Technical Summary: OCELOT – Odometry and Contact Estimation for Legged Robots

Problem Statement

Accurate odometry for legged robots in unstructured and uneven terrains remains a significant challenge, particularly when relying solely on onboard proprioceptive sensors (IMU, joint encoders, and force sensors). Unlike wheeled robots, legged systems experience intermittent contact dynamics where feet cyclically make and break contact with the ground. The fundamental limitation of proprioceptive leg odometry is the unobservability of absolute position and heading when relying exclusively on body-fixed sensors. While Error-State Extended Kalman Filters (ESEKF) are the dominant framework for propagating state via Inertial Navigation Systems (INS) and correcting drift using Zero Velocity Updates (ZUPTs), their efficacy is contingent upon accurately identifying when a foot is in a stationary "stance" phase. Existing contact estimation methods often struggle with foot slippage, fail to adapt to varying terrain characteristics, or rely on supplementary hardware (e.g., foot-mounted IMUs) and learning-based classifiers that lack calibrated uncertainty.

Methodology

The paper proposes OCELOT, a complete leg odometry pipeline based on an ESEKF that relies exclusively on standard proprioceptive data: a body-fixed IMU, joint encoders, and foot force sensors. The core innovation lies in a fused contact detection and uncertainty quantification module designed to explicitly identify and reject slippage.

1. State Estimation Framework

The system employs an ESEKF where the state is separated into a non-linear nominal state (position, velocity, orientation, IMU biases) and a linear error state.

• Propagation: The nominal state is propagated using bias-corrected IMU measurements via Euler integration.
• Correction: The filter corrects drift when a foot is determined to be in stance, assuming the foot's velocity relative to the world frame is zero ($v^W_{foot} = 0$).

2. Fused Contact Detection

To robustly determine stance phases, the system runs two parallel detectors for each foot and fuses their outputs:

• Detector 1: Force-Based GMM-Guided FSM

  • Utilizes Ground Reaction Force (GRF) data to determine physical contact.
  • Instead of fixed thresholds, it employs a Gaussian Mixture Model (GMM) fitted to a sliding window of historical force data to autonomously identify bimodal distributions (swing vs. stance).
  • A Finite State Machine (FSM) uses dynamically generated thresholds ($F_{on}$, $F_{off}$) to manage state transitions, adapting to different surface characteristics without manual tuning.
  • Outputs a continuous quality score ($q_{FSM}$) representing the likelihood of physical loading.

• Detector 2: Kinematic-Based GLRT

  • Utilizes the estimated foot velocity derived from the body IMU and joint kinematics.
  • Applies a Generalized Likelihood Ratio Test (GLRT) to evaluate the hypothesis that the foot is stationary ($H_0$) versus moving ($H_1$).
  • Unlike prior works requiring foot-mounted IMUs, this method relies solely on the main body IMU and kinematic models.
  • Outputs a continuous quality score ($q_{GLRT}$) representing kinematic stationarity.

3. Adaptive Uncertainty Quantification

The two scores are fused using a multiplicative "soft AND-gate" ($q_{final} = q_{FSM} \times q_{GLRT}$). This ensures a high confidence score only when the foot is both physically loaded and kinematically stationary.

• Dynamic Covariance: The fused score is used to compute an adaptive measurement noise covariance matrix ($R_i$) for the ESEKF.
  • High confidence (non-slip) $\rightarrow$ Low covariance (strong correction).
  • Low confidence (slip or noise) $\rightarrow$ High covariance (filter down-weights the measurement).
• Gating: An innovation-based gating step ($\chi^2$ test) further rejects statistical outliers before the final correction.

Key Contributions

1. Novel Contact Detection Framework: A fusion of a force-based GMM-FSM and a kinematic GLRT detector that eliminates the need for supplementary foot-mounted sensors while generating a continuous contact quality score.
2. Adaptive Uncertainty Estimation: A method to translate the fused contact quality score into a dynamic measurement covariance ($R_i$), allowing the ESEKF to intelligently weight measurements based on reliability and robustly reject slip events.
3. Open-Source ESEKF Pipeline: A complete state estimator for quadruped leg odometry using only onboard proprioceptive sensors.
4. Multi-Terrain Dataset: A publicly available dataset comprising 29 sequences (2.4 km total) across diverse terrains (concrete, tile, grass, pebble, rock), including synchronized proprioceptive data, RGB video, and point clouds.

Experimental Results

The authors evaluated OCELOT against seminal proprioceptive baselines (Bloesch et al., Hartley et al.) and state-of-the-art Visual-Inertial Odometry (VIO) systems (OpenVINS, VINS-Fusion) on their custom dataset.

• Proprioceptive Comparison: OCELOT significantly outperformed existing proprioceptive methods across all terrain types and metrics (ATE, AHE, RPE, Drift).
  • On Rock terrain, OCELOT achieved an Absolute Trajectory Error (ATE) of 6.857 m, compared to 15.028 m (Hartley et al.) and 30.876 m (Bloesch et al.).
  • On Concrete, OCELOT reduced ATE to 12.019 m, a substantial improvement over the baselines.
• Exteroceptive Comparison: Despite using only proprioceptive sensors, OCELOT outperformed VIO systems on challenging granular terrains (pebble, rock) and deformable surfaces (grass).
  • On Rock, VIO systems failed significantly (OpenVINS ATE: 27.279 m; VINS-Fusion: 15.719 m), whereas OCELOT maintained an ATE of 6.857 m.
  • The authors note that VIO systems struggled on highly dynamic, feature-poor surfaces (concrete, tile), leading to divergence, whereas OCELOT remained robust.
• Ablation Studies:
  • Fusion Necessity: The ablation study demonstrated that neither detector alone is sufficient. The GLRT-only detector suffered from accumulated kinematic noise on long trajectories (e.g., 23.161 m ATE on concrete), while the FSM-only detector failed on specific sequences (e.g., 9.577 m ATE on Tile) where force data alone misclassified contact. The fused model consistently achieved the lowest or near-lowest error across all terrains.
  • Covariance Impact: Sensitivity analysis confirmed that accurate covariance quantification is critical; underestimating covariance (forcing high trust in noisy data) led to severe lateral drift and yaw divergence, a failure mode observed in baseline methods that used static or poorly scaled covariances.

Significance and Claims

The paper claims that OCELOT provides a robust solution for legged odometry in environments where slippage is prevalent and external sensors (like cameras) may fail due to lack of features or dynamic lighting. By explicitly modeling contact uncertainty and fusing force and kinematic data, the method achieves accurate state estimation without the computational overhead of visual processing or the hardware complexity of foot-mounted sensors. The authors emphasize that their approach effectively handles the "unobservability" problem of absolute heading in proprioceptive systems by ensuring that only high-quality, non-slip measurements are used to correct the filter, thereby preventing the yaw divergence common in other methods. The release of the dataset and code aims to facilitate further research in legged robotics and multi-modal odometry.