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arxiv: 2605.21863 · v1 · pith:3LRH43NHnew · submitted 2026-05-21 · 💻 cs.RO

OCELOT: Odometry and Contact Estimation for Legged Robots

Pith reviewed 2026-05-22 06:10 UTC · model grok-4.3

classification 💻 cs.RO
keywords legged robotsodometrycontact estimationslippage detectionproprioceptive sensorserror-state EKFforce sensorskinematic detection
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The pith

Legged robots achieve accurate odometry from IMU, encoders, and force sensors alone by fusing force and kinematic detectors to reject slippage for ESEKF corrections.

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

The paper develops a leg odometry pipeline for legged robots that uses only proprioceptive sensors: a body-fixed IMU, joint encoders, and force sensors. An Error-State Extended Kalman Filter estimates the robot state and applies corrections whenever feet are identified as stationary. The central module runs two detectors in parallel for each foot: a force-based Gaussian Mixture Model guided Finite State Machine that confirms physical contact, and a kinematic Generalized Likelihood Ratio Test on estimated foot velocity. Quality scores from both are fused into a continuous uncertainty signal that accepts only feet that are both loaded and kinematically stationary, thereby rejecting slippage. The pipeline is tested on a 2.4 km multi-terrain dataset and benchmarked against other proprioceptive and exteroceptive methods.

Core claim

By fusing a debounced force GMM-guided FSM to confirm physical contact with a kinematic GLRT on foot velocity, the system reliably identifies stationary stance phases that serve as zero-velocity updates in an ESEKF, yielding accurate proprioceptive odometry estimates that remain robust on slippage-prone surfaces such as grass, pebble, and rock.

What carries the argument

The fused contact detection and uncertainty quantification module, which combines continuous quality scores from a force-based GMM-FSM detector and a kinematic GLRT detector to accept only feet that are both physically loaded and kinematically stationary.

If this is right

  • Accurate odometry is produced using only onboard proprioceptive sensors without cameras or LiDAR.
  • Slippage is explicitly rejected rather than treated as noise, improving robustness on varied terrains.
  • The open-source ROS2 package enables real-time deployment on legged platforms.
  • Performance matches or exceeds exteroceptive methods on the 2.4 km indoor-outdoor dataset.

Where Pith is reading between the lines

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

  • The parallel detector architecture could transfer to other mobile robots that need reliable zero-velocity updates.
  • The released multi-modal dataset may become a standard benchmark for proprioceptive odometry algorithms.
  • Lower sensor requirements could reduce hardware cost and power draw for field-deployed legged systems.
  • The uncertainty scores might be fed into higher-level planners to avoid actions during uncertain contact periods.

Load-bearing premise

The fused force-GMM-FSM and kinematic-GLRT detectors correctly identify truly stationary stance phases without systematic bias that would corrupt the zero-velocity corrections in the ESEKF.

What would settle it

Direct measurement of non-zero foot velocity during intervals the detectors classify as stationary stance, especially on slippery outdoor surfaces, would show that the contact module is introducing biased updates.

Figures

Figures reproduced from arXiv: 2605.21863 by Cagri Kilic, Emre Girgin.

Figure 1
Figure 1. Figure 1: Our contact estimation method provides robustness against various [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overall architecture of the proposed method. Our study utilizes IMU for state propagation and corrects the state based on the contact event for each [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 2
Figure 2. Figure 2: A. Preliminaries: Error-State Kalman Filter Design 1) Kinematics: For a single leg i, the forward kinematics fki and Jacobian Jv,i map the joint angles qi ∈ R N and velocities q˙i to the foot’s position p B i and linear velocity v B i in the body frame {B}: p B i = fki(qi), v B i = Jv,i(qi)q˙i . (1) We employ an ESEKF to fuse proprioceptive sensor data, which separates the state into a non-linear nominal s… view at source ↗
Figure 3
Figure 3. Figure 3: Gaussian Mixture Model fitted force histogram for each leg. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Our dataset spans diverse hard (concrete, tile), soft (grass), granular [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Example sequences and method’s predictions are visualized (in meters) and Absolute Trajectory Error (ATE) plots over time. [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The ability to correct drift caused by IMU is governed by the measurement covariance even under identical contact conditions. [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
read the original abstract

