Hybrid Internal Model: Learning Agile Legged Locomotion with Simulated Robot Response
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Abstract (arXiv)
Robust locomotion control depends on accurate state estimations. However, the sensors of most legged robots can only provide partial and noisy observations, making the estimation particularly challenging, especially for external states like terrain frictions and elevation maps. Inspired by the classical Internal Model Control principle, we consider these external states as disturbances and introduce Hybrid Internal Model (HIM) to estimate them according to the response of the robot. The response, which we refer to as the hybrid internal embedding, contains the robot's explicit velocity and implicit stability representation, corresponding to two primary goals for locomotion tasks: explicitly tracking velocity and implicitly maintaining stability. We use contrastive learning to optimize the embedding to be close to the robot's successor state, in which the response is naturally embedded. HIM has several appealing benefits: It only needs the robot's proprioceptions, i.e., those from joint encoders and IMU as observations. It innovatively maintains consistent observations between simulation reference and reality that avoids information loss in mimicking learning. It exploits batch-level information that is more robust to noises and keeps better sample efficiency. It only requires 1 hour of training on an RTX 4090 to enable a quadruped robot to traverse any terrain under any disturbances. A wealth of real-world experiments demonstrates its agility, even in high-difficulty tasks and cases never occurred during the training process, revealing remarkable open-world generalizability.
Key facts. Cited by 39 papers in the map (data through 14 Oct 2026). Builds on 34 of its 47 references that are in the map. First posted on arXiv 18 Dec 2023.
Builds on
34 of 47 references.
References · 34
- 2020Unsupervised Learning of Visual Features by Contrasting Cluster Assignmentscited by 2,857
- 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,316
- 2021Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learningcited by 998
- 2020Learning Quadrupedal Locomotion over Challenging Terraincited by 604
- 2021Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learningcited by 512
- 2021RMA: Rapid Motor Adaptation for Legged Robotscited by 508
- 2019Learning agile and dynamic motor skills for legged robotscited by 504
- 2022DayDreamer: World Models for Physical Robot Learningcited by 400
- 2019Learning by Cheatingcited by 383
- 2022Learning robust perceptive locomotion for quadrupedal robots in the wildcited by 382
- 2018Sim-to-Real: Learning Agile Locomotion For Quadruped Robotscited by 319
- 2020Learning Agile Robotic Locomotion Skills by Imitating Animalscited by 251
22 more
- 2022Rapid Locomotion via Reinforcement Learningcited by 168
- 2022Legged Locomotion in Challenging Terrains using Egocentric Visioncited by 151
- 2023Robot Parkour Learningcited by 149
- 2022Walk These Ways: Tuning Robot Control for Generalization with Multiplicity of Behaviorcited by 138
- 2022Deep Whole-Body Control: Learning a Unified Policy for Manipulation and Locomotioncited by 121
- 2022Adversarial Motion Priors Make Good Substitutes for Complex Reward Functionscited by 89
- 2021Learning Vision-Guided Quadrupedal Locomotion End-to-End with Cross-Modal Transformerscited by 79
- 2021Learning to Fly -- a Gym Environment with PyBullet Physics for Reinforcement Learning of Multi-agent Quadcopter Controlcited by 77
- 2021Minimizing Energy Consumption Leads to the Emergence of Gaits in Legged Robotscited by 76
- 2021DreamerPro: Reconstruction-Free Model-Based Reinforcement Learning with Prototypical Representationscited by 74
- 2020Multi-expert learning of adaptive legged locomotioncited by 67
- 2023DreamWaQ: Learning Robust Quadrupedal Locomotion With Implicit Terrain Imagination via Deep Reinforcement Learningcited by 66
- 2020Dynamics Randomization Revisited:A Case Study for Quadrupedal Locomotioncited by 59
- 2023Neural Volumetric Memory for Visual Locomotion Controlcited by 44
- 2022Elevation Mapping for Locomotion and Navigation using GPUcited by 43
- 2023Barkour: Benchmarking Animal-level Agility with Quadruped Robotscited by 41
- 2023DribbleBot: Dynamic Legged Manipulation in the Wildcited by 40
- 2023Legs as Manipulator: Pushing Quadrupedal Agility Beyond Locomotioncited by 39
- 2021Vision-Guided Quadrupedal Locomotion in the Wild with Multi-Modal Delay Randomizationcited by 23
- 2023Generalized Animal Imitator: Agile Locomotion with Versatile Motion Priorcited by 19
- 2021Vision-aided Dynamic Quadrupedal Locomotion on Discrete Terrain using Motion Librariescited by 13
- 2017Legged Robot State-Estimation Through Combined Forward Kinematic and Preintegrated Contact Factorscited by 6
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Citing papers per year: 2024: 9; 2025: 15; 2026: 15.
