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

翻译：本文提出了一种改进腿式机器人状态估计算法。在现有的腿式机器人基于模型的状态估计方法中，接触辅助不变扩展卡尔曼滤波器将状态定义在李群上以保持不变性，从而显著加速了收敛速度。该方法通过将接触信息作为更新步骤的测量值，实现了更精确的状态估计。然而，当模型表现出强非线性时，估计精度会下降。此类非线性可能导致初始误差累积并随时间产生较大漂移。为解决该问题，我们提出通过使用人工神经网络作为非线性函数逼近器来增强卡尔曼滤波器，从而补偿误差。此外，我们设计的神经网络遵循李群结构以确保不变性，由此形成了我们提出的不变神经增强卡尔曼滤波器。所提算法通过结合基于模型与基于学习方法的优势，提供了改进的状态估计性能。项目网页：https://seokju-lee.github.io/innkf_webpage