Online Learning of Robust Legged Odometry with Minimal Exteroceptive Supervision

Robust and accurate proprioceptive state estimation of the main body is crucial for legged robots to execute tasks in extreme environments where exteroceptive sensors, such as LiDARs and cameras, may become unreliable. In this paper, we propose DogLegs, a state estimation system for legged robots that fuses the measurements from a body-mounted inertial measurement unit (Body-IMU), joint encoders, and multiple leg-mounted IMUs (Leg-IMU) using an extended Kalman filter (EKF). The filter system contains the error states of all IMU frames. The Leg-IMUs are used to detect foot contact, thereby providing zero-velocity measurements to update the state of the Leg-IMU frames. Additionally, we compute the relative position constraints between the Body-IMU and Leg-IMUs by the leg kinematics and use them to update the main body state and reduce the error drift of the individual IMU frames. Field experimental results have shown that our proposed DogLegs system achieves better state estimation accuracy compared to the traditional leg odometry method (using only Body-IMU and joint encoders) across various terrains. We make our code and datasets publicly available to benefit the research community (https://github.com/YibinWu/DogLegs).

One of the significant challenges in legged robotics is achieving accurate odometry using only onboard proprioceptive sensors. In this study, we present a complete leg odometry pipeline based on an Error-State EKF (ESEKF) that relies exclusively on proprioceptive data: a body fixed IMU, joint encoders, and force sensors, where filter's state is corrected by feet determined to be in a stationary stance. The core of our contribution is fused contact detection and an uncertainty quantification module designed to explicitly identify and reject slippage. This module runs two detectors in parallel for each foot, 1) a debounced, force-based Gaussian Mixture Model (GMM) guided Finite State Machine (FSM) to confirm physical contact, and 2) a kinematic-based Generalized Likelihood Ratio Test (GLRT) on the estimated velocity of the foot. The continuous quality scores from both estimators are fused to detect if the foot is both physically loaded and kinematically stationary and served as an uncertainty signal for each contact. To validate our approach, we collected a multi-modal dataset of 29 sequences spanning diverse indoor and outdoor terrains (e.g., concrete, grass, pebble, and rock) total of 2.4 km long. We benchmarked our approach against both proprioceptive and exteroceptive methods. The results demonstrate our method's efficacy in providing accurate odometry estimates, robustly handling slippage-prone environments. We also share our code and real-time ROS2 package as open-source.

Kalman filter-based algorithms are fundamental for mobile robots, as they provide a computationally efficient solution to the challenging problem of state estimation. However, they rely on two main assumptions that are difficult to satisfy in practice: (a) the system dynamics must be linear with Gaussian process noise, and (b) the measurement model must also be linear with Gaussian measurement noise. Previous works have extended assumption (a) to nonlinear spaces through the Invariant Extended Kalman Filter (IEKF), showing that it retains properties similar to those of the classical Kalman filter when the system dynamics are group-affine on a Lie group. More recently, the counterpart of assumption (b) for the same nonlinear setting was addressed in [1]. By means of the proposed Iterated Invariant Extended Kalman Filter (IterIEKF), the authors of that work demonstrated that the update step exhibits several compatibility properties of the classical linear Kalman filter. In this work, we introduce a novel open-source state estimation algorithm for legged robots based on the IterIEKF. The update step of the proposed filter relies solely on proprioceptive measurements, exploiting kinematic constraints on foot velocity during contact and base-frame velocity, making it inherently robust to environmental conditions. Through extensive numerical simulations and evaluation on real-world datasets, we demonstrate that the IterIEKF outperforms the vanilla IEKF, the SO(3)-based Kalman Filter, and its iterated variant in terms of both accuracy and consistency.