mlsanityData to 14 Oct 2026

Learning Gait-Aware Quadruped Locomotion with Temporal Logic Specifications

arXiv 2607.00442 ↗First posted 1 Jul 2026cs.RO cs.AIcited by 2

On the map: Deep reinforcement learning methods → RL for robot locomotion and manipulation

Abstract (arXiv)

Reinforcement learning (RL) for quadruped locomotion commonly depends on fixed, hand-crafted, and Markovian reward functions that may limit interpretability of learned policies and may 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 (walking-trot, 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. Compared with hand-crafted rewards, an expert-switching oracle, and Text2Reward, Human-STL maintains high command-tracking success across the evaluated speed range while exhibiting substantially higher consistency with the intended speed-dependent gait structures. Videos can be found on our project website: https://stl-locomotion.github.io/.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods. Builds on 44 of its 79 references that are in the map. First posted on arXiv 1 Jul 2026.

Builds on

44 of 79 references.

Closest ancestors · 1

Same direction, newest first

  1. 2024A Learning Framework for Diverse Legged Robot Locomotion Using Barrier-Based Style Rewards24 Sep

Other references · 43

  1. 2017Proximal Policy Optimization Algorithmscited by 15,215
  2. 2017Deep reinforcement learning from human preferencescited by 3,912
  3. 2015Trust Region Policy Optimizationcited by 2,580
  4. 2016Asynchronous Methods for Deep Reinforcement Learningcited by 2,258
  5. 2021Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learningcited by 998
  6. 2020Learning Quadrupedal Locomotion over Challenging Terraincited by 604
  7. 2023Eureka: Human-Level Reward Design via Coding Large Language Modelscited by 571
  8. 2017Learning Robust Rewards with Adversarial Inverse Reinforcement Learningcited by 490
  9. 2021Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulationcited by 407
  10. 2018Sim-to-Real: Learning Agile Locomotion For Quadruped Robotscited by 319
  11. 2018A Survey of Inverse Reinforcement Learning: Challenges, Methods and Progresscited by 298
  12. 2020Learning Agile Robotic Locomotion Skills by Imitating Animalscited by 251
31 more
  1. 2020Reward Machines: Exploiting Reward Function Structure in Reinforcement Learningcited by 191
  2. 2023Text2Reward: Reward Shaping with Language Models for Reinforcement Learningcited by 160
  3. 2022Legged Locomotion in Challenging Terrains using Egocentric Visioncited by 151
  4. 2016Reinforcement Learning With Temporal Logic Rewardscited by 117
  5. 2025MuJoCo Playgroundcited by 78
  6. 2021Minimizing Energy Consumption Leads to the Emergence of Gaits in Legged Robotscited by 76
  7. 2016Q-Learning for Robust Satisfaction of Signal Temporal Logic Specificationscited by 67
  8. 2020Dynamics Randomization Revisited:A Case Study for Quadrupedal Locomotioncited by 59
  9. 2019Highly Dynamic Quadruped Locomotion via Whole-Body Impulse Control and Model Predictive Controlcited by 54
  10. 2021Fast and Efficient Locomotion via Learned Gait Transitionscited by 54
  11. 2019DeepGait: Planning and Control of Quadrupedal Gaits using Deep Reinforcement Learningcited by 50
  12. 2019Dealing with Sparse Rewards in Reinforcement Learningcited by 42
  13. 2023Barkour: Benchmarking Animal-level Agility with Quadruped Robotscited by 41
  14. 2015Robust Online Monitoring of Signal Temporal Logiccited by 39
  15. 2022Learning Free Gait Transition for Quadruped Robots via Phase-Guided Controllercited by 29
  16. 2020Temporal-Logic-Based Reward Shaping for Continuing Reinforcement Learning Taskscited by 28
  17. 2019Modular Deep Reinforcement Learning with Temporal Logic Specificationscited by 25
  18. 2023ManyQuadrupeds: Learning a Single Locomotion Policy for Diverse Quadruped Robotscited by 19
  19. 2020Model-based Reinforcement Learning from Signal Temporal Logic Specificationscited by 18
  20. 2021Learning from Demonstrations using Signal Temporal Logiccited by 17
  21. 2015Correct-by-synthesis reinforcement learning with temporal logic constraintscited by 11
  22. 2023Imitating and Finetuning Model Predictive Control for Robust and Symmetric Quadrupedal Locomotioncited by 10
  23. 2016Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupedscited by 8
  24. 2024Robust-Locomotion-by-Logic: Perturbation-Resilient Bipedal Locomotion via Signal Temporal Logic Guided Model Predictive Controlcited by 8
  25. 2024Gaitor: Learning a Unified Representation Across Gaits for Real-World Quadruped Locomotioncited by 8
  26. 2021Learning Quadruped Locomotion Policies using Logical Rulescited by 6
  27. 2023Walking-by-Logic: Signal Temporal Logic-Guided Model Predictive Control for Bipedal Locomotion Resilient to External Perturbationscited by 6
  28. 2024Learning to Adapt through Bio-Inspired Gait Strategies for Versatile Quadruped Locomotioncited by 6
  29. 2024AllGaits: Learning All Quadruped Gaits and Transitionscited by 5
  30. 2021Learning multiple gaits of quadruped robot using hierarchical reinforcement learningcited by 4
  31. 2021FastMimic: Model-based Motion Imitation for Agile, Diverse and Generalizable Quadrupedal Locomotioncited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026From LLM-Generated Specifications to Learned Quadruped Locomotioncited by 0
  2. 2026Video2STL: Grounding VLM-Generated Temporal Specifications for Robot Learningcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Gait in Eight: Efficient On-Robot Learning for Omnidirectional Quadruped Locomotion
  2. 2024Towards Dynamic Quadrupedal Gaits: A Symmetry-Guided RL Hierarchy Enables Free Gait Transitions at Varying Speeds ↗
  3. 2025Towards Dynamic Quadrupedal Gaits: A Symmetry-Guided RL Hierarchy Enables Free Gait Transitions at Varying Speeds ↗
  4. 2025Real-Time Gait Adaptation for Quadrupeds using Model Predictive Control and Reinforcement Learning
  5. 2024Reinforcement Learning For Quadrupedal Locomotion: Current Advancements And Future Perspectives
  6. 2026Learning Fault-Tolerant Locomotion with Adaptive Gait Timing
  7. 2024Adaptive Energy Regularization for Autonomous Gait Transition and Energy-Efficient Quadruped Locomotion
  8. 2025GRoQ-LoCO: Generalist and Robot-agnostic Quadruped Locomotion Control using Offline Datasets