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REVIEW 4 major objections 5 minor 24 references

Interacting Multiple Model Proprioceptive Odometry for Legged Robots

T0 review · 4 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read Treating a legged robot's stance foot as rolling (v_f = ω_f × r) instead of fixed, and fusing rolling and slip modes with an interacting multiple-model filter, cuts pose error by half to two-thirds on slippery and uneven ground at roughly 1

desk verdict A genuinely new IMM-plus-rolling combination with promising numbers, but the slip-mode mechanism is backwards as written and the tuning/experiments are underreported. read the letter →

arxiv 2603.29383 v2 pith:PCE6HGUR submitted 2026-03-31 cs.RO

Wanlei Li , Zichang Chen , Shilei Li , Xiaogang Xiong , Yunjiang Lou This is my paper · ORCID
classification cs.RO MSC 68T4093E11
keywords leggedrobotsproprioceptiveodometryinteractingmultiplemodelstateestimationrollingcontactslipdetectionerror-stateKalmanfilterinertialmeasurementunit
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

This paper tackles the drift that plagues legged-robot state estimation when only proprioceptive sensors (IMU and joint encoders) are available. It argues that the common 'point foot is stationary' assumption is a major error source because real feet roll on the ground and slip on low-friction surfaces. The proposed estimator augments the state with foot velocities and constrains each stance foot to the kinematic rolling velocity ω_f × r; it then wraps this rolling-aware filter in an interacting multiple-model (IMM) framework with two modes—rolling and slip—that differ only in foot-velocity process noise. On simulation and a real quadruped, the resulting IMM-PO filter reduces absolute trajectory error by roughly half to two-thirds relative to point-contact baselines (e.g., 0.102 m vs 0.227 m on real complex terrain) while keeping runtime around 1 ms per step. The central claim is that explicitly modeling rolling motion and adapting contact confidence through IMM yields this large, consistent improvement.

What carries the argument

The central object is the rolling-aware measurement model (Eq. 16), which constrains three quantities: the relative body–foot position (via forward kinematics), the body velocity minus the foot velocity, and the foot velocity itself to the kinematic rolling velocity ω_f × r, where r is the foot radius vector. This model is embedded in two parallel error-state Kalman filters that form an interacting multiple model; the only difference between the two modes is the foot-velocity process noise covariance Q_vf^(i) = α_i Q_vf, with α=1 for rolling and α>1 for slip. The IMM mixing and fusion equations (17–23) derive mode probabilities from innovation likelihoods, enabling online switching between t

What would settle it

Compare IMM-PO against a single-model point-contact IEKF on a soft or highly uneven terrain where rolling is not a good model; if the point-contact filter matches or beats IMM-PO, the rolling premise is not the source of the reported gains. Alternatively, remove the third measurement block in Eq. 16 (the rolling constraint on foot velocity) and keep the foot-velocity state; if accuracy is unchanged, the gains come from the state augmentation, not the rolling model.

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Extended reading notes

Core claim

The paper establishes that proprioceptive odometry for legged robots can be made substantially more accurate by augmenting the estimator state with foot velocities and modeling the stance foot's motion as rolling (v_f = ω_f × r) instead of stationary, and by wrapping this rolling-aware error-state Kalman filter in an interacting multiple-model (IMM) filter with two contact modes (rolling and slip) that differ only in foot-velocity process noise. In extensive simulations and real-world experiments on a quadruped, this design reduces ATE position error by roughly half to two-thirds relative to state-of-the-art point-contact filters and single-model rolling filters, on flat, slippery, uneven, a

Load-bearing premise

The filter assumes that a stance foot's true velocity is exactly the kinematic rolling velocity ω_f × r, with any deviation attributable to noise; if actual foot motion on a given terrain is not rolling-like (e.g., due to deformation, soft ground, or highly uneven surfaces), the rolling-aware improvement may vanish.

Editorial extensions

If this is right

  • If correct, legged robots can operate with significantly lower drift in GPS-denied or vision-degraded environments, relying only on IMU and joint encoders.
  • The two-mode IMM structure can be extended to more contact modes (finer noise discretization) or combined with exteroceptive measurements when available, potentially improving full state-estimation pipelines.
  • Explicit foot-velocity estimation offers a natural slip/contact-quality signal that could be fed to gait control or planning.
  • The rolling contact model is simple and frame-agnostic, so it may transfer to other legged platforms with spherical or curved feet without retraining.
  • The computational overhead of IMM is modest (about 1 ms per step), making the approach suitable for real-time embedded deployment.