One of the significant challenges in legged robotics is achieving accurate odometry using only onboard proprioceptive sensors. In this study, we present a complete leg odometry pipeline based on an Error-State EKF (ESEKF) that relies exclusively on proprioceptive data: a body fixed IMU, joint encoders, and force sensors, where filter's state is corrected by feet determined to be in a stationary stance. The core of our contribution is fused contact detection and an uncertainty quantification module designed to explicitly identify and reject slippage. This module runs two detectors in parallel for each foot, 1) a debounced, force-based Gaussian Mixture Model (GMM) guided Finite State Machine (FSM) to confirm physical contact, and 2) a kinematic-based Generalized Likelihood Ratio Test (GLRT) on the estimated velocity of the foot. The continuous quality scores from both estimators are fused to detect if the foot is both physically loaded and kinematically stationary and served as an uncertainty signal for each contact. To validate our approach, we collected a multi-modal dataset of 29 sequences spanning diverse indoor and outdoor terrains (e.g., concrete, grass, pebble, and rock) total of 2.4 km long. We benchmarked our approach against both proprioceptive and exteroceptive methods. The results demonstrate our method's efficacy in providing accurate odometry estimates, robustly handling slippage-prone environments. We also share our code and real-time ROS2 package as open-source.

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

1 major / 2 minor

Summary. The manuscript presents OCELOT, a proprioceptive odometry pipeline for legged robots that uses an Error-State Extended Kalman Filter (ESEKF) with corrections from feet identified as stationary. The core contribution is a fused contact detection module running a force-based GMM-guided FSM in parallel with a kinematic GLRT on foot velocity; continuous quality scores from both are combined to flag physically loaded and kinematically stationary stances while providing an uncertainty signal to reject slippage. The system is evaluated on a self-collected 2.4 km multi-terrain dataset (concrete, grass, pebble, rock) and benchmarked against both proprioceptive and exteroceptive baselines, with open-source code and ROS2 package released.

Significance. If the fused detector correctly isolates truly stationary stance phases without injecting systematic bias, the approach would strengthen proprioceptive odometry for legged platforms in unstructured environments and reduce dependence on exteroceptive sensors. The scale of the 2.4 km dataset, direct comparisons to baselines, and open-source release are concrete strengths that support reproducibility and further development.

major comments (1)
  1. [Experimental Evaluation] The central claim that the fused GMM-FSM + GLRT module 'robustly handles slippage-prone environments' rests on the assumption that declared stationary intervals contain negligible foot velocity. The experimental section reports aggregate trajectory errors but does not provide per-phase foot-velocity statistics or bias metrics during intervals flagged as stationary by the fused detector (particularly on the pebble/grass/rock sequences). This omission leaves open the possibility that partial-slip cases still contribute to zero-velocity corrections and therefore to the reported accuracy.
minor comments (2)
  1. [Method] The description of how the two continuous quality scores are fused into a single uncertainty signal (Section 3) would benefit from an explicit equation or pseudocode block to clarify the weighting and thresholding logic.
  2. [Figures] Figure captions for the contact-detection timelines should explicitly label which traces correspond to the GMM-FSM output, the GLRT output, and the fused decision to improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback and the recommendation for minor revision. We address the single major comment below.

read point-by-point responses
  1. Referee: [Experimental Evaluation] The central claim that the fused GMM-FSM + GLRT module 'robustly handles slippage-prone environments' rests on the assumption that declared stationary intervals contain negligible foot velocity. The experimental section reports aggregate trajectory errors but does not provide per-phase foot-velocity statistics or bias metrics during intervals flagged as stationary by the fused detector (particularly on the pebble/grass/rock sequences). This omission leaves open the possibility that partial-slip cases still contribute to zero-velocity corrections and therefore to the reported accuracy.

    Authors: We agree that the current manuscript reports only aggregate trajectory errors and does not include per-phase foot-velocity statistics or bias metrics for the intervals classified as stationary by the fused detector. This additional analysis would directly support the claim that the detector isolates truly stationary stances even on slippage-prone terrains. In the revised version we will add a new figure and accompanying table in the experimental section that reports, for each terrain (including pebble, grass, and rock), the mean and standard deviation of foot velocity together with any residual bias during all intervals flagged as stationary. These statistics will be computed from the same dataset used for the trajectory-error evaluation. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the ESEKF odometry derivation

full rationale

The paper describes a standard Error-State Extended Kalman Filter (ESEKF) structure for proprioceptive leg odometry, with the central contribution being the addition of two parallel contact detectors (force-based GMM-FSM and kinematic GLRT) whose continuous quality scores are fused to gate zero-velocity updates. This is an empirical sensor-fusion pipeline whose claimed accuracy on the 2.4 km dataset is validated by benchmarking rather than derived by algebraic reduction to its own fitted parameters or prior self-citations. No equation is shown to equal its input by construction, no prediction is a renamed fit, and the contact logic is presented as an independent module whose correctness is tested externally on diverse terrains. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract only; no explicit free parameters, axioms or invented entities are described. Standard EKF noise covariances and GMM parameters are presumed but not detailed.

