💻 computer science

Learning Contact Representation for Leg Odometry

This paper proposes a self-supervised representation learning framework that utilizes standard joint encoder data to accurately detect leg contact phases for odometry estimation, outperforming both supervised methods requiring force sensors and baseline probabilistic approaches without the need for additional hardware or manual labeling.

Original authors: Emre Girgin, Cagri Kilic

Published 2026-06-05

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Emre Girgin, Cagri Kilic

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a four-legged robot trying to walk across a bumpy field of rocks, grass, and concrete. To know where it is, the robot needs to figure out a very specific question: "Is my foot firmly planted on the ground right now, or is it swinging through the air?"

If the foot is planted, the robot knows that part of its body isn't moving relative to the ground. It can use that moment to "reset" its internal map and correct any drift or confusion. If the foot is swinging, that information is useless for correcting its position.

The problem is that robots often don't have fancy, expensive pressure sensors in their feet to tell them if they are touching the ground. They only have sensors in their joints (like knowing how much their knee is bent or how fast it's moving).

This paper presents a new, clever way for the robot to learn this "foot-touching" skill on its own, without needing a human to teach it or extra sensors.

The Old Way: Guessing with a Hard Rule

Traditionally, robots tried to guess if a foot was on the ground by looking at joint movements and drawing a straight line: "If the foot is low enough, it's touching. If it's high, it's swinging."

Think of this like trying to identify a cat by only looking at its tail. Sometimes a cat's tail is low (sitting), and sometimes it's high (walking). But if you only look at the tail height, you might mistake a sleeping cat for a walking one, or vice versa. This method is too rigid and gets confused easily, especially if the robot slips or the ground is squishy.

The New Way: Learning the "Vibe" of the Foot

The authors propose a system that acts like a musical ear rather than a ruler. Instead of looking for a specific height, the robot learns the "shape" or "vibe" of the data when the foot is touching versus when it's swinging.

Here is how their system works, step-by-step:

1. The "Noise-Canceling" Ear (The Denoising Autoencoder)
Imagine you are trying to learn a song, but someone keeps playing static noise over the music. A Denoising Autoencoder is like a smart student who listens to the noisy song and tries to reconstruct the original, clean melody from memory.

The robot feeds it messy joint data (the noisy song).
The robot tries to recreate the clean movement pattern (the melody).
To do this successfully, the robot must learn the underlying rules of how the leg moves. It naturally separates the "planted" movements from the "swinging" movements in its internal memory, even though no one told it which was which.

2. The "Two-Cloud" Map (The Gaussian Mixture Model)
Once the robot has learned these clean patterns, it looks at its internal memory. It sees that the data naturally forms two distinct clouds:

Cloud A: The "Stance" cloud (foot on ground).
Cloud B: The "Swing" cloud (foot in air).
Instead of drawing a hard line between them, the robot calculates a probability. It says, "I am 90% sure this is Cloud A (Stance), but maybe 10% it's Cloud B."

3. The Smart Filter (The ESEKF)
This probability is fed into the robot's navigation brain (a Kalman Filter).

If the robot is 90% sure the foot is planted: The brain says, "Okay, I trust this data! Let's use it to fix my map."
If the robot is only 40% sure (maybe the foot is slipping or just about to land): The brain says, "I'm not sure. I'll listen to this data, but I won't let it change my map too much."
If the robot is 0% sure (foot is swinging): The brain ignores the data completely.

Why This is Better

The paper tested this on a simulation and a real robot walking on concrete, grass, and rocks.

The "Teacher" Problem: Other methods tried to teach the robot by showing it "Ground Truth" (using force sensors to say "Yes, touching" or "No, not touching"). But these sensors are noisy and can be fooled by slips. The robot learned to memorize the teacher's mistakes.
The "Self-Taught" Advantage: The new method didn't need a teacher. It just learned the physics of the movement.
- Result: When the robot slipped, the "teacher-trained" robots got confused and thought they were still standing, leading to big navigation errors. The "self-taught" robot realized, "Wait, the movement pattern doesn't look like a solid stance," and ignored the bad data.

The Takeaway

The authors found that you don't need to force the robot to make a binary "Yes/No" decision about the ground. Instead, by letting the robot learn the shape of the movement data on its own, it can make a smooth, confident guess about whether to trust its feet. This makes the robot much more stable and accurate, even on rough terrain, without needing expensive extra sensors.

In short: Don't ask the robot "Is the foot down?" (Yes/No). Ask it "How much does this movement look like a foot being down?" (0% to 100%). The robot figured out the answer all by itself.

Technical Summary: Learning Contact Representation for Leg Odometry

Problem Statement

Legged robot odometry fundamentally relies on the assumption that the foot velocity relative to the world is zero during the stance phase, a constraint known as Zero-Velocity Update (ZUPT). This assumption allows kinematic chains to correct the main body's velocity drift. However, the accuracy of the entire state estimation pipeline is bounded by the precision of the contact detection algorithm.

Current approaches face significant challenges:

Sensor Limitations: Many methods rely on Ground Reaction Force (GRF) sensors at the foot tip. These sensors are prone to mechanical failure, shock-induced noise, and are often absent on minimal-sensor deployed platforms.
Slippage and Disturbances: Even when GRF sensors are present, they may remain unresponsive to unmodeled disturbances like slippage while the foot is in contact with the ground.
Binary Classification Flaws: Treating contact as a binary state (stance vs. swing) oversimplifies complex foot-terrain interactions. Hard thresholds often fail to account for transient phases (lift-off/touch-down) or sensor noise, leading to incorrect measurement updates in state estimators.
Label Dependency: Supervised learning approaches require pseudo-labels derived from GRF data, which inherit the noise and limitations of the force sensors themselves.

