Feedback Control For Cassie With Deep Reinforcement Learning
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Abstract (arXiv)
Bipedal locomotion skills are challenging to develop. Control strategies often use local linearization of the dynamics in conjunction with reduced-order abstractions to yield tractable solutions. In these model-based control strategies, the controller is often not fully aware of many details, including torque limits, joint limits, and other non-linearities that are necessarily excluded from the control computations for simplicity. Deep reinforcement learning (DRL) offers a promising model-free approach for controlling bipedal locomotion which can more fully exploit the dynamics. However, current results in the machine learning literature are often based on ad-hoc simulation models that are not based on corresponding hardware. Thus it remains unclear how well DRL will succeed on realizable bipedal robots. In this paper, we demonstrate the effectiveness of DRL using a realistic model of Cassie, a bipedal robot. By formulating a feedback control problem as finding the optimal policy for a Markov Decision Process, we are able to learn robust walking controllers that imitate a reference motion with DRL. Controllers for different walking speeds are learned by imitating simple time-scaled versions of the original reference motion. Controller robustness is demonstrated through several challenging tests, including sensory delay, walking blindly on irregular terrain and unexpected pushes at the pelvis. We also show we can interpolate between individual policies and that robustness can be improved with an interpolated policy.
Key facts. Cited by 45 papers in the map (data through 14 Oct 2026). First posted on arXiv 15 Mar 2018.
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Citing papers per year: 2021: 6; 2022: 11; 2023: 8; 2024: 7; 2025: 12; 2026: 1.
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- 2023Real-World Humanoid Locomotion with Reinforcement Learningcited by 187
- 2024HumanPlus: Humanoid Shadowing and Imitation from Humanscited by 185
- 2025BeyondMimic: From Motion Tracking to Versatile Humanoid Control via Guided Diffusioncited by 165
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- 2024Reinforcement Learning for Versatile, Dynamic, and Robust Bipedal Locomotion Controlcited by 99
- 2024TRANSIC: Sim-to-Real Policy Transfer by Learning from Online Correctioncited by 59
- 2022Adapting Rapid Motor Adaptation for Bipedal Robotscited by 54
- 2023Not Only Rewards But Also Constraints: Applications on Legged Robot Locomotioncited by 47
- 2023Robust and Versatile Bipedal Jumping Control through Reinforcement Learningcited by 36
- 2022Machine Learning for Microcontroller-Class Hardware: A Reviewcited by 28
- 2023A Survey on Physics Informed Reinforcement Learning: Review and Open Problemscited by 24
- 2023Trust Region-Based Safe Distributional Reinforcement Learning for Multiple Constraintscited by 21
33 more
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- 2021Improved Soft Actor-Critic: Mixing Prioritized Off-Policy Samples with On-Policy Experiencecited by 8
- 2025Olaf: Bringing an Animated Character to Life in the Physical Worldcited by 8
- 2021Learning Bipedal Robot Locomotion from Human Movementcited by 7
- 2024Deep Reinforcement Learning for Bipedal Locomotion: A Brief Surveycited by 7
- 2022Learning Forward Dynamics Model and Informed Trajectory Sampler for Safe Quadruped Navigationcited by 6
- 2022Improved Policy Optimization for Online Imitation Learningcited by 6
- 2022Bridging Model-based Safety and Model-free Reinforcement Learning through System Identification of Low Dimensional Linear Modelscited by 5
- 2023Infer and Adapt: Bipedal Locomotion Reward Learning from Demonstrations via Inverse Reinforcement Learningcited by 5
- 2024RL-augmented MPC Framework for Agile and Robust Bipedal Footstep Locomotion Planning and Controlcited by 5
- 2025Optimizing Bipedal Locomotion for The 100m Dash With Comparison to Human Runningcited by 5
- 2022Human-AI Shared Control via Policy Dissectioncited by 4
- 2024Multi-Fidelity Reinforcement Learning for Time-Optimal Quadrotor Re-planningcited by 4
- 2021Learning Linear Policies for Robust Bipedal Locomotion on Terrains with Varying Slopescited by 3
