{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T11:18:56Z","timestamp":1788261536048,"version":"build-2803163510"},"reference-count":30,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/biomimetics11090615","type":"journal-article","created":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T10:32:18Z","timestamp":1788258738000},"page":"615","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["TSIE: Robust Blind Locomotion Learning for Bipedal Robots via Terrain and State Implicit-Explicit Estimation"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-3728-9006","authenticated-orcid":false,"given":"Zhiyuan","family":"Liang","sequence":"first","affiliation":[{"name":"School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China"},{"name":"Institute of Machine Intelligence, University of Shanghai for Science and Technology, Shanghai 200093, China"},{"name":"Shanghai DroidUp Co., Ltd., Shanghai 200433, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-9170-5252","authenticated-orcid":false,"given":"Jie","family":"Xue","sequence":"additional","affiliation":[{"name":"School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China"},{"name":"Institute of Machine Intelligence, University of Shanghai for Science and Technology, Shanghai 200093, China"},{"name":"Shanghai DroidUp Co., Ltd., Shanghai 200433, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"visualization","vocabulary":"credit"},{"role":"conceptualization","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9754-1214","authenticated-orcid":false,"given":"Haiming","family":"Mou","sequence":"additional","affiliation":[{"name":"Shanghai DroidUp Co., Ltd., Shanghai 200433, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"resources","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9928-7272","authenticated-orcid":false,"given":"Qingdu","family":"Li","sequence":"additional","affiliation":[{"name":"Institute of Machine Intelligence, University of Shanghai for Science and Technology, Shanghai 200093, China"},{"name":"Shanghai DroidUp Co., Ltd., Shanghai 200433, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"funding-acquisition","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"}]},{"given":"Jianwei","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Informatics, University of Hamburg, 20146 Hamburg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"funding-acquisition","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1146\/annurev-control-030323-022510","article-title":"Deep reinforcement learning for robotics: A survey of real-world successes","volume":"8","author":"Tang","year":"2025","journal-title":"Annu. 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