Legged Robot State Estimation Using Invariant Neural-Augmented Kalman Filter with a Neural Compensator

This paper presents an algorithm to improve state estimation for legged robots. Among existing model-based state estimation methods for legged robots, the contact-aided invariant extended Kalman filter defines the state on a Lie group to preserve invariance, thereby significantly accelerating convergence. It achieves more accurate state estimation by leveraging contact information as measurements for the update step. However, when the model exhibits strong nonlinearity, the estimation accuracy decreases. Such nonlinearities can cause initial errors to accumulate and lead to large drifts over time. To address this issue, we propose compensating for errors by augmenting the Kalman filter with an artificial neural network serving as a nonlinear function approximator. Furthermore, we design this neural network to respect the Lie group structure to ensure invariance, resulting in our proposed Invariant Neural-Augmented Kalman Filter (InNKF). The proposed algorithm offers improved state estimation performance by combining the strengths of model-based and learning-based approaches. Project webpage: https://seokju-lee.github.io/innkf_webpage

💡 Research Summary

This paper addresses the persistent challenge of accurate state estimation for legged robots operating in environments where external sensors such as LiDAR or cameras may be unavailable or unreliable. While the contact‑aided Invariant Extended Kalman Filter (InEKF) has become a state‑of‑the‑art model‑based estimator—thanks to its definition of the robot’s pose on a Lie group (typically SEₙ(3)) which guarantees invariance and fast convergence—its reliance on a first‑order linearization of the error dynamics makes it vulnerable to strong nonlinearities. Slip at the foot, model parameter uncertainties, and high‑frequency sensor noise can cause the error dynamics to deviate significantly from the linear approximation, leading to drift over time.

To mitigate this problem, the authors propose the Invariant Neural‑Augmented Kalman Filter (InNKF), a hybrid estimator that augments the InEKF with a neural compensator (NC) designed to respect the same Lie‑group structure. The NC is realized as a SE₂(3) Group Generation Network (SEGGN) that receives a short time‑window (49 steps ≈ 0.1 s) of proprioceptive data—linear acceleration, angular velocity, joint positions/velocities, foot positions/velocities, contact states—and the current InEKF estimate. A Temporal Convolutional Network (TCN) with five hidden layers (