- 2022Boosting Exploration in Actor-Critic Algorithms by Incentivizing Plausible Novel Statescited by 3
- 2023MPC-Inspired Reinforcement Learning for Verifiable Model-Free Controlcited by 3
- 2025Contrastive Representation Learning for Robust Sim-to-Real Transfer of Adaptive Humanoid Locomotioncited by 3
- 2025RobotDancing: Residual-Action Reinforcement Learning Enables Robust Long-Horizon Humanoid Motion Trackingcited by 3
- 2025Residual MPC: Blending Reinforcement Learning with GPU-Parallelized Model Predictive Controlcited by 3
- 2021Quadruped Locomotion on Non-Rigid Terrain using Reinforcement Learningcited by 2
- 2022Harfang3D Dog-Fight Sandbox: A Reinforcement Learning Research Platform for the Customized Control Tasks of Fighter Aircraftscited by 2
- 2025NaviGait: Navigating Dynamically Feasible Gait Libraries using Deep Reinforcement Learningcited by 2
- 2022Value Summation: A Novel Scoring Function for MPC-based Model-based Reinforcement Learningcited by 1
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- 2025MASH: Cooperative-Heterogeneous Multi-Agent Reinforcement Learning for Single Humanoid Robot Locomotioncited by 1
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- 2024Data Augmentation for Automated Adaptive Rodent Trainingcited by 0
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- 2025Learning Terrain Aware Bipedal Locomotion via Reduced Dimensional Perceptual Representationscited by 0
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- 2025Learning Terrain Aware Bipedal Locomotion via Reduced Dimensional Perceptual Representations15 Dec 2025
- 2025Residual MPC: Blending Reinforcement Learning with GPU-Parallelized Model Predictive Control14 Oct 2025
- 2025NaviGait: Navigating Dynamically Feasible Gait Libraries using Deep Reinforcement Learning13 Oct 2025
- 2025RobotDancing: Residual-Action Reinforcement Learning Enables Robust Long-Horizon Humanoid Motion Tracking25 Sep 2025
- 2025Contrastive Representation Learning for Robust Sim-to-Real Transfer of Adaptive Humanoid Locomotion16 Sep 2025
- 2025MASH: Cooperative-Heterogeneous Multi-Agent Reinforcement Learning for Single Humanoid Robot Locomotion14 Aug 2025
- 2025BeyondMimic: From Motion Tracking to Versatile Humanoid Control via Guided Diffusion11 Aug 2025
- 2025Achieving Precise and Reliable Locomotion with Differentiable Simulation-Based System Identification6 Aug 2025
- 2025Optimizing Bipedal Locomotion for The 100m Dash With Comparison to Human Running5 Aug 2025
- 2025Robust RL Control for Bipedal Locomotion with Closed Kinematic Chains14 Jul 2025
33 more
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- 2024RL-augmented MPC Framework for Agile and Robust Bipedal Footstep Locomotion Planning and Control25 Jul 2024
- 2024HumanPlus: Humanoid Shadowing and Imitation from Humans15 Jun 2024
- 2024TRANSIC: Sim-to-Real Policy Transfer by Learning from Online Correction16 May 2024
- 2024Deep Reinforcement Learning for Bipedal Locomotion: A Brief Survey25 Apr 2024
- 2024Multi-Fidelity Reinforcement Learning for Time-Optimal Quadrotor Re-planning13 Mar 2024
- 2024Reinforcement Learning for Versatile, Dynamic, and Robust Bipedal Locomotion Control30 Jan 2024
- 2023MPC-Inspired Reinforcement Learning for Verifiable Model-Free Control8 Dec 2023
- 2023Infer and Adapt: Bipedal Locomotion Reward Learning from Demonstrations via Inverse Reinforcement Learning28 Sep 2023
- 2023A Survey on Physics Informed Reinforcement Learning: Review and Open Problems5 Sep 2023
- 2023Not Only Rewards But Also Constraints: Applications on Legged Robot Locomotion24 Aug 2023
- 2023Characterization of Human Balance through a Reinforcement Learning-based Muscle Controller8 Aug 2023
- 2023Real-World Humanoid Locomotion with Reinforcement Learning6 Mar 2023
- 2023Robust and Versatile Bipedal Jumping Control through Reinforcement Learning19 Feb 2023
- 2023Trust Region-Based Safe Distributional Reinforcement Learning for Multiple Constraints26 Jan 2023
- 2022Harfang3D Dog-Fight Sandbox: A Reinforcement Learning Research Platform for the Customized Control Tasks of Fighter Aircrafts13 Oct 2022
- 2022Boosting Exploration in Actor-Critic Algorithms by Incentivizing Plausible Novel States1 Oct 2022
- 2022Learning Low-Frequency Motion Control for Robust and Dynamic Robot Locomotion29 Sep 2022
