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.

Robotic painting tasks in the real world are often made complicated by the highly complex and stochastic nature of the dynamics that underlie, e.g., physical contact between the painting tool and a canvas, color blendings between painting mediums, and many more. Simulation-based inverse graphics algorithms, for example, can not be directly transferred to the real-world due in large to the considerable gap in the viable range of painting strokes the robot can accurately generate onto the physical canvas. In this paper, we aim at minimizing this gap by appealing to a data-driven skill learning approach. The core idea lies in allowing the robot to learn continuous stroke-level skills that jointly encodes action trajectories and painted outcomes from an extensive collection of human demonstrations. We demonstrate the efficacy of our method through extensive real-world experiments using a 4-dof torque-controllable manipulator with a digital canvas(iPad).