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arxiv: 2605.15122 · v1 · pith:SFIHO6ULnew · submitted 2026-05-14 · 💻 cs.RO · cs.LG· cs.SY· eess.SY

CoCo-InEKF: State Estimation with Learned Contact Covariances in Dynamic, Contact-Rich Scenarios

Michael Baumgartner , David M\"uller , Agon Serifi , Ruben Grandia , Espen Knoop , Markus Gross , Moritz B\"acher This is my paper

Pith reviewed 2026-06-30 20:02 UTC · model grok-4.3

classification 💻 cs.RO cs.LGcs.SYeess.SY
keywords state estimationlegged robotsinvariant extended Kalman filtercontact covariancesneural networkdynamic motionbipedal robotvelocity estimation
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The pith

CoCo-InEKF replaces binary contact states with learned continuous covariances in an invariant EKF for legged robot velocity estimation.

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

The paper introduces CoCo-InEKF, a differentiable invariant extended Kalman filter that incorporates continuous contact velocity covariances predicted by a lightweight neural network. The network is trained end-to-end on state-error loss to handle partial contact and directional slippage without heuristic labels. This modulation of contact confidence improves linear velocity accuracy and filter consistency on a bipedal robot during dynamic motions. The approach demonstrates robustness in both simulation and real-world experiments with complex ground interactions.

Core claim

By training a neural network to output contact velocity covariances for predefined candidate points and integrating them into an invariant EKF, the filter dynamically adjusts for nuanced contact conditions ranging from firm contact to slippage or none, yielding superior accuracy-efficiency tradeoffs and consistency for linear velocity estimation without binary decisions or manual labels.

What carries the argument

Differentiable invariant extended Kalman filter modulated by continuous contact velocity covariances predicted by a lightweight neural network trained end-to-end on state-error loss.

If this is right

  • Enables robust execution of challenging motions such as dancing and complex ground interactions in simulation and the real world.
  • Delivers a superior accuracy-efficiency tradeoff for linear velocity estimation compared to baseline methods.
  • Improves overall filter consistency relative to traditional binary contact approaches.
  • Eliminates dependence on heuristic ground-truth contact labels for training.
  • Remains insensitive to the precise placement of contact candidate points.

Where Pith is reading between the lines

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

  • The covariance prediction could extend to other legged platforms by adapting the automated candidate selection procedure.
  • The uncertainty information from covariances might integrate into motion planning for safer navigation in uncertain terrain.
  • Collecting diverse real-world interaction data could further reduce simulation-to-reality gaps in training.
  • Onboard efficiency gains may support higher-frequency control loops in high-speed locomotion tasks.

Load-bearing premise

A lightweight neural network trained end-to-end on state-error loss can produce contact velocity covariances that correctly capture nuanced contact conditions and improve the invariant EKF without introducing instability.

What would settle it

A controlled test showing higher velocity estimation error or filter divergence when using the learned covariances versus binary contact baselines during a partial-contact or slippage scenario.

Figures

Figures reproduced from arXiv: 2605.15122 by Agon Serifi, David M\"uller, Espen Knoop, Markus Gross, Michael Baumgartner, Moritz B\"acher, Ruben Grandia.

Figure 1
Figure 1. Figure 1: CoCo-InEKF. Given a set of predefined contact candidates and the proprioceptive sensor data from the IMU and actuators of a robot, a learned contact module predicts contact velocity covariances for use in an Invariant EKF. deployment of impressive reinforcement learning controllers, these methods underperform when evaluated on state estimation accuracy alone, as we will show in our evaluation. This paper p… view at source ↗
Figure 2
Figure 2. Figure 2: Training setup. Per learning iteration, we collect a training dataset of ground-truth states and sensor measurements by forward￾simulating a pretrained policy in E environments. The contact module predicts contact velocity covariances based on the sensor history (IMU + actuator data). These covariances are passed to the differentiable InEKF, rolling out the state estimate for L time steps. We compute a los… view at source ↗
Figure 3
Figure 3. Figure 3: Contact Covariance. Visualization of the contact covariance total standard deviation p tr(BΣCi ) and contact point velocity magnitude during a forward-walking gait of our robot, along with ground-truth contacts. C. Metrics Offline metrics are based on [42]. We report absolute trajectory error (ATE), computed over the trajectory after aligning the initial state, as well as the root mean square error (RMSE),… view at source ↗
Figure 5
Figure 5. Figure 5: We hypothesize that as our method reasons about [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: Foot contact candidate configurations. As used in the evaluation and ablation study for dancing motions. Configurations (a) and (b), with 4 and 8 candidates respectively, were handpicked. All others have 8 candidates and were automatically generated using our proposed sampling method. motions (N = 10, over the full body). For each test case, we hand-select a baseline and compare it to 9 samples from the au… view at source ↗
Figure 6
Figure 6. Figure 6: Consistency. Visualization of the normalized estimation error squared (NEES) of the combined core state of baseline InEKF approaches vs. our proposed CoCo-InEKF for 100 dance motion sequences. CoCo-InEKF’s NEES values are more consistent with the expected 95% confidence interval of a χ 2 distribution. We omit the Hybrid Baseline, as it performs near identical to the Hybrid Baseline+. the contact states eit… view at source ↗
read the original abstract

