Year: 2025
Type: article
Abstract: Existing state estimation algorithms for legged robots that rely on proprioceptive sensors often overlook foot slippage and leg deformation in the physical world, leading to large estimation errors. To address this limitation, we propose a comprehensive measurement model that accounts for both foot slippage and variable leg length by analyzing the relative motion between foot contact points and the robot's body center. We show that leg length is an observable quantity, meaning that its value can be explicitly inferred by designing an auxiliary filter. To this end, we introduce a dual estimation framework that iteratively employs a parameter filter to estimate the leg length parameters and a state filter to estimate the robot's state. To prevent error accumulation in this iterative framework, we construct a partial measurement model for the parameter filter using the leg static equation. This approach ensures that leg length estimation relies solely on joint torques and foot contact forces, avoiding the influence of state estimation errors on the parameter estimation. Unlike leg length that can be directly estimated, foot slippage cannot be measured directly with the current sensor configuration. However, since foot slippage occurs at a low frequency, it can be treated as outliers in the measurement data. To mitigate the impact of these outliers, we propose the$\beta$-Kalman filter ($\beta$-KF), which redefines the estimation loss in canonical Kalman filtering using$\beta$-divergence. This divergence can assign low weights to outliers in an adaptive manner, thereby enhancing the robustness of the estimation algorithm. These techniques together form the dual$\beta$-Kalman filter (Dual$\beta$-KF), a novel algorithm for robust state estimation in legged robots. Experimental results on the Unitree GO2 robot demonstrate that the Dual$\beta$-KF significantly outperforms state-of-the-art methods.
Authors: Tianyi Zhang, Wenhan Cao, Chang Liu, Tao Zhang, Jiangtao Li, Shengbo Eben Li
Institutions: Tsinghua University, Peking University
Language: English
Subfield: Biomedical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: Joint Research Centre
OpenAlex ID: W4411270126