Reading between the lines

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

  • The paper attributes the gains to the rolling model, but the ablation does not test a foot-velocity state with the standard zero-velocity constraint. If the gains are largely due to the extra foot-velocity state acting as a noise-shaping buffer rather than the rolling constraint itself, the mechanism would need to be reinterpreted, although the empirical results could still hold.
  • On terrain where foot deformation is significant (e.g., soft ground), the rolling model's assumption of a single radius vector r will break down; a promising extension is to treat r as an uncertain parameter or to add a third mode for deformed contact.
  • The IMM mode probabilities could serve as an online slip/contact-quality signal, which could be fed back to the locomotion controller to reduce slip proactively.
  • The analysis of the learned baseline suggests that implicit recurrent adaptation struggles with long-horizon contact switching; combining IMM's explicit mode structure with learned innovation models might yield robust hybrid estimators, though the paper does not explore this.
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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

4 major / 5 minor

Summary. The paper proposes an IMM-based proprioceptive odometry (IMM-PO) for legged robots. The state is augmented with foot velocities, and a rolling-contact constraint v_f = ω_f × r is used as a pseudo-measurement. Two contact modes (nominal rolling and slippery) are fused via the IMM, with modes differing only in the foot-velocity process noise Q_vf. Experiments in Gazebo and on an AlienGo robot compare IMM-PO against KF, ESKF, IEKF, ESKF-VB, KalmanNet, and a single-model rolling ESKF-R, reporting consistent improvements in ATE and RPE on flat, slippery, uneven, and slope scenes. The paper also includes an ablation study and a detailed KalmanNet failure analysis.

Significance. If the reported results are robust, the paper makes a useful contribution to proprioceptive odometry: it is the first to combine an explicit rolling-contact model with IMM-based mode adaptation for legged robots, and the reported gains over well-established baselines are substantial (e.g., on real complex terrain ATEpos 0.102 m vs 0.227 m for IEKF). The ESKF/IMM mathematics are standard and internally consistent, and the headline percentages check out against Table I. However, the significance is conditional on resolving the mechanism issue and on providing statistical support for the experimental claims; as written, the central explanatory claim appears to be contradicted by the filter equations.

major comments (4)
  1. [§III-C3 (Eq. 16) and Remark 2] The stated mechanism for the slip mode is inverted. Remark 2 claims that enlarging Q_vf 'weakens constraint confidence,' but in Eq. (16) the rolling constraint is enforced as a direct pseudo-measurement on v_f. For a direct measurement, the Kalman gain K = P_vf H^T (H P_vf H^T + R_k)^{-1} increases as Q_vf (and hence predicted P_vf) increases, pulling the posterior v_f more tightly onto ω_f × r. Thus the slip mode hardens, not weakens, the rolling constraint. This contradicts the explanation of Fig. 8 and the interpretation of the ablation in Table III. The authors should either change the design (e.g., use mode-dependent R_k for the rolling pseudomeasurement) or provide an alternative analysis showing how a larger Q_vf can produce the claimed effect.
  2. [§IV-A, Tables I–III] All quantitative results are from single runs with no error bars, no standard deviations, and no repeated trials. The abstract and conclusions claim 'superior pose estimation accuracy' over state-of-the-art methods, which requires evidence that the improvements are not due to chance or a favorable run. In simulation, multiple seeds are inexpensive; for real-world data, at least several trials should be reported. Please provide mean ± std and, where appropriate, statistical significance tests.
  3. [§IV-C and §III-C3] The method's performance depends on several reported-but-not-quantified parameters: the slip-mode noise scale α_2, the Markov transition matrix Π, the foot radius vector r, the process noise Q_vf, and measurement noise R_k. None of these are given numerically, and no sensitivity analysis is presented. Since the central advantage of IMM-PO is attributed to this mode adaptation, the absence of parameter values and robustness analysis makes the empirical contribution difficult to reproduce and assess.
  4. [§IV-A, Table I (Uneven Terrain)] On uneven terrain, the single-model rolling filter ESKF-R is worse than the point-contact IEKF (ATEpos 0.7595 vs 0.6513), yet IMM-PO is dramatically better (0.2720). This is surprising given Remark 1's own caveat that the rolling model is less accurate on uneven terrain. The paper does not explain why adding an IMM to a worse underlying model produces such a large improvement. Without a plausible mechanism (or a sensitivity analysis over the IMM parameters), this result is not convincing and suggests the improvement may stem from an unintended effect such as the extra foot-velocity state acting as a low-pass filter.
minor comments (5)
  1. [§IV (beginning of section)] The text says 'The training details and error analysis of KalmanNet are provided in []' — the citation is empty. Since Sec. IV-D contains this material, the reference should be to that section or to a numbered citation.
  2. [§IV-B] The sentence 'The robot navigated in the indoor flat surface and complex terrain, as indicated in Fig. 3' appears to reference the wrong figure; the real experiments are shown in Fig. 6, not Fig. 3.
  3. [§IV-D] The KalmanNet analysis is extensive and somewhat tangential to the paper's main contribution. Consider moving it to an appendix or condensing it, as it interrupts the flow of the experimental section.
  4. [Table IV and §IV-C] Table IV shows IMM-PO has a runtime of 1.00 ms versus 0.49 ms for ESKF-R — a two-fold increase. Calling this 'comparable computational efficiency' is optimistic, even though both are within real-time limits.
  5. [§III-B] The state dimension is stated as 39, but this is not explicitly derived. Adding a short dimension count (p, v, G, 4 foot positions, 4 foot velocities, ba, bω) would help the reader verify the formulation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: IMM weights are Bayesian likelihood-based, comparisons are external, and the central accuracy claim is not equivalent to the method's inputs by construction.

