friction characteristics is available, precluding a quantitative comparison,' so this qualitative discussion is not load-bearing for the accuracy claim. No load-bearing self-citations or imported uniqueness theorems appear in the derivation. The lack of error bars, the single validation trajectory, and the unspecified procedure for choosing the latent dimension of 2 are statistical and reporting concerns, not circularity, because no equation or fitted parameter is renamed as a prediction by construction.

Assumptions & free parameters 6 free parameters · 6 assumptions · 1 invented entities

The central claim rests on six fitted hyperparameters and modeling choices (latent dimension, particle count, network architectures, learning settings, noise covariances, EM stopping), plus domain assumptions about the rigid-body model, Markovian 2D latent dynamics, Gaussian noise, and representativeness of a single validation trajectory. The only invented entity is the latent state z, which has no independent empirical evidence.

free parameters (6)
  • Latent state dimension = 2
    Reported in Section V-A as 'determined to be 2'; the selection procedure is not described, so it may have been tuned on validation performance.
  • Particle count for SMC = 200
    Section V-A states '200 particles were used for the SMC methods'; no sensitivity analysis is given.
  • Neural network architectures = Latent dynamics: 1 hidden layer of 32; friction: 2 hidden layers of 32, Mish activation
    Section V-A; chosen via a hyperparameter search that is not detailed.
  • Learning rate and batch sizes = lr 0.001; NN batch 64, RNN batch 128; LVM batch not stated
    Section V-A; standard hyperparameters, but LVM training details are incomplete.
  • Process and measurement noise covariances Q and R = Not reported
    Included in theta and learned from data (Section III-A); their fitted values affect identifiability and prediction uncertainty.
  • EM convergence tolerance and number of iterations = Not reported
    Algorithm 1 stops when Q increments tend to zero, but no threshold or iteration count is given.
assumptions (6)
  • domain assumption The rigid-body inverse dynamics model (1) with lumped parameters is an adequate base model.
    The entire PSSM structure (Eq. 4) is built on this model; if gearbox elasticity or motor-side dynamics are significant, the latent states must absorb them.
  • domain assumption Friction torque is a function of the extended state (q, q_dot, z) and can be represented by a neural network.
    The paper assumes this representational flexibility (Section III-A) without proving it for the specific physical friction process.
  • ad hoc to paper The latent state dynamics are Markovian and of fixed dimension 2.
    No physical derivation is given; Section V-A says dimension 2 was 'determined' without showing identifiability or model selection.
  • domain assumption Additive Gaussian process and measurement noise with constant covariances Q and R.
    Stated in Eq. (5); standard but not validated against the actual noise characteristics of the KUKA encoder and motor-current measurements.
  • domain assumption The validation trajectory is representative of the operating conditions of interest.
    Only one 31.4 s trajectory is used for validation (Sections IV-A and V-B), with no repeats or load variation.
  • standard math EM and SMC converge to a useful optimum for the nonconvex objective.
    EM is guaranteed to increase likelihood but not to reach a global optimum; SMC with 200 particles introduces Monte Carlo error, and no diagnostics are reported (Section III-B).
invented entities (1)
  • Latent dynamic state z
    purpose: To encode unmodeled friction dynamics such as hysteresis, stiction, temperature and load effects that are not present in the measured state.
    The latent state is never measured and the paper provides no external falsifiable prediction derived from it; its usefulness is shown only indirectly through improved open-loop prediction on one trajectory.

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Pith. "Pith review of Probabilistic Latent Variable Modeling for Dynamic Friction Identification and Estimation." pith.science (2026). https://pith.science/paper/HWAY6UXC

@misc{pith2026241215756,
  author       = {Pith},
  title        = {Pith review of: Probabilistic Latent Variable Modeling for Dynamic Friction Identification and Estimation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HWAY6UXC}},
  note         = {Machine review of arXiv:2412.15756}
}
read the original abstract

