Learning Symmetric and Low-energy Locomotion
Not on the map. Why?
Abstract (arXiv)
Learning locomotion skills is a challenging problem. To generate realistic and smooth locomotion, existing methods use motion capture, finite state machines or morphology-specific knowledge to guide the motion generation algorithms. Deep reinforcement learning (DRL) is a promising approach for the automatic creation of locomotion control. Indeed, a standard benchmark for DRL is to automatically create a running controller for a biped character from a simple reward function. Although several different DRL algorithms can successfully create a running controller, the resulting motions usually look nothing like a real runner. This paper takes a minimalist learning approach to the locomotion problem, without the use of motion examples, finite state machines, or morphology-specific knowledge. We introduce two modifications to the DRL approach that, when used together, produce locomotion behaviors that are symmetric, low-energy, and much closer to that of a real person. First, we introduce a new term to the loss function (not the reward function) that encourages symmetric actions. Second, we introduce a new curriculum learning method that provides modulated physical assistance to help the character with left/right balance and forward movement. The algorithm automatically computes appropriate assistance to the character and gradually relaxes this assistance, so that eventually the character learns to move entirely without help. Because our method does not make use of motion capture data, it can be applied to a variety of character morphologies. We demonstrate locomotion controllers for the lower half of a biped, a full humanoid, a quadruped, and a hexapod. Our results show that learned policies are able to produce symmetric, low-energy gaits. In addition, speed-appropriate gait patterns emerge without any guidance from motion examples or contact planning.
Key facts. Cited by 53 papers in the map (data through 7 Oct 2026). First posted on arXiv 24 Jan 2018.
Builds on
No reference list yet.
Built on by
Citing papers per year: 2019: 1; 2020: 0; 2021: 14; 2022: 11; 2023: 11; 2024: 3; 2025: 7; 2026: 6.
53 papers.
Sort:
By area:
- 2021How to Train Your Robot with Deep Reinforcement Learning; Lessons We've Learnedcited by 201
- 2021Character Controllers Using Motion VAEscited by 182
- 2021Embodied Intelligence via Learning and Evolutioncited by 154
- 2023Trace and Pace: Controllable Pedestrian Animation via Guided Trajectory Diffusioncited by 137
- 2021Learning Vision-Guided Quadrupedal Locomotion End-to-End with Cross-Modal Transformerscited by 71
- 2022Real-Time Style Modelling of Human Locomotion via Feature-Wise Transformations and Local Motion Phasescited by 71
- 2022Adversarial Motion Priors Make Good Substitutes for Complex Reward Functionscited by 68
- 2021Minimizing Energy Consumption Leads to the Emergence of Gaits in Legged Robotscited by 67
- 2025InterMimic: Towards Universal Whole-Body Control for Physics-Based Human-Object Interactionscited by 67
- 2021Fast and Efficient Locomotion via Learned Gait Transitionscited by 50
- 2023Neural Categorical Priors for Physics-Based Character Controlcited by 37
- 2023Not Only Rewards But Also Constraints: Applications on Legged Robot Locomotioncited by 33
38 more
- 2023Composite Motion Learning with Task Controlcited by 26
- 2025UniPhys: Unified Planner and Controller with Diffusion for Flexible Physics-Based Character Controlcited by 24
- 2022ControlVAE: Model-Based Learning of Generative Controllers for Physics-Based Characterscited by 21
- 2021AMP: Adversarial Motion Priors for Stylized Physics-Based Character Controlcited by 18