Robust state estimation for highly dynamic motion of legged robots remains challenging, especially in dynamic, contact-rich scenarios. Traditional approaches often rely on binary contact states that fail to capture the nuances of partial contact or directional slippage. This paper presents CoCo-InEKF, a differentiable invariant extended Kalman filter that utilizes continuous contact velocity covariances instead of binary contact states. These learned covariances allow the method to dynamically modulate contact confidence, accounting for more nuanced conditions ranging from firm contact to directional slippage or no contact. To predict these covariances for a set of predefined contact candidate points, we employ a lightweight neural network trained end-to-end using a state-error loss. This approach eliminates the need for heuristic ground-truth contact labels. In addition, we propose an automated contact candidate selection procedure and demonstrate that our method is insensitive to their exact placement. Experiments on a bipedal robot demonstrate a superior accuracy-efficiency tradeoff for linear velocity estimation, as well as improved filter consistency compared to baseline methods. This enables the robust execution of challenging motions, including dancing and complex ground interactions -- both in simulation and in the real world.

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

0 major / 2 minor

Summary. The manuscript presents CoCo-InEKF, a differentiable invariant extended Kalman filter (InEKF) for state estimation in legged robots that replaces binary contact states with continuous contact velocity covariances predicted by a lightweight neural network. The network is trained end-to-end on a state-error loss without requiring heuristic contact labels. An automated contact candidate selection method is proposed, and the approach is demonstrated to be robust to candidate placement. Experiments on a bipedal robot in simulation and hardware show improved accuracy and consistency in linear velocity estimation over baselines, supporting complex motions such as dancing and ground interactions.

Significance. This work addresses a significant challenge in robust state estimation for dynamic, contact-rich legged locomotion by learning to modulate contact confidence continuously. If the empirical results are reproducible, it offers an efficient way to integrate data-driven components into invariant filters. The manuscript earns credit for its end-to-end training procedure that avoids labeled data, the ablation studies on contact candidate placement and training, and the real-world experiments validating performance on challenging tasks.

minor comments (2)
  1. [Abstract] Abstract: the claim of a 'superior accuracy-efficiency tradeoff' would be strengthened by including one or two key quantitative metrics (e.g., velocity RMSE reduction or consistency metric) rather than qualitative description alone.
  2. The description of how the neural network outputs are mapped to the covariance matrices in the InEKF update equations would benefit from an explicit equation or pseudocode block to improve reproducibility.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. No specific major comments were listed in the report.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper presents a differentiable InEKF that incorporates continuous contact velocity covariances produced by a lightweight NN. The NN is trained end-to-end on a state-error loss to output those covariances; this is a conventional learning procedure that maps sensor inputs to filter parameters, not a derivation that reduces by construction to its own fitted values or to a self-citation. No equations are shown that equate a claimed prediction to a fitted input, no uniqueness theorem is invoked via self-citation, and no ansatz is smuggled. The central claims rest on simulation/hardware experiments and ablations that directly test accuracy, consistency, and robustness; these are externally falsifiable and independent of the training loop itself. The approach therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Abstract-only; ledger entries are limited to elements explicitly named in the provided text.

free parameters (1)
  • neural network weights
    Trained end-to-end via state-error loss; values are fitted to robot data rather than derived from first principles.
axioms (1)
  • domain assumption State-error loss is sufficient to train contact covariances without heuristic ground-truth contact labels
    Explicitly stated as eliminating the need for such labels.

pith-pipeline@v0.9.1-grok · 5761 in / 1182 out tokens · 34385 ms · 2026-06-30T20:02:07.347283+00:00 · methodology

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Forward citations

Cited by 2 Pith papers

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    ConstrainedMimic integrates operational space control and control barrier functions into RL tracking policies to enforce arbitrary runtime constraints on humanoid kinematics and dynamics while preserving contact modes...

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