Bridging the Sim-to-Real Gap in Humanoid Dynamics via Learned Nonlinear Operators

A central challenge in humanoid robotic control is bridging the gap between simulated and real-world physics to enhance robot learning. This gap often leads to execution failures due to discrepancies in dynamics, actuator behavior, and unmodeled perturbations. This gap manifests as nonlinear variations at the level of each individual motor, and becomes even more unpredictable when the humanoid interacts with objects of varying weights. To better align simulation and real-world physics for robot learning, we curate SimLifter, the first dataset specifically designed to bridge the sim-to-real gap, even under the increased variability introduced by diverse payload interactions.SimLifter contains 257,493 frames, and systematically captures multimodal signals—including joint positions, velocities, torques, motor temperatures, and equivalent torques—across four standard payloads, three humanoid robots, and two actuation frequencies, covering both isolated joint movements and full upper-body coordination.We further introduce GAPONet, a novel reinforcement learning framework designed to enable robust policy transfer from simulation to the real world. Based on Unstacked Deep Operator Network (DeepOnet) and Reinforcement Learning (RL), GAPONet estimates the discrepancies between simulation and real-world executions of the same policy by learning a nonlinear operator over multiple force modalities. It also demonstrates strong extrapolative generalization to unseen robots and zero-shot actions. On previously unseen humanoid robots, GAPONet shows substantial gains in zero-shot motion tracking, improving accuracy across all joints by over 40% on average compared to PD control with default hyperparameters, and up to 50% under maximum payload. In the goal-directed object delivery task, GAPONet improves accuracy by 70% under maximum payload over direct target action execution.