State estimation is an important aspect in many robotics applications. In this work, we consider the task of obtaining accurate state estimates for robotic systems by enhancing the dynamics model used in state estimation algorithms. Existing frameworks such as moving horizon estimation (MHE) and the unscented Kalman filter (UKF) provide the flexibility to incorporate nonlinear dynamics and measurement models. However, this implies that the dynamics model within these algorithms has to be sufficiently accurate in order to warrant the accuracy of the state estimates. To enhance the dynamics models and improve the estimation accuracy, we utilize a deep learning framework known as knowledge-based neural ordinary differential equations (KNODEs). The KNODE framework embeds prior knowledge into the training procedure and synthesizes an accurate hybrid model by fusing a prior first-principles model with a neural ordinary differential equation (NODE) model. In our proposed LEARNEST framework, we integrate the data-driven model into two novel model-based state estimation algorithms, which are denoted as KNODE-MHE and KNODE-UKF. These two algorithms are compared against their conventional counterparts across a number of robotic applications; state estimation for a cartpole system using partial measurements, localization for a ground robot, as well as state estimation for a quadrotor. Through simulations and tests using real-world experimental data, we demonstrate the versatility and efficacy of the proposed learning-enhanced state estimation framework.

翻译：状态估计是众多机器人应用中的重要环节。本文旨在通过增强状态估计算法中的动力学模型，实现机器人系统的高精度状态估计。现有框架如移动时域估计（MHE）和无迹卡尔曼滤波（UKF）能够灵活融入非线性动力学与测量模型，但这要求算法内部的动力学模型具有足够高的精度以保证状态估计的准确性。为提升动力学模型精度并改善估计效果，我们采用了一种基于知识的神经常微分方程（KNODE）深度学习框架。KNODE框架将先验知识嵌入训练过程，通过融合基于第一性原理的先验模型与神经常微分方程（NODE）模型，合成了精确的混合模型。在所提出的LEARNEST框架中，我们将数据驱动模型集成至两种新型基于模型的状态估计算法中，分别命名为KNODE-MHE和KNODE-UKF。通过多个机器人应用场景的对比实验（包括基于部分测量值的小车-倒立摆系统状态估计、地面机器人定位以及四旋翼飞行器状态估计），我们将这两种算法与传统对应算法进行了比较。仿真与真实实验数据测试结果表明，该学习增强型状态估计框架具有良好的普适性与有效性。