mlsanityData to 14 Oct 2026

Minimizing Energy Consumption Leads to the Emergence of Gaits in Legged Robots

arXiv 2111.01674 ↗First posted 25 Oct 2021cs.RO cs.AI cs.CVcited by 76

Not on the map. Why?

Cited by 25 in Deep reinforcement learning methods, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Legged locomotion is commonly studied and expressed as a discrete set of gait patterns, like walk, trot, gallop, which are usually treated as given and pre-programmed in legged robots for efficient locomotion at different speeds. However, fixing a set of pre-programmed gaits limits the generality of locomotion. Recent animal motor studies show that these conventional gaits are only prevalent in ideal flat terrain conditions while real-world locomotion is unstructured and more like bouts of intermittent steps. What principles could lead to both structured and unstructured patterns across mammals and how to synthesize them in robots? In this work, we take an analysis-by-synthesis approach and learn to move by minimizing mechanical energy. We demonstrate that learning to minimize energy consumption plays a key role in the emergence of natural locomotion gaits at different speeds in real quadruped robots. The emergent gaits are structured in ideal terrains and look similar to that of horses and sheep. The same approach leads to unstructured gaits in rough terrains which is consistent with the findings in animal motor control. We validate our hypothesis in both simulation and real hardware across natural terrains. Videos at https://energy-locomotion.github.io

Key facts. Cited by 76 papers in the map (data through 14 Oct 2026). Builds on 15 of its 42 references that are in the map. First posted on arXiv 25 Oct 2021.

Builds on

15 of 42 references.

References · 15

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2017Proximal Policy Optimization Algorithmscited by 15,215
  3. 2015High-Dimensional Continuous Control Using Generalized Advantage Estimationcited by 2,026
  4. 2020Learning Quadrupedal Locomotion over Challenging Terraincited by 604
  5. 2021RMA: Rapid Motor Adaptation for Legged Robotscited by 508
  6. 2019Learning agile and dynamic motor skills for legged robotscited by 504
  7. 2018Sim-to-Real: Learning Agile Locomotion For Quadruped Robotscited by 319
  8. 2020Learning Agile Robotic Locomotion Skills by Imitating Animalscited by 251
  9. 2018Learning to Walk via Deep Reinforcement Learningcited by 158
  10. 2017Preparing for the Unknown: Learning a Universal Policy with Online System Identificationcited by 141
  11. 2018Learning Symmetric and Low-energy Locomotioncited by 61
  12. 2019Sim-to-Real Transfer for Biped Locomotioncited by 56
3 more
  1. 2021Fast and Efficient Locomotion via Learned Gait Transitionscited by 54
  2. 2020Rapidly Adaptable Legged Robots via Evolutionary Meta-Learningcited by 43
  3. 2020Learning a Contact-Adaptive Controller for Robust, Efficient Legged Locomotioncited by 24

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 2; 2022: 17; 2023: 13; 2024: 20; 2025: 14; 2026: 10.

76 papers.

