[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-327150-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-327150-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","learning-gait-aware-quadruped-locomotion-with-temporal-logic-specifications","Learning Gait-Aware Quadruped Locomotion with Temporal Logic Specifications","","Quadruped locomotion with reinforcement learning often relies on fixed, hand-crafted, Markovian reward functions that restrict interpretability and provide limited explicit control over gait behavior. The work proposes a framework using parameterized constraints expressed in Signal Temporal Logic (STL) to specify safety bounds, gait synchronization, command tracking, and actuation limits, then derives a reward shaping mechanism from STL robustness. Parametric STL templates are calibrated from reference rollouts across speed regimes and produce dense shaped rewards compatible with PPO, yielding tighter velocity tracking and more stable training on Barkour in MuJoCo MJX while using parallelization and domain randomization.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & 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hand-crafted Markovian rewards insufficient for quadruped gait learning?","Question",{"text":63,"@type":64},"They limit policy interpretability and lack explicit control over gait behaviors and contact-sequence structure, which is critical for multi-gait locomotion and smooth speed-regime transitions.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How does the proposed method specify desired gait behaviors?",{"text":68,"@type":64},"It uses parameterized constraints expressed in Signal Temporal Logic (STL), including safety bounds, gait synchronization constraints, command tracking, and actuation bounds.",{"name":70,"@type":61,"acceptedAnswer":71},"How are STL-based rewards computed and used for reinforcement learning?",{"text":72,"@type":64},"The method calibrates parametric STL templates from reference rollouts and computes rewards using smooth approximations of STL robustness over the rollouts to provide dense learning signals compatible with 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Temporal Logic Specifications  \nMerve Atasever Cagan Bakirci Alfredo Reina Corona  \nKeyan Azbijari Jyotirmoy V. Deshmukh  \nUniversity of Southern California, Los Angeles, California, USA {atasever,cbakirci,reinacor,azbijari,[jdeshmuk](jdeshmuk}@usc.edu)[}](jdeshmuk}@usc.edu)[@usc.edu](jdeshmuk}@usc.edu)  \nAbstract:  \nReinforcement learning (RL) for quadruped locomotion commonly depends on fixed, hand-crafted, and Markovian reward functions that limit both interpretability of learned policies and lack explicit control over gait behaviors. We introduce a framework where distinct gaits are specified using parameterized constraints expressed in Signal Temporal Logic (STL) . These include safety bounds, gait synchronization constraints, command tracking, and actuation bounds. From these specifications, we develop a reward shaping mechanism that provides learning agents a dense, continuous reward landscape that encodes desired behavior. We define parametric STL templates for three speed regimes (walkingtrot, trot, bound), calibrate their parameters from reference rollouts, and compute rewards from using smooth approximations of STL robustness over the rollouts. The generated rewards can be used to provide shaped gradients compatible with Proximal Policy Optimization (PPO) . We instantiate the approach on Google’s Barkour quadruped robot in MuJoCo XLA (MJX) . We use parallelization within the simulator to improve training speeds and use domain randomization to robustify learned policies. We show that compared to a baseline of hand-crafted rewards, the STL-shaped rewards yield tighter velocity tracking and more stable training. Videos can be found on our project website:  \n[https://stl-locomotion.github.io/](https://stl-locomotion.github.io/) .  \nKeywords: Quadrupedal Locomotion, Reinforcement Learning, STL  \n1 Introduction  \nLegged robots, including both bipeds and quadrupeds, have made remarkable progress in recent years, with modern platforms exhibiting agile walking, crawling, running, and more in increasingly challenging settings [1, 2, 3, 4, 5, 6] . Despite this progress, achieving animal-level robustness across diverse speed regimes and gait patterns remains an open challenge. Classical model-based control approaches, such as differential dynamic programming (DDP) and model predictive control (MPC), have enabled impressive quadrupedal behaviors by explicitly optimizing trajectories under dynamics and contact constraints. However, their performance often depends on accurate system models and carefully designed cost functions, all of which can be difficult to obtain on real hardware.[7, 8, 9] . Reinforcement learning (RL) offers a complementary path by directly optimizing closedloop policies in simulation, and recent advances in high-fidelity physics engines and standardized legged-locomotion platforms, such as MuJoCo, Isaac Gym, Google Barkour, Unitree A1/Go1, and ANYmal, have further accelerated progress in this direction.[10, 11, 12, 13] .  \nA key requirement for quadrupedal locomotion is the ability to operate across multiple speed regimes by switching between distinct gait patterns. For example, walking, trotting, and bounding differ not only in velocity but also in their contact timing, duty factors, and employed support structures. Locomotion controllers must therefore satisfy several objectives simultaneously: accurate command tracking over a wide range of speeds, safety and stability under disturbances, and structured gait be-  \nFigure 1: Overall Pipeline.  \nhavior whose contact patterns remain appropriate for the commanded regime. State-of-the-art deep RL pipelines address the first objective, and partially the second through carefully engineered reward terms, curriculum learning, and domain randomization [14, 11, 13] . However, these reward functions are often difficult to interpret, and they provide only indirect control over co","cbCairnTQuzxyzMA","https://ap.wps.com/l/cbCairnTQuzxyzMA","pdf",3866713,16,"English","# Introduction\n## Multi-gait locomotion objective\n## Limitations of hand-crafted and indirect reward control\n## STL specifications and robustness as rewards","[{\"question\":\"Why are fixed hand-crafted Markovian rewards insufficient for quadruped gait learning?\",\"answer\":\"They limit policy interpretability and lack explicit control over gait behaviors and contact-sequence structure, which is critical for multi-gait locomotion and smooth speed-regime transitions.\"},{\"question\":\"How does the proposed method specify desired gait behaviors?\",\"answer\":\"It uses parameterized constraints expressed in Signal Temporal Logic (STL), including safety bounds, gait synchronization constraints, command tracking, and actuation bounds.\"},{\"question\":\"How are STL-based rewards computed and used for reinforcement learning?\",\"answer\":\"The method calibrates parametric STL templates from reference rollouts and computes rewards using smooth approximations of STL robustness over the rollouts to provide dense learning signals compatible with PPO.\"}]","Learning Gait-Aware Quadruped Locomotion with Temporal Logic Specifications | PDF",1789976552]