pith-pipeline@v0.9.0 · 5795 in / 1163 out tokens · 60355 ms · 2026-05-22T06:10:50.700462+00:00 · methodology

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Reference graph

Works this paper leans on

36 extracted references · 36 canonical work pages · 1 internal anchor

  1. [1]

    Legged robots

    Claudio Semini and Pierre-Brice Wieber. Legged robots. InEncyclo- pedia of Robotics, pages 1–8. Springer, 2020

  2. [2]

    Into the robotic depths: Analysis and insights from the darpa subterranean challenge.Annual Review of Control, Robotics, and Autonomous Systems, 6(1):477–502, 2023

    Timothy H Chung, Viktor Orekhov, and Angela Maio. Into the robotic depths: Analysis and insights from the darpa subterranean challenge.Annual Review of Control, Robotics, and Autonomous Systems, 6(1):477–502, 2023

  3. [3]

    Leg odometry for SLAM

    Marco Camurri and Matias Mattamala. Leg odometry for SLAM. In Luca Carlone, Ayoung Kim, Timothy Barfoot, Daniel Cremers, and Frank Dellaert, editors,SLAM Handbook. From Localization and Mapping to Spatial Intelligence. Cambridge University Press, 2026

  4. [4]

    Dead reckoning navigation for walking robots

    Gerald P Roston and Eric P Krotkov. Dead reckoning navigation for walking robots. Technical report, 1991

  5. [5]

    State estimation for legged robots-consistent fusion of leg kinematics and imu.Robotics, 17:17–24, 2013

    Michael Bloesch, Marco Hutter, Mark A Hoepflinger, Stefan Leuteneg- ger, Christian Gehring, C David Remy, and Roland Siegwart. State estimation for legged robots-consistent fusion of leg kinematics and imu.Robotics, 17:17–24, 2013

  6. [6]

    Zero-velocity detection—an algorithm evaluation.IEEE transactions on biomedical engineering, 57(11):2657–2666, 2010

    Isaac Skog, Peter Handel, John-Olof Nilsson, and Jouni Rantakokko. Zero-velocity detection—an algorithm evaluation.IEEE transactions on biomedical engineering, 57(11):2657–2666, 2010

  7. [7]

    State estimation for legged robots on unstable and slippery terrain

    Michael Bloesch, Christian Gehring, P ´eter Fankhauser, Marco Hutter, Mark A Hoepflinger, and Roland Siegwart. State estimation for legged robots on unstable and slippery terrain. In2013 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages 6058–6064. IEEE, 2013

  8. [8]

    Left-invariant extended kalman filter and attitude estimation

    Silvere Bonnabel. Left-invariant extended kalman filter and attitude estimation. In2007 46th IEEE Conference on Decision and Control, pages 1027–1032. IEEE, 2007

  9. [9]

    The invariant extended kalman filter as a stable observer.IEEE Transactions on Automatic Control, 62(4):1797–1812, 2016

    Axel Barrau and Silvere Bonnabel. The invariant extended kalman filter as a stable observer.IEEE Transactions on Automatic Control, 62(4):1797–1812, 2016

  10. [10]

    Legged robot state-estimation through combined forward kinematic and preinte- grated contact factors

    Ross Hartley, Josh Mangelson, Lu Gan, Maani Ghaffari Jadidi, Jef- frey M Walls, Ryan M Eustice, and Jessy W Grizzle. Legged robot state-estimation through combined forward kinematic and preinte- grated contact factors. In2018 IEEE International Conference on Robotics and Automation (ICRA), pages 4422–4429. IEEE, 2018

  11. [11]

    Contact-Aided Invariant Extended Kalman Filtering for Legged Robot State Estimation

    Ross Hartley, Maani Ghaffari Jadidi, Jessy W Grizzle, and Ryan M Eustice. Contact-aided invariant extended kalman filtering for legged robot state estimation.arXiv preprint arXiv:1805.10410, 2018

  12. [12]

    Legged robot state estimation in slippery environments using invariant ex- tended kalman filter with velocity update

    Sangli Teng, Mark Wilfried Mueller, and Koushil Sreenath. Legged robot state estimation in slippery environments using invariant ex- tended kalman filter with velocity update. In2021 IEEE International Conference on Robotics and Automation (ICRA), pages 3104–3110. IEEE, 2021

