Contact-Anchored Proprioceptive Odometry

• Contact-anchored proprioceptive odometry is a method that uses foot contact events as fixed anchors to correct drifting inertial estimates in legged robots.
• It integrates inertial sensing, joint encoder data, and online contact detection to provide robust state estimates in challenging, GPS-denied environments.
• Various frameworks—including filtering, factor-graph optimization, and learning-based pipelines—demonstrate improved accuracy and cross-platform performance across diverse terrains.

Contact-anchored proprioceptive odometry is a family of state estimation methodologies for legged—especially multi-limbed—robots operating in perceptually challenging or GPS-denied environments. The central premise is to fuse inertial sensing, joint encoder data, and online contact detection to leverage the intermittent but spatially precise positional constraints induced by stable ground contacts. By treating each reliable footfall or contact event as a kinematic anchor, the estimator suppresses unbounded drift from inertial integration and resolves otherwise unobservable global states (such as elevation and yaw), thereby providing odometry robust to exteroceptive sensor outage, high dynamic motion, and unstructured terrain. This approach encompasses a diverse range of filtering, factor-graph, and learning-based pipelines, each explicitly modeling both the hybrid contact process and the associated kinematic/dynamic coupling, as found in classical works such as COCLO (Yang et al., 2019) and in recent advances including CAPO (Sun et al., 19 Feb 2026), The Kinetics Observer (Demont et al., 2024), and multi-IMU/leg frameworks (Wu et al., 6 Mar 2025, Xavier et al., 2023).

1. State Representations and Contact Modeling

Contact-anchored proprioceptive odometry frameworks extend the standard inertial navigation state to include not only the robot base pose and velocity (e.g., $(\mathbf p_{WB}, \mathbf v_{WB}, \mathbf R_{WB})$), but also a set of latent or explicit contact variables. The contact state may be realized as:

• Discrete or probabilistic contact flags per leg/point (e.g., $c^i \in \{0,1\}$ or $[0,1]$), detected via thresholding on estimated wrenches (Sun et al., 19 Feb 2026, Yang et al., 2019), learned classifiers over proprioceptive data (Lin et al., 2021), or zero-velocity GLRT tests on foot-mounted IMUs (Wu et al., 6 Mar 2025).
• Footfall/world anchor points: The world-frame position of each contact (e.g., $\mathbf c^W_i$ in CAPO), recorded on every touchdown event and held fixed during stance.
• Augmented state for rest or reaction pose: The Kinetics Observer tracks both current and rest poses of contacts, as well as their associated reaction forces and wrenches (Demont et al., 2024).

Filtering approaches such as SR-UKF (Yang et al., 2019), MEKF (Demont et al., 2024), invariant EKF (Lin et al., 2021), and multi-sensor EKF (Wu et al., 6 Mar 2025, Xavier et al., 2023) propagate the state and correct by imposing contact-induced velocity, position, or force constraints. Factor-graph methods treat contact points as trajectory landmarks (Agrawal et al., 2022), introducing explicit zero-velocity or point-anchoring factors. Learning-based and hybrid methods incorporate detected contact states as side channels or as constraints applied within MLP or autoregressive architectures (Luo et al., 24 Nov 2025).

2. Contact-Aided Process and Measurement Models

The process model typically follows standard strapdown integration, with IMU-derived position and velocity predictions. Innovations arise in:

• Swing/stance dual models: Feet detected as in stance have their world positions held (or process noise reduced) during prediction, while swing feet propagate forward kinematically (Yang et al., 2019).
• Kinematic anchors: At each time step, the world-frame position of contacts supplies an "anchoring" update, enforcing the fixedness (no-slip) of the contacting foot, which is fused with the base state via Kalman measurement update (Sun et al., 19 Feb 2026, Lin et al., 2021, Demont et al., 2024).
• Contact-induced velocity constraints: When in contact, the velocity of the end-effector in the world frame is set to zero; in the filter this appears as $v + \omega \times r^i = 0$ for the $i$-th foot in the robot frame (Yang et al., 2019, Agrawal et al., 2022).
• Support-plane and elevation drift correction: Height clustering and time-decayed "snapping" to previously observed support planes are employed to mitigate accumulated vertical drift due to noisy or biased foot contact observations (Sun et al., 19 Feb 2026).