Methodology

The authors propose a self-supervised representation learning framework that utilizes only standard proprioceptive sensors (joint encoders) to detect contact, eliminating the need for force sensor augmentation or human labeling.

1. State Estimation Framework

The system employs an Error-State Extended Kalman Filter (ESEKF). Instead of filtering nominal states directly, it decouples the system into a non-linear nominal state and a linear error state. The filter uses a measurement function based on the predicted world-frame velocity of the stance foot. Crucially, the measurement covariance matrix is dynamically scaled based on the continuous probability of the stance state, rather than using a constant covariance or hard threshold.

2. Contact Detection Architectures

The study compares three distinct approaches to contact detection:

Unsupervised Baseline (HMM-GMM): A Hidden Markov Model (HMM) where emission probabilities are modeled by a Gaussian Mixture Model (GMM) fitted directly to raw kinematic data (vertical foot position, 3D foot velocity, and calf torque). This approach is limited by the assumption that raw kinematic data follows a bimodal Gaussian distribution, which the authors demonstrate is often not the case due to non-linear intersections between stance and swing manifolds.
Supervised Baselines (CNN/GRU): Deep neural networks (1D CNN and Gated Recurrent Unit) trained via Binary Cross-Entropy loss. These models use GRF-derived pseudo-labels as ground truth to map kinematics to binary contact states.
Proposed Self-Supervised Framework (DAE-GMM):
- Denoising Autoencoder (DAE): A neural network (CNN or GRU based) is trained to reconstruct the original kinematic sequence from a noisy, augmented version of the input. The objective is to learn a latent representation ( $Z$ ) where the underlying physical states (stance vs. swing) are naturally disentangled.
- Latent Space Modeling: The latent codes produced by the encoder are fitted with an unsupervised 2-component GMM. This isolates the physical contact modes into distinct probabilistic manifolds.
- Continuous Belief: Unlike binary classifiers, this framework outputs a continuous posterior probability of the stance state. This probability is used to scale the measurement covariance in the ESEKF, allowing the filter to dynamically reject unreliable kinematic data (e.g., during swing or slippage) without hard thresholds.

3. Input Features

To avoid the "curse of dimensionality" and ill-conditioned covariance matrices, the models utilize a specific 5D subset of features:

Vertical foot position relative to the base ( $p^B_{foot,z}$ ).
3D foot velocity estimated by forward kinematics ( $v^B_{rel}$ ).
Estimated calf torque ( $\tau_{calf}$ ).

Key Contributions

Label-Free Representation Learning: A self-supervised framework that extracts continuous contact probabilities strictly from joint kinematics without relying on GRF sensors or pseudo-labels.
Dynamic ESEKF Formulation: A measurement uncertainty model driven by the latent generative belief, which scales the measurement covariance matrix dynamically rather than using static thresholds.
Empirical Validation of Probability Density Estimation: Evidence suggesting that contact detection is better formulated as a self-supervised probability density estimation task rather than a supervised binary classification task. The study demonstrates that superior classification accuracy on pseudo-labels does not necessarily correlate with better downstream odometry performance.

Experimental Results

The framework was evaluated on the TartanGround simulation dataset and a real-world dataset involving concrete, grass, and rock terrains.

Classification vs. Odometry: While supervised models (CNN/GRU) achieved higher classification metrics (Precision/Recall/F1) against GRF-based pseudo-labels, they underperformed in downstream leg odometry tasks compared to the proposed self-supervised methods.
Slippage Robustness: In scenarios involving slippage, supervised models tended to overestimate the stance duration because they relied on noisy GRF signals. The self-supervised DAE methods correctly identified the lack of reliable stance, producing near-zero stance probabilities during unstable contact, thereby preventing erroneous state corrections.
Odometry Accuracy: The proposed DAE (CNN) and DAE (GRU) methods achieved the lowest Absolute Trajectory Error (ATE), Absolute Heading Error (AHE), and other error metrics in both simulation and real-world tests.
- In real-world tests, the DAE (CNN) reduced ATE to 17.20m compared to 21.95m for the best supervised CNN and 25.36m for GRF thresholding.
Temporal Context: Ablation studies revealed that increasing the input window size caused the latent space to form a non-linear ring manifold due to periodic gait dynamics, which degraded GMM performance. Consequently, a window size of $W=1$ was found to be optimal for preserving a linearly separable latent space.

Significance and Claims

The paper claims that formulating contact detection as a self-supervised continuous probability density estimation task is a more robust approach than supervised binary classification for legged odometry.

Hardware Agnosticism: The method enables robust state estimation on robots lacking force sensors, relying solely on standard joint encoders.
Handling Uncertainty: By outputting a continuous belief rather than a binary state, the system can better handle the inherent ambiguity of foot-terrain interactions, such as slippage and compliance, which binary classifiers often misinterpret.
Generalization: The self-supervised approach avoids the domain shift issues associated with training on noisy GRF pseudo-labels, leading to better generalization in real-world environments.

The authors conclude that while binary contact classification is fundamentally ill-posed due to unmodeled dynamics, a probabilistic, self-supervised approach provides a superior foundation for downstream state estimation.