- 2024Symmetry Considerations for Learning Task Symmetric Robot Policiescited by 18
- 2021Discovering Diverse Athletic Jumping Strategiescited by 15
- 2023AdaptNet: Policy Adaptation for Physics-Based Character Controlcited by 15
- 2021A GAN-Like Approach for Physics-Based Imitation Learning and Interactive Character Controlcited by 12
- 2022A Survey on Reinforcement Learning Methods in Character Animationcited by 12
- 2022Generative GaitNetcited by 11
- 2022Learning to Get Upcited by 11
- 2025A Unified and General Humanoid Whole-Body Controller for Versatile Locomotioncited by 10
- 2022Cascaded Compositional Residual Learning for Complex Interactive Behaviorscited by 9
- 2025GROVE: A Generalized Reward for Learning Open-Vocabulary Physical Skillcited by 9
- 2022ASE: Large-Scale Reusable Adversarial Skill Embeddings for Physically Simulated Characterscited by 6
- 2023On discrete symmetries of robotics systems: A group-theoretic and data-driven analysiscited by 6
- 2022Learning Bipedal Walking On Planned Footsteps For Humanoid Robotscited by 5
- 2023Learning to Transfer In-Hand Manipulations Using a Greedy Shape Curriculumcited by 5
- 2021Efficient Hyperparameter Optimization for Physics-based Character Animationcited by 4
- 2021An Adaptable Approach to Learn Realistic Legged Locomotion without Examplescited by 4
- 2023Addressing imperfect symmetry: A novel symmetry-learning actor-critic extensioncited by 4
- 2026ZEST: Zero-shot Embodied Skill Transfer for Athletic Robot Controlcited by 4
- 2023Bidirectional GaitNet: A Bidirectional Prediction Model of Human Gait and Anatomical Conditionscited by 3
- 2021Quadruped Locomotion on Non-Rigid Terrain using Reinforcement Learningcited by 2
- 2022Co-design of Embodied Neural Intelligence via Constrained Evolutioncited by 1
- 2022Sample Efficient Dynamics Learning for Symmetrical Legged Robots:Leveraging Physics Invariance and Geometric Symmetriescited by 1
- 2023An Investigation of Time Reversal Symmetry in Reinforcement Learningcited by 1
- 2024Semantic-Geometric-Physical-Driven Robot Manipulation Skill Transfer via Skill Library and Tactile Representationcited by 1
- 2026AdaptManip: Learning Adaptive Whole-Body Object Lifting and Delivery with Online Recurrent State Estimationcited by 1
- 2019Self-Imitation Learning of Locomotion Movements through Termination Curriculumcited by 0
- 2021An Energy-Saving Snake Locomotion Gait Policy Obtained Using Deep Reinforcement Learningcited by 0
- 2021Modelling Human Kinetics and Kinematics during Walking using Reinforcement Learningcited by 0
- 2023Deriving Rewards for Reinforcement Learning from Symbolic Behaviour Descriptions of Bipedal Walkingcited by 0
- 2024Reinforcement Learning from Wild Animal Videoscited by 0
- 2025SATA: Safe and Adaptive Torque-Based Locomotion Policies Inspired by Animal Learningcited by 0
- 2025GBC: Generalized Behavior-Cloning Framework for Whole-Body Humanoid Imitationcited by 0
- 2025Reduced-Order Model-Guided Reinforcement Learning for Demonstration-Free Humanoid Locomotioncited by 0
- 2026Sim-to-Real of Humanoid Locomotion Policies via Joint Torque Space Perturbation Injectioncited by 0
50 most cited of 53 All 53 (JSON)
- 2026Lambda-Hold Control: Human-Like Movement Emerges from a Minimal Task Reward in Predictive Musculoskeletal Simulation17 Aug 2026
- 2026Reflex: Reinforcement Learning with Reflection Symmetry Exploitation in State-Based Continuous Control22 May 2026
- 2026Neural Assistive Impulses: Synthesizing Exaggerated Motions for Physics-based Characters7 Apr 2026
- 2026Sim-to-Real of Humanoid Locomotion Policies via Joint Torque Space Perturbation Injection23 Mar 2026