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- 2024NaVILA: Legged Robot Vision-Language-Action Model for Navigationcited by 211
- 2025ASAP: Aligning Simulation and Real-World Physics for Learning Agile Humanoid Whole-Body Skillscited by 130
- 2025HOMIE: Humanoid Loco-Manipulation with Isomorphic Exoskeleton Cockpitcited by 76
- 2024GRUtopia: Dream General Robots in a City at Scalecited by 59
- 2025BeamDojo: Learning Agile Humanoid Locomotion on Sparse Footholdscited by 46
- 2024CTS: Concurrent Teacher-Student Reinforcement Learning for Legged Locomotioncited by 25
- 2025Rethinking the Embodied Gap in Vision-and-Language Navigation: A Holistic Study of Physical and Visual Disparitiescited by 25
- 2026Perceptive Humanoid Parkour: Chaining Dynamic Human Skills via Motion Matchingcited by 19
- 2024World Model-based Perception for Visual Legged Locomotioncited by 18
- 2025Bridging the Sim-to-Real Gap for Athletic Loco-Manipulationcited by 13
- 2024Robust Robot Walker: Learning Agile Locomotion over Tiny Trapscited by 7
- 2024PIP-Loco: A Proprioceptive Infinite Horizon Planning Framework for Quadrupedal Robot Locomotioncited by 7
27 more
- 2024SLR: Learning Quadruped Locomotion without Privileged Informationcited by 6
- 2025TAR: Teacher-Aligned Representations via Contrastive Learning for Quadrupedal Locomotioncited by 5
- 2024GRAM: Generalization in Deep RL with a Robust Adaptation Modulecited by 3
- 2025Investigating Lagrangian Neural Networks for Infinite Horizon Planning in Quadrupedal Locomotioncited by 3
- 2025Bipedalism for Quadrupedal Robots: Versatile Loco-Manipulation through Risk-Adaptive Reinforcement Learningcited by 3
- 2025Contrastive Representation Learning for Robust Sim-to-Real Transfer of Adaptive Humanoid Locomotioncited by 3
- 2025FALCON: Actively Decoupled Visuomotor Policies for Loco-Manipulation with Foundation-Model-Based Coordinationcited by 3
- 2024Neural Internal Model Control: Learning a Robust Control Policy via Predictive Error Feedbackcited by 2
- 2025Transferable Latent-to-Latent Locomotion Policy for Efficient and Versatile Motion Control of Diverse Legged Robotscited by 2
- 2025CHyLL: Learning Continuous Neural Representations of Hybrid Systemscited by 2
- 2026Toward Reliable Sim-to-Real Predictability for MoE-based Robust Quadrupedal Locomotioncited by 2
- 2026Agent-Driven Autonomous Reinforcement Learning Research: Iterative Policy Improvement for Quadruped Locomotioncited by 2
- 2025MULE: Multi-terrain and Unknown Load Adaptation for Effective Quadrupedal Locomotioncited by 1
- 2025GRoQ-LoCO: Generalist and Robot-agnostic Quadruped Locomotion Control using Offline Datasetscited by 1
- 2026Mind Your Steps: A General Learning Framework for Accurate Humanoid Foothold Trackingcited by 1
- 2025ATRos: Learning Energy-Efficient Agile Locomotion for Wheeled-legged Robotscited by 0
- 2026CMR: Contractive Mapping Embeddings for Robust Humanoid Locomotion on Unstructured Terrainscited by 0
- 2026Data-Driven Physics Embedded Dynamics with Predictive Control and Reinforcement Learning for Quadrupedscited by 0
- 2026KiRAS: Keyframe Guided Self-Imitation for Robust and Adaptive Skill Learning in Quadruped Robotscited by 0
- 2026Learning Task-Invariant Properties via Dreamer: Enabling Efficient Policy Transfer for Quadruped Robotscited by 0
