The presence of sensor noise, missing states and inadequate future prediction capabilities imposes significant limitations on the locomotion performance of bipedal robots operating in unstructured terrain. Conventional methods generally depend on long-term history observations to reconstruct single-frame privileged information. However, these methods fail to acknowledge the pivotal function of short-term history in rapid state responses and the significance of future state prediction in anticipating potential risks. The proposed framework is a Long–Short World Model (LSWM), which integrates state reconstruction and future state prediction to enhance the locomotion capabilities of bipedal robots in complex environments. The LSWM framework comprises two modules: a state reconstruction module (SRM) and a future state prediction module (SPM). The state reconstruction module employs long-term history observations to reconstruct privileged information in the current short-term history, thereby effectively improving the system’s robustness to sensor noise and enhancing state observability. The future state prediction module enhances the robot’s adaptability to complex environments and unpredictable scenarios by predicting the robot’s future short-term privileged information. We conducted extensive comparative experiments in simulation as well as in a variety of real-world indoor and outdoor environments. In the indoor stair-climbing task, LSWM achieved a 94% success rate, outperforming the current state-of-the-art baseline methods by at least 34%, thereby demonstrating its substantial performance advantages in complex and dynamic environments.

Robust blind locomotion over complex unstructured terrains relies on accurate estimation of robot states and surrounding terrain geometry. However, under real-world deployment conditions without exteroceptive perception, it remains challenging to accurately estimate robot states and infer surrounding terrain structures solely from noisy proprioceptive observations. Existing methods commonly learn single-scale implicit terrain representations from historical proprioceptive observations and explicitly estimate robot states. However, they lack explicit terrain estimation and may lose critical geometric details. Moreover, single-scale terrain information is insufficient to capture both local geometric structures and global terrain trends. To address these issues, we propose a Terrain and State Implicit-Explicit Estimation (TSIE) framework to improve the locomotion capability of bipedal robots over complex terrains. TSIE encodes long-horizon proprioceptive observations using a Long Short-Term Memory (LSTM) network and introduces a dual-branch architecture consisting of a Terrain Implicit-Explicit Estimator (Terrain-IE) and a State Implicit-Explicit Estimator (State-IE). Terrain-IE performs multi-scale terrain implicit-explicit estimation by explicitly estimating a local high-resolution height map and implicitly reconstructing a global low-resolution height map. By preserving gradient connections between the two terrain branches, Terrain-IE enables joint implicit-explicit training of multi-scale terrain representations, improving terrain understanding and estimation accuracy. State-IE explicitly estimates the base linear velocity and foot-centered height map, while implicitly reconstructing future proprioceptive states to further improve tracking performance and locomotion robustness. We validate TSIE through simulation and real-world experiments on a full-sized bipedal robot platform with a height of $170\mathrm{cm}$ and a mass of $35\mathrm{kg}$. Experimental results show that TSIE outperforms baseline methods in complex-terrain traversal capability, terrain and state estimation accuracy, and velocity-tracking stability. Real-world deployment further demonstrates the robustness of TSIE across indoor and outdoor complex terrains, achieving a 95% success rate in continuous stair ascent and descent tasks.