full rationale

The paper's derivation chain is a standard error-state Kalman filter plus IMM. The rolling pseudo-measurement (Eq. 16) is a stated physical/geometric ansatz (Remark 1 explicitly calls it a simplified approximation), not a quantity fitted to the ATE numbers. Mode probabilities are computed from innovation likelihoods (Eqs. 20-22) using the measurement model and mode-dependent process noise; they are not derived from the reported pose errors, so no fitted input is renamed as a prediction. The ablation (Table III: ESKF-R vs IMM-PO) and external baselines (IEKF, ESKF, ESKF-VB, KalmanNet) provide an independent empirical check; the claimed accuracy gain is not an identity with the filter's construction. The only apparent self-citation ([16], for IMM background) is not load-bearing. The skeptic's observation that enlarging Q_vf increases the Kalman gain on the direct v_f measurement in Eq. (16), potentially hardening the rolling constraint rather than weakening it, is a substantive correctness/mechanism concern; it does not make the pose-accuracy claim circular because the equations do not reduce the result to a fitted parameter or to the method's own output. Unreported values for α_2, Π, r, Q_vf, and R_k, and the empty citation '[]' for KalmanNet training details, are reproducibility/referencing gaps, not circularity. Consequently, no circular step can be quoted from the paper.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The central claim rests on one geometric constant (r) plus several state-estimation tuning blocks (alpha_2, Pi, Q_vf, R_k) that the paper does not report; one approximate physical model (rolling contact, Eq. 5); two modeling decisions stated only in remarks (slip-as-noise, two-mode sufficiency); and two trusted instrumentation chains (Gazebo contact dynamics and motion capture). The ESKF/IMM machinery is standard and not counted. Because the unstated tuning constants determine the mode probabilities and hence the claimed accuracy advantage, the reader cannot currently separate the design contribution from the tuning contribution.