- 2026CoRe-MoE: Contrastive Reweighted Mixture of Experts for Multi-Terrain Humanoid Locomotion with Gait Adaptationcited by 0
- 2026IMPACT: Learning Internal-Model Predictive Control for Forceful Robotic Manipulationcited by 0
- 2026GUIDE: Goal-Initialized Directional Understanding for End-to-End Legged Navigationcited by 0
- 2026IDEA: Insensitive to Dynamics Mismatch via Effect Alignment for Sim-to-Real Transfer in Multi-Agent Controlcited by 0
- 2026Stability-aware Residual Reinforcement Learning Framework for Robotic Manipulator Disturbance Compensationcited by 0
- 2026Bridging Body and Brain: Gene-Driven Morphology--Control Co-Designcited by 0
- 2026PROMO: Preference-conditioned Multi-Objective Reinforcement Learning for Quadrupedal Robotscited by 0
- 2026PROMO: Preference-conditioned Multi-Objective Reinforcement Learning for Quadrupedal Robots1 Oct 2026
- 2026Bridging Body and Brain: Gene-Driven Morphology--Control Co-Design25 Sep 2026
- 2026Stability-aware Residual Reinforcement Learning Framework for Robotic Manipulator Disturbance Compensation18 Sep 2026
- 2026IDEA: Insensitive to Dynamics Mismatch via Effect Alignment for Sim-to-Real Transfer in Multi-Agent Control25 Jun 2026
- 2026GUIDE: Goal-Initialized Directional Understanding for End-to-End Legged Navigation9 Jun 2026
- 2026IMPACT: Learning Internal-Model Predictive Control for Forceful Robotic Manipulation9 Jun 2026
- 2026Mind Your Steps: A General Learning Framework for Accurate Humanoid Foothold Tracking6 Jun 2026
- 2026CoRe-MoE: Contrastive Reweighted Mixture of Experts for Multi-Terrain Humanoid Locomotion with Gait Adaptation3 Jun 2026
- 2026Learning Task-Invariant Properties via Dreamer: Enabling Efficient Policy Transfer for Quadruped Robots3 Apr 2026
- 2026Agent-Driven Autonomous Reinforcement Learning Research: Iterative Policy Improvement for Quadruped Locomotion28 Mar 2026
- 2026KiRAS: Keyframe Guided Self-Imitation for Robust and Adaptive Skill Learning in Quadruped Robots16 Mar 2026
- 2026Data-Driven Physics Embedded Dynamics with Predictive Control and Reinforcement Learning for Quadrupeds15 Mar 2026
27 more
- 2026Perceptive Humanoid Parkour: Chaining Dynamic Human Skills via Motion Matching17 Feb 2026
- 2026CMR: Contractive Mapping Embeddings for Robust Humanoid Locomotion on Unstructured Terrains3 Feb 2026
- 2026Toward Reliable Sim-to-Real Predictability for MoE-based Robust Quadrupedal Locomotion31 Jan 2026
- 2025CHyLL: Learning Continuous Neural Representations of Hybrid Systems10 Dec 2025
- 2025FALCON: Actively Decoupled Visuomotor Policies for Loco-Manipulation with Foundation-Model-Based Coordination4 Dec 2025
- 2025ATRos: Learning Energy-Efficient Agile Locomotion for Wheeled-legged Robots11 Oct 2025
- 2025Contrastive Representation Learning for Robust Sim-to-Real Transfer of Adaptive Humanoid Locomotion16 Sep 2025
- 2025Bipedalism for Quadrupedal Robots: Versatile Loco-Manipulation through Risk-Adaptive Reinforcement Learning27 Jul 2025
- 2025Rethinking the Embodied Gap in Vision-and-Language Navigation: A Holistic Study of Physical and Visual Disparities17 Jul 2025
- 2025Investigating Lagrangian Neural Networks for Infinite Horizon Planning in Quadrupedal Locomotion19 Jun 2025
- 2025GRoQ-LoCO: Generalist and Robot-agnostic Quadruped Locomotion Control using Offline Datasets16 May 2025