Precise identification of dynamic models in robotics is essential to support control design, friction compensation, output torque estimation, etc. A longstanding challenge remains in the identification of friction models for robotic joints, given the numerous physical phenomena affecting the underlying friction dynamics which result into nonlinear characteristics and hysteresis behaviour in particular. These phenomena proof difficult to be modelled and captured accurately using physical analogies alone. This has motivated researchers to shift from physics-based to data-driven models. Currently, these methods are still limited in their ability to generalize effectively to typical industrial robot deployement, characterized by high- and low-velocity operations and frequent direction reversals. Empirical observations motivate the use of dynamic friction models but these remain particulary challenging to establish. To address the current limitations, we propose to account for unidentified dynamics in the robot joints using latent dynamic states. The friction model may then utilize both the dynamic robot state and additional information encoded in the latent state to evaluate the friction torque. We cast this stochastic and partially unsupervised identification problem as a standard probabilistic representation learning problem. In this work both the friction model and latent state dynamics are parametrized as neural networks and integrated in the conventional lumped parameter dynamic robot model. The complete dynamics model is directly learned from the noisy encoder measurements in the robot joints. We use the Expectation-Maximisation (EM) algorithm to find a Maximum Likelihood Estimate (MLE) of the model parameters. The effectiveness of the proposed method is validated in terms of open-loop prediction accuracy in comparison with baseline methods, using the Kuka KR6 R700 as a test platform.

Figures

Figures reproduced from arXiv: 2412.15756 by the authors.

Figure 1
Figure 1. Experimental test setup with KUKA KR6 R700. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Absolute errors of the open-loop estimations of the different [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. The estimated friction characteristics for the different models [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. K-VARK: Kernelized Variance-Aware Residual Kalman Filter for Sensorless Force Estimation in Collaborative Robots

    cs.RO 2025-12 conditional novelty 6.0 of 10

    K-VARK combines a kernelized movement-primitive model of residual joint torques with an adaptive Kalman filter to estimate external forces on a 6-DoF robot without force sensors.

Reference graph

Works this paper leans on

24 extracted references · 24 canonical work pages · cited by 1 Pith paper

  1. [16]

    Scholl, M

    P. Scholl, M. Iskandar, S. Wolf, J. Lee, A. Bacho, A. Dietrich, A. Albu- Sch¨affer and G. Kutyniok, ”Learning-based adaption of robotic friction models,” in Robotics and Computer-Integrated Manufacturing , vol. 89, art. no. 102780, Oct. 2024

    work page 2024

  2. [17]

    Hirose and R

    N. Hirose and R. Tajima, ”Modeling of rolling friction by recurrent neural network using LSTM,” in IEEE International Conference on Robotics and Automation (ICRA) , pp. 6471-6478, Aug. 2017

    work page 2017

  3. [1]

    Haddadin, A

    S. Haddadin, A. De Luca, A. Albu-Sch :ar, ”Robot Collisions: A Survey on Detection, Isolation, and Identification” in IEEE Transactions on Robotics, vol. 33, no. 6, Dec. 2017

    work page 2017

  4. [2]

    Kim, ”Moment of inertia and friction torque coefficient identification in a servo drive system,” IEEE Transactions on Industrial Electronics , vol

    S. Kim, ”Moment of inertia and friction torque coefficient identification in a servo drive system,” IEEE Transactions on Industrial Electronics , vol. 66, no. 1, pp. 60-70, Jan. 2019

    work page 2019

  5. [3]

    Pennestr `ı, V

    E. Pennestr `ı, V . Rossi and P. Salvini, ”Review and comparison of dry friction force models,” in Nonlinear Dynamics, vol. 83, pp. 1785–1801, Mar. 2016

    work page 2016

  6. [4]

    K. J. ˚Astrom and C. De Wit, ”Revisiting the LuGre friction model,” in IEEE Control Systems Magazine, Institute of Electrical and Electronics Engineers, vol. 28, no. 6, pp.101-114, Dec. 2008

    work page 2008

  7. [5]

    Lampaert, F

    V . Lampaert, F. Al-Bender and J. Swevers, ”A generalized Maxwell- slip friction model appropriate for control purposes,” in 2003 IEEE International Workshop on Workload Characterization, vol. 4, pp. 1170- 1177, Aug. 2003

    work page 2003

  8. [6]

    Weigand, N

    J. Weigand, N. Gafur and M. Ruskowski, ”Flatness Based Control of an Industrial Robot Joint Using Secondary Encoders,” in Robotics and Computer-Integrated Manufacturing, vol. 68, art. no. 102039, Apr. 2021

    work page 2021

Show all 24 references
  1. [7]

    Iskandar and S

    M. Iskandar and S. Wolf, ”Dynamic friction model with thermal and load dependency: modeling, compensation, and external force estimation,” in 2019 International Conference on Robotics and Automation (ICRA) , pp. 7367-7373, Aug. 2019