The observation model includes direct IMU measurements (gyroscope and accelerometer), encoder-driven joint kinematics, and, crucially, intermittent or continuous zero-velocity and position constraints arising from detected contacts. Where available, torque-derived force estimation, leg-mounted F/T sensors, and multiple IMUs deliver redundancy and robustness, allowing robust detection and probabilistic gating of contact events (Wu et al., 6 Mar 2025, Xavier et al., 2023, Demont et al., 2024).

3. Algorithmic Structures and Computation

Contact-anchored proprioceptive odometry is realized through a variety of algorithmic frameworks, each exploiting contact-induced sparsity differently:

• Kalman/invariant filtering: Process propagation and observation update are interleaved at high frequency (100–2000 Hz). Contact events trigger zero-velocity or position updates, which "reset" the unobservable states of the inertial system—especially critical for velocity, Z-height, and yaw (Yang et al., 2019, Lin et al., 2021, Xavier et al., 2023).
• Factor graph optimization: Contact anchoring is formulated via landmark or non-slip factors in a batch or incremental optimizer (e.g., iSAM2, Levenberg–Marquardt), leveraging forward kinematics and IMU preintegration for high-precision factor connections (Agrawal et al., 2022).
• MEKF/SE(n) filtering with viscoelastic contacts: The Kinetics Observer (Demont et al., 2024) introduces a viscoelastic spring-damper model between current and rest contact frames, assimilating noisy wrench and F/T sensor measurements for tight geometric-dynamic coupling.
• Learning-based and hybrid methods: AutoOdom (Luo et al., 24 Nov 2025) and neural contact estimators (Lin et al., 2021) employ deep networks for end-to-end sequence modeling. Contact anchoring is imposed via zero-velocity constraints or explicit correction layers inside the autoregressive predictor during recursive rollout, leveraging sim-to-real transfer and ablation for robust real-world operation.

A recurring principle is on-contact constraint enforcement: instantaneous or periodically triggered corrections are applied to otherwise drifting inertial states based on the latest detected kinematic anchor, with various smoothing and outlier rejection strategies depending on the application. Extensions include the use of multi-IMU setups to enable flexible modeling of nonrigid limbs, heel-toe roll, and structural deformation (Xavier et al., 2023).

4. Performance, Experimental Validation, and Comparative Results

Contact-anchored proprioceptive odometry achieves substantial improvements in trajectory consistency, drift mitigation, and failure robustness compared to purely IMU-centric or kinematic-only approaches, especially in the absence of exteroceptive cues (vision, LIDAR, GPS). Key experimental findings include:

• Flat, ramp, and stair terrain evaluation: COCLO reduces terminal position drift by up to 6.5% (vs. 22% for visual-inertial odometry) on outdoor ramps and consistently outperforms VINS in stair environments (Yang et al., 2019).
• Long-range walking and nonplanar motion: The Kinetics Observer demonstrates subcentimeter XY error and subdegree yaw error on 20 m walks (HRP-2Kai, HRP-5P), with significant error reduction over leg-odometry baselines (Demont et al., 2024).
• Cross-platform generalization: Kinematic chain factor graphs yield 27–43% average error reduction in pose estimation for both quadrupeds and humanoids, as demonstrated on A1, Anymal C, and Atlas (Agrawal et al., 2022).
• Robustness and redundancy: DogLegs demonstrates improved drift performance (RMSE, Z-drift, RPE) over single-IMU or sole-body state estimators, leveraging per-leg IMUs and encoder information (Wu et al., 6 Mar 2025). Multi-IMU estimation on Atalante halves RMS errors and drastically reduces Z drift versus single-IMU baselines (Xavier et al., 2023).
• Learning-based benchmarking: AutoOdom's contact-anchored version outperforms prior state-of-the-art (Legolas) by 57.2% in absolute trajectory error and 36.2% in relative pose error (Luo et al., 24 Nov 2025).

