HG-LLIO: Hierarchical Ground-reaction-force-aided Learning Leg-inertial Odometry

Accurate state estimation is essential for quadruped robots operating in environments where exteroceptive sensing—such as LiDAR or cameras—is unavailable. This makes proprioceptive odometry critical for maintaining consistent state estimation. Among the existing approaches, recent learning-based, leg-inertial odometry methods rely primarily on internal sensor observations and do not explicitly account for variations in system dynamics, such as changes in externally added masses. We propose the hierarchical ground-reaction-force-aided learning leg-inertial odometry (HG-LLIO) framework, a physics-informed proprioceptive odometry framework that explicitly incorporates payload information and ground reaction force (GRF) estimation as a physically meaningful intermediate representation. The HG-LLIO framework consists of two stages: a GRF estimation network that fuses proprioceptive measurements with payload mass and location, followed by an odometry network that predicts incremental position and orientation changes using the estimated GRF as a latent physical feature. Uncertainty is modeled based on a likelihood-based regression formulation that jointly estimates prediction mean and covariance. Simulation-based evaluations in the Isaac Gym and Gazebo environments demonstrate that explicitly accounting for payload variations improves the consistency of odometry estimation under changing load conditions. While the impact on mean error reduction is limited, introducing GRF-guided intermediate representations contributes to more stable and interpretable uncertainty behavior across dynamic scenarios. These results indicate that integrating payload awareness and physically grounded intermediate variables enhances estimation robustness and uncertainty characterization in perception-degraded environments, even in the presence of inherent accumulated drifts.