free parameters (4)
  • alpha_2 (slip-mode foot-velocity noise scale) = not reported (alpha_1 = 1 nominal)
    Defines the entire slip mode via Q_vf^(slip) = alpha_2 Q_vf (Sec. III-C3). With alpha_2 unreported, the method's central adaptivity cannot be reproduced or checked for sensitivity.
  • Markov transition matrix Pi = [pi_ji] = not reported
    Determines mode-switching dynamics in the IMM mixing step (Eq. 17); no values or sensitivity analysis are given.
  • Foot radius vector r = not reported (described as determined by foot geometry)
    Appears in the rolling constraint (Eq. 5) and the measurement function h_r (Eq. 16). For the AlienGo foot it should be a known physical constant, but no value is stated and no sensitivity analysis is given.
  • Base foot-velocity process noise Q_vf and measurement noise R_k = not reported
    Anchor the likelihood ratio between modes and thus the mode probabilities; standard tuning constants whose values are never stated.
assumptions (7)
  • domain assumption Rolling-contact model: stance-foot velocity equals omega_f x r with r fixed by foot geometry (Eq. 5)
    Replaces the zero-velocity point-contact constraint and is the paper's key modeling premise. Remark 1 concedes it is approximate on uneven terrain, and Table I shows the single-model rolling filter underperforms IEKF there.
  • domain assumption Slip changes only the scale of foot-velocity process noise, not the measurement structure (Remark 2)
    Justifies why the two IMM modes share the same measurement function and differ only in Q_vf; if slip altered the measurement model, likelihood-based mode discrimination would be misspecified.
  • domain assumption Two modes (nominal rolling plus slip) suffice for practical contact conditions (Remark 3)
    The paper asserts additional modes are unreliable and costly; the ablation shows the three-mode IMM-T gains only about 0.02 m ATEpos over IMM-PO, supporting but not proving the saturation claim.
  • standard math Innovation likelihoods are Gaussian (Eq. 21)
    Standard IMM/EKF assumption; contact impacts at touchdown likely produce non-Gaussian innovations, a concern the paper does not address.
  • standard math ESKF linearization and small-error-state representation are valid
    Standard EKF machinery inherited from [8]; no new justification is required.
  • domain assumption Gazebo contact and friction model faithfully reproduces real foot-ground interaction
    The simulation scenarios are the main evidence for the rolling model, including the Fig. 4 foot-velocity ground truth; the simulator's sphere-contact dynamics mirror the kinematics the model assumes.
  • domain assumption Motion-capture ground truth is accurate to about 0.1 mm
    All real-world error metrics rest on this stated positional accuracy of the motion capture system.

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Cite this review

Pith. "Pith review of Interacting Multiple Model Proprioceptive Odometry for Legged Robots." pith.science (2026). https://pith.science/paper/PCE6HGUR

@misc{pith2026260329383,
  author       = {Pith},
  title        = {Pith review of: Interacting Multiple Model Proprioceptive Odometry for Legged Robots},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PCE6HGUR}},
  note         = {Machine review of arXiv:2603.29383}
}
read the original abstract

State estimation for legged robots remains challenging because legged odometry generally suffers from limited observability and therefore depends critically on measurement constraints to suppress drift. When exteroceptive sensors are unreliable or degraded, such constraints are mainly derived from proprioceptive measurements, particularly contact-related leg kinematics information. However, most existing proprioceptive odometry methods rely on an idealized point-contact assumption, which is often violated during real locomotion. Consequently, the effectiveness of proprioceptive constraints may be significantly reduced, resulting in degraded estimation accuracy. To address these limitations, we propose an interacting multiple model (IMM)-based proprioceptive odometry framework for legged robots. By incorporating multiple contact hypotheses within a unified probabilistic framework, the proposed method enables online mode switching and probabilistic fusion under varying contact conditions. Extensive simulations and real-world experiments demonstrate that the proposed method achieves superior pose estimation accuracy over state-of-the-art methods while maintaining comparable computational efficiency.

Figures

Figures reproduced from arXiv: 2603.29383 by the authors.

Figure 1
Figure 1. Illustration of rolling and slippery contacts between the robot foot and [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Some snapshots of the four simulation scenarios are presented, [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. further shows the foot velocity along the X axis. During the stance phase, the foot velocity is not strictly zero, which is consistent with the rolling-contact, and the estimated velocity closely matches the ground truth. Quantitative results in Table I show that incorporating the rolling effect (ESKF-R) significantly reduces the position errors compared with IEKF, with ATE and RPE reduced by 43.1% and 43.5%, respec… view at source ↗
Figures from the paper (5 more)
Figure 5
Figure 5. Figure 5: Estimated trajectories and attitude errors in the slippery scenario. [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: Some snapshots of the two real experiment scenarios are presented, [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 8
Figure 8. Figure 8: Temporal evolution of mode switching in IMM-PO and the ground [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]
Figure 9
Figure 9. Figure 9: Representative XY trajectory comparison on a long real-world [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 10
Figure 10. Figure 10: Evolution of the closed-loop stability indicator along the trajectory. [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]

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Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.