A plausible implication is that the recurring combination of contact anchoring, height correction, yaw consistency, and multi-modal fusion is now a de facto state-of-the-art standard for reliable proprioceptive odometry in legged robotics.

5. Special Cases and Extensions

While most research targets terrestrial legged robots, contact-anchored odometry extends to other morphologies and actuation schemes:

• Tensegrity robots: Contact-aided invariant EKFs, leveraging geometric constraints and cable-length information, deliver odometric drift (∼4.2%) comparable to rigid platforms, despite complex, nonrigid kinematics (Tong et al., 2024).
• Wheel-legged and bipedal systems: CAPO demonstrates robust operation across point-foot, wheel-legged, and quadruped platforms, with optional adaptive modules (such as IKVel-CKF) for noisy velocity conditions and heading estimation through geometric consistency under multiple concurrent contacts (Sun et al., 19 Feb 2026).
• Heel-toe and flexible gait handling: Multi-IMU architectures relax rigid foot-flat assumptions, permitting stance updates even under foot-roll or nontrivial contact transitions (Xavier et al., 2023).

6. Open Challenges and Future Directions

While contact-anchored proprioceptive odometry sets the benchmark for robust on-board state estimation under exteroceptive denial, several frontiers remain:

• Slip and nonholonomic contact modeling: Current frameworks predominantly assume no-slip contacts; realistic modeling and adaptive detection of slip (especially critical for wheel-legged robots and nonrigid terrains) is an open problem (Sun et al., 19 Feb 2026).
• Probabilistic and adaptive contact gating: Most techniques use simple thresholds or deterministic gating for contact status; probabilistic, sensor-fusion-based, or learned gating remains underexplored but necessary for generalization to variable robot platforms and complex environments.
• Integration with mapping and SLAM: While contact-anchored odometry stabilizes local pose estimates, combining with map-based corrections for long-loop closure, especially under high drift or missing contacts, is a scalable research direction.

A final observation is that public codebases (e.g., github.com/ShineMinxing/Ros2Go2Estimator.git (Sun et al., 19 Feb 2026)) and open datasets are increasingly available, which supports reproducible benchmarking and cross-system evaluation.

7. Representative Approaches: Summary Table

Method / Paper	Core Filtering Approach	Notable Contributions
COCLO (Yang et al., 2019)	SR-UKF	Contact-centric fusion, stance/swing hybrid, outperforming VINS
The Kinetics Observer (Demont et al., 2024)	MEKF + contact viscoelastic	6D contact force/torque, integral Newton–Euler fusion
CAPO (Sun et al., 19 Feb 2026)	EKF + torque-based anchoring	Height clustering, CKF foot velocities, geometric yaw update
Kinematic-Chain Factor Graph (Agrawal et al., 2022)	Factor graph w/ contact points	MAP-level constraint fusion, generalizable across morphologies
DogLegs (Wu et al., 6 Mar 2025)	Multi-IMU EKF	Leg-IMU–driven updates, kinematic constraints and zero-velocity fusion
Tensegrity SE(3) IEKF (Tong et al., 2024)	IEKF + geometric constraints	Cable-based shape reconstruction, contact-aided correction
AutoOdom (contact-anchored) (Luo et al., 24 Nov 2025)	Neural autoregressive	Two-stage sim-to-real, zero-velocity anchoring integrated in MLP

These schemes collectively demonstrate the breadth of modern contact-anchored proprioceptive odometry, unifying model-based, learning-driven, and factor-graph paradigms through the principled exploitation of contact constraints, thereby realizing drift-robust state estimation solely from body-mounted and proprioceptive sensors.