- 2025MULE: Multi-terrain and Unknown Load Adaptation for Effective Quadrupedal Locomotion1 May 2025
- 2025TAR: Teacher-Aligned Representations via Contrastive Learning for Quadrupedal Locomotion26 Mar 2025
- 2025Transferable Latent-to-Latent Locomotion Policy for Efficient and Versatile Motion Control of Diverse Legged Robots22 Mar 2025
- 2025HOMIE: Humanoid Loco-Manipulation with Isomorphic Exoskeleton Cockpit18 Feb 2025
- 2025Bridging the Sim-to-Real Gap for Athletic Loco-Manipulation15 Feb 2025
- 2025BeamDojo: Learning Agile Humanoid Locomotion on Sparse Footholds14 Feb 2025
- 2025ASAP: Aligning Simulation and Real-World Physics for Learning Agile Humanoid Whole-Body Skills3 Feb 2025
- 2024NaVILA: Legged Robot Vision-Language-Action Model for Navigation5 Dec 2024
- 2024GRAM: Generalization in Deep RL with a Robust Adaptation Module5 Dec 2024
- 2024Neural Internal Model Control: Learning a Robust Control Policy via Predictive Error Feedback20 Nov 2024
- 2024World Model-based Perception for Visual Legged Locomotion25 Sep 2024
- 2024PIP-Loco: A Proprioceptive Infinite Horizon Planning Framework for Quadrupedal Robot Locomotion14 Sep 2024
- 2024Robust Robot Walker: Learning Agile Locomotion over Tiny Traps11 Sep 2024
- 2024GRUtopia: Dream General Robots in a City at Scale15 Jul 2024
- 2024SLR: Learning Quadruped Locomotion without Privileged Information7 Jun 2024
- 2024CTS: Concurrent Teacher-Student Reinforcement Learning for Legged Locomotion17 May 2024
- 2024CTS: Concurrent Teacher-Student Reinforcement Learning for Legged Locomotioncited by 25
- 2024SLR: Learning Quadruped Locomotion without Privileged Informationcited by 6
- 2024GRAM: Generalization in Deep RL with a Robust Adaptation Modulecited by 3
- 2025Bipedalism for Quadrupedal Robots: Versatile Loco-Manipulation through Risk-Adaptive Reinforcement Learningcited by 3
- 2025Contrastive Representation Learning for Robust Sim-to-Real Transfer of Adaptive Humanoid Locomotioncited by 3
- 2025Transferable Latent-to-Latent Locomotion Policy for Efficient and Versatile Motion Control of Diverse Legged Robotscited by 2
- 2026Toward Reliable Sim-to-Real Predictability for MoE-based Robust Quadrupedal Locomotioncited by 2
- 2026Agent-Driven Autonomous Reinforcement Learning Research: Iterative Policy Improvement for Quadruped Locomotioncited by 2
- 2025ATRos: Learning Energy-Efficient Agile Locomotion for Wheeled-legged Robotscited by 0
- 2026Data-Driven Physics Embedded Dynamics with Predictive Control and Reinforcement Learning for Quadrupedscited by 0
- 2026GUIDE: Goal-Initialized Directional Understanding for End-to-End Legged Navigationcited by 0
- 2026Stability-aware Residual Reinforcement Learning Framework for Robotic Manipulator Disturbance Compensationcited by 0
12 most cited of 13 All 13 (JSON)
- 2026PROMO: Preference-conditioned Multi-Objective Reinforcement Learning for Quadrupedal Robots1 Oct 2026
- 2026Stability-aware Residual Reinforcement Learning Framework for Robotic Manipulator Disturbance Compensation18 Sep 2026
- 2026GUIDE: Goal-Initialized Directional Understanding for End-to-End Legged Navigation9 Jun 2026
- 2026Agent-Driven Autonomous Reinforcement Learning Research: Iterative Policy Improvement for Quadruped Locomotion28 Mar 2026