- 2026AdaptManip: Learning Adaptive Whole-Body Object Lifting and Delivery with Online Recurrent State Estimation16 Feb 2026
- 2026ZEST: Zero-shot Embodied Skill Transfer for Athletic Robot Control30 Jan 2026
- 2025Reduced-Order Model-Guided Reinforcement Learning for Demonstration-Free Humanoid Locomotion23 Sep 2025
- 2025GBC: Generalized Behavior-Cloning Framework for Whole-Body Humanoid Imitation13 Aug 2025
- 2025UniPhys: Unified Planner and Controller with Diffusion for Flexible Physics-Based Character Control17 Apr 2025
- 2025GROVE: A Generalized Reward for Learning Open-Vocabulary Physical Skill5 Apr 2025
- 2025InterMimic: Towards Universal Whole-Body Control for Physics-Based Human-Object Interactions27 Feb 2025
- 2025SATA: Safe and Adaptive Torque-Based Locomotion Policies Inspired by Animal Learning18 Feb 2025
38 more
- 2025A Unified and General Humanoid Whole-Body Controller for Versatile Locomotion5 Feb 2025
- 2024Reinforcement Learning from Wild Animal Videos5 Dec 2024
- 2024Semantic-Geometric-Physical-Driven Robot Manipulation Skill Transfer via Skill Library and Tactile Representation18 Nov 2024
- 2024Symmetry Considerations for Learning Task Symmetric Robot Policies7 Mar 2024
- 2023Deriving Rewards for Reinforcement Learning from Symbolic Behaviour Descriptions of Bipedal Walking16 Dec 2023
- 2023An Investigation of Time Reversal Symmetry in Reinforcement Learning28 Nov 2023
- 2023AdaptNet: Policy Adaptation for Physics-Based Character Control30 Sep 2023
- 2023Addressing imperfect symmetry: A novel symmetry-learning actor-critic extension6 Sep 2023
- 2023Not Only Rewards But Also Constraints: Applications on Legged Robot Locomotion24 Aug 2023
- 2023Neural Categorical Priors for Physics-Based Character Control14 Aug 2023
- 2023Bidirectional GaitNet: A Bidirectional Prediction Model of Human Gait and Anatomical Conditions7 Jun 2023
- 2023Composite Motion Learning with Task Control5 May 2023
- 2023Trace and Pace: Controllable Pedestrian Animation via Guided Trajectory Diffusion4 Apr 2023
- 2023Learning to Transfer In-Hand Manipulations Using a Greedy Shape Curriculum14 Mar 2023
- 2023On discrete symmetries of robotics systems: A group-theoretic and data-driven analysis21 Feb 2023
- 2022Cascaded Compositional Residual Learning for Complex Interactive Behaviors17 Dec 2022
- 2022Sample Efficient Dynamics Learning for Symmetrical Legged Robots:Leveraging Physics Invariance and Geometric Symmetries13 Oct 2022
- 2022ControlVAE: Model-Based Learning of Generative Controllers for Physics-Based Characters12 Oct 2022
- 2022Learning Bipedal Walking On Planned Footsteps For Humanoid Robots26 Jul 2022
- 2022Co-design of Embodied Neural Intelligence via Constrained Evolution21 May 2022
- 2022ASE: Large-Scale Reusable Adversarial Skill Embeddings for Physically Simulated Characters4 May 2022
- 2022Learning to Get Up30 Apr 2022
- 2022Adversarial Motion Priors Make Good Substitutes for Complex Reward Functions28 Mar 2022
- 2022A Survey on Reinforcement Learning Methods in Character Animation7 Mar 2022
- 2022Generative GaitNet28 Jan 2022
- 2022Real-Time Style Modelling of Human Locomotion via Feature-Wise Transformations and Local Motion Phases12 Jan 2022
- 2021An Adaptable Approach to Learn Realistic Legged Locomotion without Examples28 Oct 2021
- 2021Minimizing Energy Consumption Leads to the Emergence of Gaits in Legged Robots25 Oct 2021
- 2021Learning Vision-Guided Quadrupedal Locomotion End-to-End with Cross-Modal Transformers8 Jul 2021
- 2021Quadruped Locomotion on Non-Rigid Terrain using Reinforcement Learning7 Jul 2021
- 2021A GAN-Like Approach for Physics-Based Imitation Learning and Interactive Character Control21 May 2021
