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arxiv: 2605.23100 · v1 · pith:U7VYU2XOnew · submitted 2026-05-21 · 💻 cs.RO

Four Simple Proprioceptive Estimators for Legged Robots

Frank Dellaert , Chiyun Noh , Varun Agrawal , Ayoung Kim This is my paper

Pith reviewed 2026-05-25 05:12 UTC · model grok-4.3

classification 💻 cs.RO
keywords legged robotsproprioceptive estimationIMU driftfoot contactsstate estimationfactor graphsfixed-lag smoothingodometry
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The pith

Four proprioceptive estimators for legged robots use foot contacts to mitigate IMU drift.

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

The paper develops four increasingly expressive estimators for the floating-base state of legged robots, which includes attitude, position, velocity, and IMU biases. These estimators use intermittent foot contacts with the environment to correct for the drift that occurs in consumer-grade inertial measurement units. The sequence starts with a contact-aided invariant extended Kalman filter at a reduced update rate, then replaces the update with a small factor graph, and finally applies fixed-lag smoothing over contact episodes with optional evolving bias. This sequence is presented to support proprioceptive odometry in legged systems.

Core claim

The paper claims that modeling foot contacts as zero-velocity or foothold constraints within a sequence of estimators from extended Kalman filter through factor graph to fixed-lag smoother allows effective mitigation of inertial drift for accurate estimation of attitude, position, velocity, and biases in legged robots.

What carries the argument

Foot contact constraints incorporated into invariant EKF, factor graph, and fixed-lag smoother formulations for state estimation.

If this is right

  • The estimators maintain performance even when contact updates occur at a reduced rate.
  • Replacing measurement updates with factor graphs provides a more flexible modeling approach.
  • Fixed-lag smoothers can handle contact-episode footholds with or without an evolving IMU bias.
  • All variants share the same floating-base state representation.

Where Pith is reading between the lines

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

  • Such estimators could be tested for robustness across different terrains where contact detection varies in reliability.
  • The methods may serve as a baseline for comparing more advanced sensor fusion techniques in legged locomotion.
  • Extending the smoother to longer lag windows might further reduce accumulated errors in extended operations.

Load-bearing premise

Foot contacts can be reliably detected and provide useful constraints when modeled at a reduced contact update rate.

What would settle it

Running the estimators on data where foot contact detection is intentionally degraded or absent, showing no improvement over standard inertial navigation alone.

Figures

Figures reproduced from arXiv: 2605.23100 by Ayoung Kim, Chiyun Noh, Frank Dellaert, Varun Agrawal.

Figure 1
Figure 1. Figure 1: Local graph update for the invariant filter. The predicted semidirect-product state [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Fixed-lag smoother with a single persistent bias variable. Each [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Evolving-bias inertial structure. The combined preintegrated factors connect neighboring base [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Experimental platform used in the GaRLILEO dataset. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Representative trajectory comparisons of the four GTSAM variants on (a) the CorriLoop sequence [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
read the original abstract

Legged robots carry an IMU, but the inertial solution drifts because consumer-grade IMUs are noisy. However, the feet create intermittent contacts with the environment that can be used to mitigate that drift. This report develops a sequence of increasingly expressive legged robot state estimators that leverage this. In all cases, the floating-base state comprises attitude, position, velocity, and IMU biases. To model foot contacts, we start from the contact-aided invariant EKF of Hartley et al., albeit at a reduced contact update rate. This is then augmented by replacing the measurement update by a small factor graph. Finally, we turn the same factors into a fixed-lag smoother with contact-episode footholds, with and without an evolving IMU bias. To facilitate reproducibility and further research in proprioceptive legged odometry, all four variants are available in GTSAM (Dellaert et. al), and we additionally provide a ROS2-compatible implementation.

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 / 3 minor

Summary. The manuscript presents four proprioceptive floating-base state estimators for legged robots that use intermittent foot contacts to mitigate IMU drift. The floating-base state includes attitude, position, velocity, and IMU biases. The sequence begins with the contact-aided invariant EKF of Hartley et al. (at reduced contact update rate), then replaces the measurement update with a small factor graph, and finally formulates the same factors as a fixed-lag smoother using contact-episode footholds (with and without evolving IMU bias). All four variants, plus a ROS2-compatible implementation, are released in GTSAM to support reproducibility in legged odometry.

Significance. If the released implementations match the described factors, the paper supplies accessible, open-source tools that build directly on established contact-aided methods. The incremental progression from EKF to factor graph to fixed-lag smoother provides clear implementation guidance for the robotics community, and the GTSAM release is a concrete contribution to reproducibility.

minor comments (3)
  1. Abstract: the claim of 'increasingly expressive' estimators would be strengthened by a one-sentence note on the computational trade-offs or intended deployment scenarios for each variant.
  2. The reduced contact update rate relative to Hartley et al. is mentioned but not quantified; a brief statement of the chosen rate and its rationale would improve clarity without altering the central contribution.
  3. Ensure the bibliography entry for Dellaert et al. (GTSAM) includes the most recent version or DOI for completeness.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive review and recommendation to accept. The summary accurately captures the manuscript's contributions regarding the sequence of contact-aided estimators and the open GTSAM implementations.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's derivation chain begins with the externally cited contact-aided invariant EKF of Hartley et al. and incrementally replaces its update step with factor-graph and fixed-lag smoother formulations whose factors are standard GTSAM primitives. No equation reduces to a self-definition, no fitted parameter is relabeled as a prediction, and the sole self-citation (to the GTSAM library) is merely for the open-source implementation rather than a load-bearing theoretical premise. The central claim is availability of four variants, which is independent of any internal loop.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on the domain assumption that foot contacts provide usable constraints and on the prior method of Hartley et al.; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Foot contacts can be detected and used to provide intermittent constraints that mitigate IMU drift
    Inherited from the contact-aided invariant EKF of Hartley et al. and used as the basis for all four estimators.

pith-pipeline@v0.9.0 · 5693 in / 1300 out tokens · 22920 ms · 2026-05-25T05:12:10.746406+00:00 · methodology

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Reference graph

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