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  1. 2024Deep Reinforcement Learning for Robotics: A Survey of Real-World Successescited by 176
  2. 2022Rapid Locomotion via Reinforcement Learningcited by 168
  3. 2023Extreme Parkour with Legged Robotscited by 164
  4. 2022Legged Locomotion in Challenging Terrains using Egocentric Visioncited by 151
  5. 2023Robot Parkour Learningcited by 149
  6. 2024Open-TeleVision: Teleoperation with Immersive Active Visual Feedbackcited by 145
  7. 2024Expressive Whole-Body Control for Humanoid Robotscited by 139
  8. 2022Walk These Ways: Tuning Robot Control for Generalization with Multiplicity of Behaviorcited by 138
  9. 2022Deep Whole-Body Control: Learning a Unified Policy for Manipulation and Locomotioncited by 121
  10. 2024Reinforcement Learning for Versatile, Dynamic, and Robust Bipedal Locomotion Controlcited by 99
  11. 2022A Walk in the Park: Learning to Walk in 20 Minutes With Model-Free Reinforcement Learningcited by 83
  12. 2022Adapting Rapid Motor Adaptation for Bipedal Robotscited by 54
38 more
  1. 2021Coupling Vision and Proprioception for Navigation of Legged Robotscited by 51
  2. 2024Mobile-TeleVision: Predictive Motion Priors for Humanoid Whole-Body Controlcited by 51
  3. 2025AMO: Adaptive Motion Optimization for Hyper-Dexterous Humanoid Whole-Body Controlcited by 51
  4. 2022Retrospectives on the Embodied AI Workshopcited by 46
  5. 2025BeamDojo: Learning Agile Humanoid Locomotion on Sparse Footholdscited by 46
  6. 2021Learning to Jump from Pixelscited by 45
  7. 2023Legs as Manipulator: Pushing Quadrupedal Agility Beyond Locomotioncited by 39
  8. 2023Hybrid Internal Model: Learning Agile Legged Locomotion with Simulated Robot Responsecited by 39
  9. 2023Robust and Versatile Bipedal Jumping Control through Reinforcement Learningcited by 36
  10. 2022CPG-RL: Learning Central Pattern Generators for Quadruped Locomotioncited by 34
  11. 2023Learning and Adapting Agile Locomotion Skills by Transferring Experiencecited by 33
  12. 2024Learning Smooth Humanoid Locomotion through Lipschitz-Constrained Policiescited by 30
  13. 2022Learning Torque Control for Quadrupedal Locomotioncited by 29
  14. 2025Learning Getting-Up Policies for Real-World Humanoid Robotscited by 26
  15. 2022Learning Visual Locomotion with Cross-Modal Supervisioncited by 25
  16. 2023Grow Your Limits: Continuous Improvement with Real-World RL for Robotic Locomotioncited by 24
  17. 2022ViNL: Visual Navigation and Locomotion Over Obstaclescited by 23
  18. 2024CaT: Constraints as Terminations for Legged Locomotion Reinforcement Learningcited by 23
  19. 2024World Model-based Perception for Visual Legged Locomotioncited by 18
  20. 2023Controlling the Solo12 Quadruped Robot with Deep Reinforcement Learningcited by 16
  21. 2024Constrained Reinforcement Learning with Smoothed Log Barrier Functioncited by 15
  22. 2024SoloParkour: Constrained Reinforcement Learning for Visual Locomotion from Privileged Experiencecited by 14
  23. 2022Learning to Get Upcited by 11
  24. 2022Cascaded Compositional Residual Learning for Complex Interactive Behaviorscited by 10
  25. 2024Dexterous Legged Locomotion in Confined 3D Spaces with Reinforcement Learningcited by 9
  26. 2022Learning to Walk by Steering: Perceptive Quadrupedal Locomotion in Dynamic Environmentscited by 8
  27. 2025StyleLoco: Generative Adversarial Distillation for Natural Humanoid Robot Locomotioncited by 8
  28. 2024SLR: Learning Quadruped Locomotion without Privileged Informationcited by 6
  29. 2024Constrained Skill Discovery: Quadruped Locomotion with Unsupervised Reinforcement Learningcited by 6
  30. 2025Unsupervised Skill Discovery as Exploration for Learning Agile Locomotioncited by 6
  31. 2022Learning Semantics-Aware Locomotion Skills from Human Demonstrationcited by 5
  32. 2023Puppeteer and Marionette: Learning Anticipatory Quadrupedal Locomotion Based on Interactions of a Central Pattern Generator and Supraspinal Drivecited by 5
  33. 2024Adaptive Energy Regularization for Autonomous Gait Transition and Energy-Efficient Quadruped Locomotioncited by 5
  34. 2025DreamPolicy: A Unified World-model Policy for Scalable Humanoid Locomotioncited by 5
  35. 2025Non-conflicting Energy Minimization in Reinforcement Learning based Robot Controlcited by 5
  36. 2025SLIM: Sim-to-Real Legged Instructive Manipulation via Long-Horizon Visuomotor Learningcited by 4
  37. 2025Deep RL Needs Deep Behavior Analysis: Exploring Implicit Planning by Model-Free Agents in Open-Ended Environmentscited by 4
  38. 2025Spectral Normalization for Lipschitz-Constrained Policies on Learning Humanoid Locomotioncited by 3

50 most cited of 76 All 76 (JSON)