  13. [13]

    Contact-aided invariant extended kalman filtering for legged robot state estimation

    Ross Hartley, Maani Ghaffari Jadidi, Jessy Grizzle, and Ryan M Eustice. Contact-aided invariant extended kalman filtering for legged robot state estimation. InProceedings of Robotics: Science and Systems, Pittsburgh, Pennsylvania, June 2018

  14. [14]

    Proprio- ceptive state estimation for quadruped robots using invariant kalman filtering and scale-variant robust cost functions

    Hilton Marques Souza Santana, Jo ˜ao Carlos Virgolino Soares, Ylenia Nistic`o, Marco Antonio Meggiolaro, and Claudio Semini. Proprio- ceptive state estimation for quadruped robots using invariant kalman filtering and scale-variant robust cost functions. In2024 IEEE-RAS 23rd International Conference on Humanoid Robots (Humanoids), pages 213–220. IEEE, 2024

  15. [15]

    Adaptive invariant extended kalman filter for legged robot state estimation

    Kyung-Hwan Kim, DongHyun Ahn, Dong-hyun Lee, JuYoung Yoon, and Dong Jin Hyun. Adaptive invariant extended kalman filter for legged robot state estimation. In2025 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 3063–

  16. [16]

    Legged robot state estimation with dynamic contact event information.IEEE Robotics and Automation Letters, 6(4):6733–6740, 2021

    Joon-Ha Kim, Seungwoo Hong, Gwanghyeon Ji, Seunghun Jeon, Jemin Hwangbo, Jun-Ho Oh, and Hae-Won Park. Legged robot state estimation with dynamic contact event information.IEEE Robotics and Automation Letters, 6(4):6733–6740, 2021

  17. [17]

    Invariant smoother for legged robot state estimation with dynamic contact event information

    Ziwon Yoon, Joon-Ha Kim, and Hae-Won Park. Invariant smoother for legged robot state estimation with dynamic contact event information. IEEE Transactions on Robotics, 40:193–212, 2023

  18. [18]

    Learning inertial odometry for dynamic legged robot state estimation

    Russell Buchanan, Marco Camurri, Frank Dellaert, and Maurice Fallon. Learning inertial odometry for dynamic legged robot state estimation. InConference on robot learning, pages 1575–1584. PMLR, 2022

  19. [19]

    Legolas: Deep leg-inertial odometry

    Justin Wasserman, Ananye Agarwal, Rishabh Jangir, Girish Chowd- hary, Deepak Pathak, and Abhinav Gupta. Legolas: Deep leg-inertial odometry. In8th Annual Conference on Robot Learning, 2024

  20. [20]

    Drift-free humanoid state estimation fusing kinematic, inertial and lidar sensing

    Maurice F Fallon, Matthew Antone, Nicholas Roy, and Seth Teller. Drift-free humanoid state estimation fusing kinematic, inertial and lidar sensing. In2014 IEEE-RAS International Conference on Hu- manoid Robots, pages 112–119. IEEE, 2014

  21. [21]

    Unsupervised contact learning for humanoid estimation and control

    Nicholas Rotella, Stefan Schaal, and Ludovic Righetti. Unsupervised contact learning for humanoid estimation and control. In2018 IEEE International Conference on Robotics and Automation (ICRA), pages 411–417. IEEE, 2018

  22. [22]

    Probabilistic contact estimation and impact detection for state esti- mation of quadruped robots.IEEE Robotics and Automation Letters, 2(2):1023–1030, 2017

    Marco Camurri, Maurice Fallon, St ´ephane Bazeille, Andreea Rad- ulescu, Victor Barasuol, Darwin G Caldwell, and Claudio Semini. Probabilistic contact estimation and impact detection for state esti- mation of quadruped robots.IEEE Robotics and Automation Letters, 2(2):1023–1030, 2017

  23. [23]

    Dynamic locomotion on slippery ground.IEEE Robotics and Automation Letters, 4(4):4170–4176, 2019

    Fabian Jenelten, Jemin Hwangbo, Fabian Tresoldi, C Dario Bellicoso, and Marco Hutter. Dynamic locomotion on slippery ground.IEEE Robotics and Automation Letters, 4(4):4170–4176, 2019

  24. [24]

    Multi-imu proprioceptive odometry for legged robots

    Shuo Yang, Zixin Zhang, Benjamin Bokser, and Zachary Manchester. Multi-imu proprioceptive odometry for legged robots. In2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 774–779. IEEE, 2023

