This paper introduces a novel proprioceptive state estimator for legged robots that combines model-based filters with deep neural networks. In environments where vision systems are not reliable, proprioceptive state estimators become indispensable. Traditionally, proprioceptive state estimators are based on model-based approaches, which rely solely on contact foot kinematics as measurements. In contrast, learning-based approaches have obtained new measurements, such as displacement and covariance, by leveraging real-world data in a supervised manner. In this work, we develop a state estimation framework that trains a neural measurement network (NMN) to estimate the base's linear velocity and foot contact probability, which are then employed as measurements in an invariant extended Kalman filter. Our approach relies solely on simulation data for training, as it allows us to obtain extensive data easily. We address the sim-to-real gap by adapting existing learning techniques and regularization. To validate our proposed method, we conduct hardware experiments using a quadruped robot on four types of terrain: flat, debris, soft, and slippery. In our experiments, the proposed method demonstrates significant improvements over the model-based state estimator, achieving an average reduction in Absolute Trajectory Error (ATE) by${6 1. 8 \%}$for position and${8. 5 \%}$for velocity.

Several earlier studies have shown impressive control performance in complex robotic systems by designing the controller using a neural network and training it with model-free reinforcement learning. However, these outstanding controllers with natural motion style and high task performance are developed through extensive reward engineering, which is a highly laborious and time-consuming process of designing numerous reward terms and determining suitable reward coefficients. In this work, we propose a novel reinforcement learning framework for training neural network controllers for complex robotic systems consisting of bothrewardsandconstraints. To let the engineers appropriately reflect their intent to constraints and handle them with minimal computation overhead, two constraint types and an efficient policy optimization algorithm are suggested. The learning framework is applied to train locomotion controllers for several legged robots with different morphology and physical attributes to traverse challenging terrains. Extensive simulation and real-world experiments demonstrate that performant controllers can be trained with significantly less reward engineering, by tuning only a single reward coefficient. Furthermore, a more straightforward and intuitive engineering process can be utilized, thanks to the interpretability and generalizability of constraints. The summary video is available athttps://youtu.be/KAlm3yskhvM.