    2019

  2. [8]

    M. A. Tadese, F. Yumbla, J. -S. Yi, W. Lee, J. Park and H. Moon, ”Passivity Guaranteed Dynamic Friction Model With Temperature and Load Correction: Modeling and Compensation for Collaborative Indus- trial Robot,” in IEEE Access, vol. 9, pp. 71210-71221, Apr. 2021

    2021

  3. [9]

    X. Tu, Y . Zhou, P. Zhao, ”Modeling the Static Friction in a Robot Joint by Genetically Optimized BP Neural Network,” in Journal of Intelligent and Robotic Systems vol. 94, pp. 29–41 Apr. 2019

    2019

  4. [10]

    X. Liu, F. Zhao, S. S. Ge, Y . Wu and X. Mei, ”End-Effector Force Estimation for Flexible-Joint Robots With Global Friction Approxi- mation Using Neural Networks,” in IEEE Transactions on Industrial Informatics, vol. 15, no. 3, pp. 1730-1741, Mar. 2019

    2019

  5. [11]

    K. Guo, Y . Pan and H. Yu, ”Composite Learning Robot Control With Friction Compensation: A Neural Network-Based Approach,” in IEEE Transactions on Industrial Electronics , vol. 66, no. 10, pp. 7841-7851, Oct. 2019

    2019

  6. [12]

    Simoni, M

    L. Simoni, M. Beschi, G. Legnani and A. Visioli, ”Friction modeling with temperature effects for industrial robot manipulators,” In Proceed- ings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3524– 3529. Dec. 2015

    2015

  7. [13]

    On the inclusion of temperature in the friction model of industrial robots,

    L. Simoni, M. Beschi, G. Legnani, and A. Visioli, “On the inclusion of temperature in the friction model of industrial robots,” in IFACPaper- sOnLine, vol. 50, no. 1, pp. 3482–3487, Jul. 2017

    2017

  8. [14]

    Carlson, A

    F.B. Carlson, A. Robertsson and R. Johansson, ”Modeling and identifica- tion of position and temperature dependent friction phenomena without temperature sensing,” in Proceedings of the IEEE/RSJ International Conference onIntelligent Robots and Systems , pp. 3045–3051. Dec. 2015

    2015

  9. [15]

    L. Gao, J. Yuan, Z. Han, S. Wang and N. Wang, ”A friction model with velocity, temperature and load torque effects for collaborative industrial robot joints,” in IEEE International Conference on Intelligent Robots and Systems (IROS) , pp. 3027-3032, Dec. 2017

    2017

  10. [18]

    Leboutet, J

    Q. Leboutet, J. Roux, A. Janot, J. Rogeli and G. Cheng, ”Inertial Parameter Identification in Robotics: A Survey,” in Applied Sciences , V ol. 11, p.4303, May 2021

    2021

  11. [19]

    Swevers, W

    J. Swevers, W. Verdonck and J. De Schutter, ”Dynamic Model Identifi- cation for Industrial Robots,” in IEEE Control Systems Magazine , vol. 27, no. 5, pp. 58-71, Oct. 2007

    2007

  12. [20]

    Gautier and W

    M. Gautier and W. Khalil, ”Direct calculation of minimum set of inertial parameters of serial robots,” in IEEE Transactions on Robotics and Automation, vol. 6, no. 3, pp. 368-373, Jun. 1990

    1990

  13. [21]

    Tjahjowidodo, F

    T. Tjahjowidodo, F. Al-Bender, and H. Van Brussel, ”Friction identifica- tion and compensation in a DC motor,” in Proceedings of the 16th IFAC World Congres, Jul. 2005

    2005

  14. [22]

    McLachlan and T

    G. McLachlan and T. Krishnan, ”The EM algorithm and extensions. Second Edition,” in John Wiley and Sons , 2008

    2008

  15. [23]

    S :arkk:a and L

    S. S :arkk:a and L. Svensson, ”Bayesian filtering and smoothing. Second Edition,” in Cambridge University Press , 2023

    2023

  16. [24]

    Weigand, J

    J. Weigand, J. G ¨otz, J. Ulmen and M. Ruskowski, ”Dataset and Baseline for an Industrial Robot Identification Benchmark,” in 6th Edition of the Workshop on Nonlinear System Identification Benchmarks , Apr. 2022

    2022

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Reviewed August 11, 2026 · model on record in the stance chip above.