TSIE: Robust Blind Locomotion Learning for Bipedal Robots via Terrain and State Implicit-Explicit Estimation

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 170cm and a mass of 35kg. 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.