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 which 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.

翻译：现有依赖本体感知传感器的足式机器人状态估计算法通常忽略了物理世界中的足部滑移和腿部变形，导致较大的估计误差。为克服这一局限性，我们提出了一种综合测量模型，通过分析足部接触点与机器人身体中心之间的相对运动，同时考虑了足部滑移和可变腿长。我们证明腿长是一个可观测量，这意味着通过设计辅助滤波器可以显式推断其值。为此，我们引入了一种双估计框架，迭代地使用参数滤波器估计腿长参数，并使用状态滤波器估计机器人状态。为防止该迭代框架中的误差累积，我们利用腿部静力学方程为参数滤波器构建了部分测量模型。该方法确保腿长估计仅依赖于关节扭矩和足部接触力，避免了状态估计误差对参数估计的影响。与可直接估计的腿长不同，在当前传感器配置下无法直接测量足部滑移。然而，由于足部滑移发生在低频段，可将其视为测量数据中的异常值。为减轻这些异常值的影响，我们提出了beta卡尔曼滤波器（beta KF），该滤波器使用beta散度重新定义了标准卡尔曼滤波中的估计损失。该散度能够以自适应方式为异常值分配低权重，从而增强估计算法的鲁棒性。这些技术共同构成了双beta卡尔曼滤波器（Dual beta KF），这是一种用于足式机器人鲁棒状态估计的新型算法。在Unitree GO2机器人上的实验结果表明，Dual beta KF显著优于现有最先进方法。