[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83300-en":3,"doc-seo-83300-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83300,1374391974564,"Clementine","https://ap-avatar.wpscdn.com/avatar/14000253aa45c000a9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779874745381141002",8,"Research & Report","Physics Guided Biomechanical Gait Adaptation for Humanoid Locomotion on Extreme Sloped Terrains","Model-free reinforcement learning has advanced humanoid locomotion, yet control on steep, continuous slopes remains insufficiently addressed. Sloped terrains introduce persistent gravitational bias that simultaneously challenges dynamic stability and posture regulation, and generic rewards often lead to conservative low–center-of-mass crouched gaits. HumoSlope proposes a two-stage physics-guided method: a slope-adaptive ZMP regularizer and a Biomechanical Slope Gait Adapter that modulates CoM height and limb coordination. Sim-to-real results show robust blind traversal of outdoor grass slopes up to 62.7% grade (32.1°).","Physics-Guided Biomechanical Gait Adaptation for Humanoid Locomotion on Extreme Sloped Terrains  \narXiv :2607 .07830v 1 [ cs .RO] 8 Jul 2026  \nXuanyu Chen 1,⋆, Mohan Liu 1,⋆, Dengchen Mei 1 , Zhihao Gu 1 , Haitian Zhang 1 , Kaimin Mao 1  \nHaiyue Zhu2 , Shijun Yan2 , Lin Wang 1 ,†  \n1Nanyang Technological University 2A*STAR ⋆ Co-first Authors †Corresponding Author  \nFigure 1: Real-world locomotion on sloped terrains. Our robot traverses grassy slopes up to 62.7%(32 .1◦ ) grade and generalizes to slippery surfaces, grass, wavy terrains, and level walkways.  \nAbstract: Model-free reinforcement learning has enabled impressive humanoid locomotion; however, control on steep slopes remains largely unexplored. Unlike flat or discrete terrains, sloped terrains impose a persistent gravitational bias that demands simultaneous stability and posture control. Consequently, under generic reward formulations, policies can converge to slow, conservative lowcenter-of-mass (CoM) crouched gaits. In this work, we propose a novel twostage physics-guided framework, dubbed HumoSlope, dedicated to robust humanoid locomotion on diverse sloped terrains. Specifically, Stage I establishes a terrain-consistent balance prior by introducing a slope-adaptive Zero Moment Point (ZMP) regularizer evaluated directly on the local inclined support plane rather than a world-horizontal reference. To prevent the resulting policy from defaulting to a crouched posture, Stage II introduces the Biomechanical Slope Gait Adapter (BSGA) . Utilizing extracted macroscopic terrain descriptors as privileged, training-only signals, BSGA dynamically gates soft reward priors to modulate CoM height and lower-limb coordination based on the estimated slope geometry—encouraging hip-dominant uphill propulsion and knee-oriented downhill braking. Crucially, the deployed actor remains entirely proprioceptive, requiring no online exteroceptive sensing. Extensive Sim-to-Real experiments demonstrate that our framework effectively mitigates posture degeneration and enables blind, continuous traversal of outdoor grass slopes up to 62.7%(32 .1◦ ), validating a physics-guided approach to challenging slope terrain adaptation.  \nKeywords: Humanoid Locomotion, Sloped Terrains, Reinforcement Learning  \n1 Introduction  \nIn recent years, model-free humanoid locomotion control has undergone a substantial advance thanks to massively parallel simulation and Sim-to-Real reinforcement learning pipelines [1, 2, 3] . Recent policies can traverse challenging terrains such as stairs, stepping stones, and parkour-style obstacles [4, 5, 6] . However, continuous steep slopes remain underexplored as a dedicated locomotion regime, despite being common in daily environments and outdoor robot deployment, such as ramps, grassy slopes, uneven outdoor paths, and natural hillsides. Prior studies often include inclined surfaces as one case within broader multi-terrain evaluations, however, they provide limited analysis of how slope grade affects traversal limits, posture, joint loading, and gait adaptation [7, 8, 9, 10] .  \nThis distinction matters because an incline imposes a critical gravitational bias on the whole body rather than requiring only short-horizon foothold selection or recovery. As the slope increases, the robot must maintain dynamic stability while controlling posture under shifted Center of Mass (CoM) projection, altered support geometry, and sustained lower-limb loading. These effects are further amplified on rough outdoor slopes, where local surface irregularities interact with the global terrain inclination. Hence, the key research question is: how can a humanoid maintain simultaneous stability and posture control under a persistent gravitational bias in extreme sloped terrains? Under generic reward formulations, e.g., [11], we observe an undesired low-CoM strategy in modelfree humanoid slope locomotion: the policy remains persistently crouched, resembling a “Groucho gait” [12, 13](see Fig. 4b), with sl","cbCaibRcnPPDIgjJ","https://ap.wps.com/l/cbCaibRcnPPDIgjJ","pdf",11312600,2,1,12,"English","en",105,"# Introduction\n## Problem: gravitational bias and crouched-gait degeneration\n## Proposed approach: HumoSlope two-stage physics-guided framework\n## Stage I: slope-adaptive ZMP regularizer\n## Stage II: Biomechanical Slope Gait Adapter (BSGA)\n## Sim-to-Real validation and outdoor traversal","[{\"question\":\"Why are extreme sloped terrains harder than flat or discrete terrains for humanoid locomotion?\",\"answer\":\"A slope creates a persistent gravitational bias that shifts the center-of-mass projection and alters support geometry, requiring simultaneous dynamic stability and posture control over sustained lower-limb loading.\"},{\"question\":\"What problem occurs under generic reward formulations in humanoid slope locomotion?\",\"answer\":\"Policies can converge to slow, conservative low–center-of-mass crouched gaits, often resembling a “Groucho gait,” which degrades posture quality and limits further slope traversal.\"},{\"question\":\"How does HumoSlope improve robustness without relying on online exteroceptive sensing?\",\"answer\":\"Stage I uses a slope-adaptive ZMP regularizer evaluated on the local inclined support plane, while Stage II employs BSGA that gates reward priors using training-time terrain descriptors; the deployed actor remains fully proprioceptive.\"}]",1784186601,30,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"physics-guided-biomechanical-gait-adaptation-for-humanoid-locomotion-on-extreme-sloped-terrains","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/physics-guided-biomechanical-gait-adaptation-for-humanoid-locomotion-on-extreme-sloped-terrains/83300/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-24","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why are extreme sloped terrains harder than flat or discrete terrains for humanoid locomotion?","Question",{"text":75,"@type":76},"A slope creates a persistent gravitational bias that shifts the center-of-mass projection and alters support geometry, requiring simultaneous dynamic stability and posture control over sustained lower-limb loading.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What problem occurs under generic reward formulations in humanoid slope locomotion?",{"text":80,"@type":76},"Policies can converge to slow, conservative low–center-of-mass crouched gaits, often resembling a “Groucho gait,” which degrades posture quality and limits further slope traversal.",{"name":82,"@type":73,"acceptedAnswer":83},"How does HumoSlope improve robustness without relying on online exteroceptive sensing?",{"text":84,"@type":76},"Stage I uses a slope-adaptive ZMP regularizer evaluated on the local inclined support plane, while Stage II employs BSGA that gates reward priors using training-time terrain descriptors; 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