- 2021Discovering Diverse Athletic Jumping Strategies2 May 2021
- 2021Efficient Hyperparameter Optimization for Physics-based Character Animation26 Apr 2021
- 2021Fast and Efficient Locomotion via Learned Gait Transitions9 Apr 2021
- 2021AMP: Adversarial Motion Priors for Stylized Physics-Based Character Control5 Apr 2021
- 2021Character Controllers Using Motion VAEs26 Mar 2021
- 2021Modelling Human Kinetics and Kinematics during Walking using Reinforcement Learning15 Mar 2021
- 2021An Energy-Saving Snake Locomotion Gait Policy Obtained Using Deep Reinforcement Learning8 Mar 2021
50 newest of 53 All 53 (JSON)
- 2021A GAN-Like Approach for Physics-Based Imitation Learning and Interactive Character Controlcited by 12
- 2026AdaptManip: Learning Adaptive Whole-Body Object Lifting and Delivery with Online Recurrent State Estimationcited by 1
- 2019Self-Imitation Learning of Locomotion Movements through Termination Curriculumcited by 0
- 2026AdaptManip: Learning Adaptive Whole-Body Object Lifting and Delivery with Online Recurrent State Estimation16 Feb 2026
- 2021A GAN-Like Approach for Physics-Based Imitation Learning and Interactive Character Control21 May 2021
- 2019Self-Imitation Learning of Locomotion Movements through Termination Curriculum27 Jul 2019
- 2021How to Train Your Robot with Deep Reinforcement Learning; Lessons We've Learnedcited by 201
- 2021Character Controllers Using Motion VAEscited by 182
- 2021Embodied Intelligence via Learning and Evolutioncited by 154
- 2021Learning Vision-Guided Quadrupedal Locomotion End-to-End with Cross-Modal Transformerscited by 71
- 2022Real-Time Style Modelling of Human Locomotion via Feature-Wise Transformations and Local Motion Phasescited by 71
- 2022Adversarial Motion Priors Make Good Substitutes for Complex Reward Functionscited by 68
- 2021Minimizing Energy Consumption Leads to the Emergence of Gaits in Legged Robotscited by 67
- 2025InterMimic: Towards Universal Whole-Body Control for Physics-Based Human-Object Interactionscited by 67
- 2021Fast and Efficient Locomotion via Learned Gait Transitionscited by 50
- 2023Neural Categorical Priors for Physics-Based Character Controlcited by 37
- 2023Not Only Rewards But Also Constraints: Applications on Legged Robot Locomotioncited by 33
- 2023Composite Motion Learning with Task Controlcited by 26
12 most cited of 48 All 48 (JSON)
- 2026Lambda-Hold Control: Human-Like Movement Emerges from a Minimal Task Reward in Predictive Musculoskeletal Simulation17 Aug 2026
- 2026Reflex: Reinforcement Learning with Reflection Symmetry Exploitation in State-Based Continuous Control22 May 2026
- 2026Neural Assistive Impulses: Synthesizing Exaggerated Motions for Physics-based Characters7 Apr 2026
- 2026Sim-to-Real of Humanoid Locomotion Policies via Joint Torque Space Perturbation Injection23 Mar 2026
- 2026ZEST: Zero-shot Embodied Skill Transfer for Athletic Robot Control30 Jan 2026
- 2025Reduced-Order Model-Guided Reinforcement Learning for Demonstration-Free Humanoid Locomotion23 Sep 2025
- 2025GBC: Generalized Behavior-Cloning Framework for Whole-Body Humanoid Imitation13 Aug 2025
- 2025UniPhys: Unified Planner and Controller with Diffusion for Flexible Physics-Based Character Control17 Apr 2025
- 2025GROVE: A Generalized Reward for Learning Open-Vocabulary Physical Skill5 Apr 2025
- 2025InterMimic: Towards Universal Whole-Body Control for Physics-Based Human-Object Interactions27 Feb 2025
- 2025SATA: Safe and Adaptive Torque-Based Locomotion Policies Inspired by Animal Learning18 Feb 2025
- 2025A Unified and General Humanoid Whole-Body Controller for Versatile Locomotion5 Feb 2025
12 newest of 48 All 48 (JSON)