Attention-Based Neural-Augmented Kalman Filter for Legged Robot State Estimation

TL;DR

The paper addresses slip-induced bias in legged-robot state estimation by augmenting an Invariant EKF with a slip-conditioned Neural Compensator that uses cross-attention to modulate a post-update correction. The compensator is trained in two stages (autoencoder latent learning and attention-based compensation) and relies on a continuous foot slip level as context. Experiments on indoor terrains (gravel, Teflon, stairs) and outdoor grass demonstrate substantial reductions in relative position error compared to Slip Rejection, Learned Contact, and InNKF, with robust performance and real-time speed (~580 Hz). This approach enhances odometry reliability in slip-prone environments, enabling more robust autonomous legged locomotion while preserving the filter structure.

Abstract

In this letter, we propose an Attention-Based Neural-Augmented Kalman Filter (AttenNKF) for state estimation in legged robots. Foot slip is a major source of estimation error: when slip occurs, kinematic measurements violate the no-slip assumption and inject bias during the update step. Our objective is to estimate this slip-induced error and compensate for it. To this end, we augment an Invariant Extended Kalman Filter (InEKF) with a neural compensator that uses an attention mechanism to infer error conditioned on foot-slip severity and then applies this estimate as a post-update compensation to the InEKF state (i.e., after the filter update). The compensator is trained in a latent space, which aims to reduce sensitivity to raw input scales and encourages structured slip-conditioned compensations, while preserving the InEKF recursion. Experiments demonstrate improved performance compared to existing legged-robot state estimators, particularly under slip-prone conditions.

Figures (6)

• Figure 1: Relationship between foot slip level and normalized state estimation errors of the InEKF on the overall terrain. Dots denote per-timestep errors, and colored markers show the mean $\pm$ one standard deviation within slip.
• Figure 2: Training process of the Neural Compensator. It consists of two steps: Step 1 corresponds to autoencoder training, and Step 2 represents attention mechanism training. The snowflake symbol indicates a frozen model, while the fire symbol denotes a fine-tuned component.
• Figure 3: Structure of the AttenNKF. The Neural Compensator, composed of the Encoder-Decoder and Attention modules trained in Section \ref{['section:attennkf']}-A, is augmented into the InEKF to generate the compensated state.
• Figure 4: Real-world scenario of the indoor experimental environment, consisting of: (1) a gravel field with 30 mm-diameter pebbles, (2) a Teflon sheet with a low friction coefficient (0.10–0.15), and (3) a three-tier staircase (60 cm width, 30 cm depth, 10 cm height per step) designed for both uphill and downhill traversal.
• Figure 5: The state estimation results of the indoor experiments. Left: trajectories on the $x$–$y$ plane. Right: time histories of the estimated states ($x$, $y$, $z$); background shading denotes foot slip level (0–1). Color legend: black—Ground Truth (GT); green—Slip Rejection (SR); orange—Learned Contact (LC); blue—Invariant Neural-Augmented Kalman Filter (InNKF); red—Attention-Based Neural-Augmented Kalman Filter (AttenNKF, proposed method).