State estimation for legged robots is challenging due to their highly dynamic motion and limitations imposed by sensor accuracy. By integrating Kalman filtering, optimization, and learning-based modalities, we propose a hybrid solution that combines proprioception and exteroceptive information for estimating the state of the robot's trunk. Leveraging joint encoder and IMU measurements, our Kalman filter is enhanced through a single-rigid body model that incorporates ground reaction force control outputs from convex Model Predictive Control optimization. The estimation is further refined through Gated Recurrent Units, which also considers semantic insights and robot height from a Vision Transformer autoencoder applied on depth images. This framework not only furnishes accurate robot state estimates, including uncertainty evaluations, but can minimize the nonlinear errors that arise from sensor measurements and model simplifications through learning. The proposed methodology is evaluated in hardware using a quadruped robot on various terrains, yielding a 65% improvement on the Root Mean Squared Error compared to our VIO SLAM baseline. Code example: https://github.com/AlexS28/OptiState

翻译：四足机器人的状态估计因其高度动态的运动特性及传感器精度限制而面临挑战。通过融合卡尔曼滤波、优化与学习方法，我们提出了一种混合方案，结合本体感知与外部感知信息来估计机器人躯干状态。利用关节编码器和惯性测量单元数据，我们的卡尔曼滤波器通过单刚体模型得到增强——该模型融合了凸模型预测控制优化生成的地面反作用力控制输出。状态估计通过门控循环单元进一步优化，该单元同时考虑了从深度图像视觉Transformer自编码器中提取的语义信息与机器人高度。该框架不仅能提供包含不确定性评估的精确机器人状态估计，还可通过学习最小化传感器测量与模型简化导致的非线性误差。我们在四足机器人硬件上对不同地形进行了评估，与视觉惯性SLAM基线相比，均方根误差降低了65%。代码示例：https://github.com/AlexS28/OptiState