- 2026Data-Driven Physics Embedded Dynamics with Predictive Control and Reinforcement Learning for Quadrupeds15 Mar 2026
- 2026Toward Reliable Sim-to-Real Predictability for MoE-based Robust Quadrupedal Locomotion31 Jan 2026
- 2025ATRos: Learning Energy-Efficient Agile Locomotion for Wheeled-legged Robots11 Oct 2025
- 2025Contrastive Representation Learning for Robust Sim-to-Real Transfer of Adaptive Humanoid Locomotion16 Sep 2025
- 2025Bipedalism for Quadrupedal Robots: Versatile Loco-Manipulation through Risk-Adaptive Reinforcement Learning27 Jul 2025
- 2025Transferable Latent-to-Latent Locomotion Policy for Efficient and Versatile Motion Control of Diverse Legged Robots22 Mar 2025
- 2024GRAM: Generalization in Deep RL with a Robust Adaptation Module5 Dec 2024
- 2024SLR: Learning Quadruped Locomotion without Privileged Information7 Jun 2024
12 newest of 13 All 13 (JSON)
- 2024NaVILA: Legged Robot Vision-Language-Action Model for Navigationcited by 211
- 2025ASAP: Aligning Simulation and Real-World Physics for Learning Agile Humanoid Whole-Body Skillscited by 130
- 2025HOMIE: Humanoid Loco-Manipulation with Isomorphic Exoskeleton Cockpitcited by 76
- 2024GRUtopia: Dream General Robots in a City at Scalecited by 59
- 2025BeamDojo: Learning Agile Humanoid Locomotion on Sparse Footholdscited by 46
- 2026Perceptive Humanoid Parkour: Chaining Dynamic Human Skills via Motion Matchingcited by 19
- 2025Bridging the Sim-to-Real Gap for Athletic Loco-Manipulationcited by 13
- 2024Robust Robot Walker: Learning Agile Locomotion over Tiny Trapscited by 7
- 2024PIP-Loco: A Proprioceptive Infinite Horizon Planning Framework for Quadrupedal Robot Locomotioncited by 7
- 2025Investigating Lagrangian Neural Networks for Infinite Horizon Planning in Quadrupedal Locomotioncited by 3
- 2024Neural Internal Model Control: Learning a Robust Control Policy via Predictive Error Feedbackcited by 2
- 2025CHyLL: Learning Continuous Neural Representations of Hybrid Systemscited by 2
- 2025MULE: Multi-terrain and Unknown Load Adaptation for Effective Quadrupedal Locomotioncited by 1
12 most cited of 18 All 18 (JSON)
- 2026Bridging Body and Brain: Gene-Driven Morphology--Control Co-Design25 Sep 2026
- 2026IDEA: Insensitive to Dynamics Mismatch via Effect Alignment for Sim-to-Real Transfer in Multi-Agent Control25 Jun 2026
- 2026IMPACT: Learning Internal-Model Predictive Control for Forceful Robotic Manipulation9 Jun 2026
- 2026Mind Your Steps: A General Learning Framework for Accurate Humanoid Foothold Tracking6 Jun 2026
- 2026Perceptive Humanoid Parkour: Chaining Dynamic Human Skills via Motion Matching17 Feb 2026
- 2026CMR: Contractive Mapping Embeddings for Robust Humanoid Locomotion on Unstructured Terrains3 Feb 2026
- 2025CHyLL: Learning Continuous Neural Representations of Hybrid Systems10 Dec 2025
- 2025Investigating Lagrangian Neural Networks for Infinite Horizon Planning in Quadrupedal Locomotion19 Jun 2025
- 2025GRoQ-LoCO: Generalist and Robot-agnostic Quadruped Locomotion Control using Offline Datasets16 May 2025
- 2025MULE: Multi-terrain and Unknown Load Adaptation for Effective Quadrupedal Locomotion1 May 2025
- 2025HOMIE: Humanoid Loco-Manipulation with Isomorphic Exoskeleton Cockpit18 Feb 2025
- 2025Bridging the Sim-to-Real Gap for Athletic Loco-Manipulation15 Feb 2025
12 newest of 18 All 18 (JSON)