  25. [25]

    Doglegs: Robust proprioceptive state estimation for legged robots using multiple leg- mounted imus.arXiv preprint arXiv:2503.04580, 2025

    Yibin Wu, Jian Kuang, Shahram Khorshidi, Xiaoji Niu, Lasse Kling- beil, Maren Bennewitz, and Heiner Kuhlmann. Doglegs: Robust proprioceptive state estimation for legged robots using multiple leg- mounted imus.arXiv preprint arXiv:2503.04580, 2025

  26. [26]

    Legged robot state estimation using invariant kalman filtering and learned contact events.arXiv preprint arXiv:2106.15713, 2021

    Tzu-Yuan Lin, Ray Zhang, Justin Yu, and Maani Ghaffari. Legged robot state estimation using invariant kalman filtering and learned contact events.arXiv preprint arXiv:2106.15713, 2021

  27. [27]

    Legged robot state estimation with invariant extended kalman filter using neural measurement network

    Donghoon Youm, Hyunsik Oh, Suyoung Choi, Hyeongjun Kim, Se- unghun Jeon, and Jemin Hwangbo. Legged robot state estimation with invariant extended kalman filter using neural measurement network. In2025 IEEE International Conference on Robotics and Automation (ICRA), pages 670–676. IEEE, 2025

  28. [28]

    Evidential deep learning to quantify classification uncertainty.Advances in neural information processing systems, 31, 2018

    Murat Sensoy, Lance Kaplan, and Melih Kandemir. Evidential deep learning to quantify classification uncertainty.Advances in neural information processing systems, 31, 2018

  29. [29]

    Leg-kilo: Robust kinematic- inertial-lidar odometry for dynamic legged robots.IEEE Robotics and Automation Letters, 9(10):8194–8201, 2024

    Guangjun Ou, Dong Li, and Hanmin Li. Leg-kilo: Robust kinematic- inertial-lidar odometry for dynamic legged robots.IEEE Robotics and Automation Letters, 9(10):8194–8201, 2024

  30. [30]

    Co-ral: Com- plementary radar-leg odometry with 4-dof optimization and rolling contact

    Sangwoo Jung, Wooseong Yang, and Ayoung Kim. Co-ral: Com- plementary radar-leg odometry with 4-dof optimization and rolling contact. In2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 13289–13296. IEEE, 2024

  31. [31]

    Cerberus: Low-drift visual-inertial-leg odometry for agile locomotion

    Shuo Yang, Zixin Zhang, Zhengyu Fu, and Zachary Manchester. Cerberus: Low-drift visual-inertial-leg odometry for agile locomotion. In2023 IEEE International Conference on Robotics and Automation (ICRA), pages 4193–4199. IEEE, 2023

  32. [32]

    A micro lie theory for state estimation in robotics,

    Joan Sola, Jeremie Deray, and Dinesh Atchuthan. A micro lie theory for state estimation in robotics.arXiv preprint arXiv:1812.01537, 2018

  33. [33]

    Openvins: A research platform for visual-inertial estimation

    Patrick Geneva, Kevin Eckenhoff, Woosik Lee, Yulin Yang, and Guoquan Huang. Openvins: A research platform for visual-inertial estimation. In2020 IEEE International Conference on Robotics and Automation (ICRA), pages 4666–4672. IEEE, 2020

  34. [34]

    A general optimization-based framework for local odometry estimation with multiple sensors, 2019

    Tong Qin, Jie Pan, Shaozu Cao, and Shaojie Shen. A general optimization-based framework for local odometry estimation with multiple sensors, 2019

  35. [35]

    Extending kalibr: Calibrating the extrinsics of multiple imus and of individual axes

    Joern Rehder, Janosch Nikolic, Thomas Schneider, Timo Hinzmann, and Roland Siegwart. Extending kalibr: Calibrating the extrinsics of multiple imus and of individual axes. In2016 IEEE international conference on robotics and automation (ICRA), pages 4304–4311. IEEE, 2016

  36. [36]

    Challenges for monocular 6-d object pose estimation in robotics.IEEE Transactions on Robotics, 40:4065–4084, 2024

    Stefan Thalhammer, Dominik Bauer, Peter H ¨onig, Jean-Baptiste Weibel, Jose Garcia-Rodriguez, and Markus Vincze. Challenges for monocular 6-d object pose estimation in robotics.IEEE Transactions on Robotics, 40:4065–4084, 2024