- 2022Value Summation: A Novel Scoring Function for MPC-based Model-based Reinforcement Learning16 Sep 2022
- 2022Improved Policy Optimization for Online Imitation Learning29 Jul 2022
- 2022Human-AI Shared Control via Policy Dissection31 May 2022
- 2022Adapting Rapid Motor Adaptation for Bipedal Robots30 May 2022
- 2022Machine Learning for Microcontroller-Class Hardware: A Review29 May 2022
- 2022Bridging Model-based Safety and Model-free Reinforcement Learning through System Identification of Low Dimensional Linear Models11 May 2022
- 2022Learning Forward Dynamics Model and Informed Trajectory Sampler for Safe Quadruped Navigation19 Apr 2022
- 2022Custom Sine Waves Are Enough for Imitation Learning of Bipedal Gaits with Different Styles8 Apr 2022
- 2021OstrichRL: A Musculoskeletal Ostrich Simulation to Study Bio-mechanical Locomotion11 Dec 2021
- 2021Improved Soft Actor-Critic: Mixing Prioritized Off-Policy Samples with On-Policy Experience24 Sep 2021
- 2021Quadruped Locomotion on Non-Rigid Terrain using Reinforcement Learning7 Jul 2021
- 2021Learning Bipedal Robot Locomotion from Human Movement26 May 2021
- 2021Learning Linear Policies for Robust Bipedal Locomotion on Terrains with Varying Slopes4 Apr 2021
- 2021Reinforcement Learning for Robust Parameterized Locomotion Control of Bipedal Robots26 Mar 2021
- 2024Reinforcement Learning for Versatile, Dynamic, and Robust Bipedal Locomotion Controlcited by 99
- 2025High-Performance Reinforcement Learning on Spot: Optimizing Simulation Parameters with Distributional Measurescited by 10
- 2024Deep Reinforcement Learning for Bipedal Locomotion: A Brief Surveycited by 7
- 2024RL-augmented MPC Framework for Agile and Robust Bipedal Footstep Locomotion Planning and Controlcited by 5
- 2024Multi-Fidelity Reinforcement Learning for Time-Optimal Quadrotor Re-planningcited by 4
- 2025Contrastive Representation Learning for Robust Sim-to-Real Transfer of Adaptive Humanoid Locomotioncited by 3
- 2025RobotDancing: Residual-Action Reinforcement Learning Enables Robust Long-Horizon Humanoid Motion Trackingcited by 3
- 2025Residual MPC: Blending Reinforcement Learning with GPU-Parallelized Model Predictive Controlcited by 3
- 2025NaviGait: Navigating Dynamically Feasible Gait Libraries using Deep Reinforcement Learningcited by 2
- 2025Achieving Precise and Reliable Locomotion with Differentiable Simulation-Based System Identificationcited by 1
- 2025Robust RL Control for Bipedal Locomotion with Closed Kinematic Chainscited by 0
- 2025Learning Terrain Aware Bipedal Locomotion via Reduced Dimensional Perceptual Representationscited by 0
12 most cited of 13 All 13 (JSON)
- 2026ARC-RL: A Reinforcement Learning Playground Inspired by ARC Raiders19 May 2026
- 2025Learning Terrain Aware Bipedal Locomotion via Reduced Dimensional Perceptual Representations15 Dec 2025
- 2025Residual MPC: Blending Reinforcement Learning with GPU-Parallelized Model Predictive Control14 Oct 2025
- 2025NaviGait: Navigating Dynamically Feasible Gait Libraries using Deep Reinforcement Learning13 Oct 2025
- 2025RobotDancing: Residual-Action Reinforcement Learning Enables Robust Long-Horizon Humanoid Motion Tracking25 Sep 2025
- 2025Contrastive Representation Learning for Robust Sim-to-Real Transfer of Adaptive Humanoid Locomotion16 Sep 2025
- 2025Achieving Precise and Reliable Locomotion with Differentiable Simulation-Based System Identification6 Aug 2025
- 2025Robust RL Control for Bipedal Locomotion with Closed Kinematic Chains14 Jul 2025
- 2025High-Performance Reinforcement Learning on Spot: Optimizing Simulation Parameters with Distributional Measures24 Apr 2025
- 2024RL-augmented MPC Framework for Agile and Robust Bipedal Footstep Locomotion Planning and Control25 Jul 2024
- 2024Deep Reinforcement Learning for Bipedal Locomotion: A Brief Survey25 Apr 2024
- 2024Multi-Fidelity Reinforcement Learning for Time-Optimal Quadrotor Re-planning13 Mar 2024
12 newest of 13 All 13 (JSON)
- 2023Real-World Humanoid Locomotion with Reinforcement Learningcited by 187
- 2024HumanPlus: Humanoid Shadowing and Imitation from Humanscited by 185
- 2021Reinforcement Learning for Robust Parameterized Locomotion Control of Bipedal Robotscited by 116
- 2024TRANSIC: Sim-to-Real Policy Transfer by Learning from Online Correctioncited by 59
- 2022Adapting Rapid Motor Adaptation for Bipedal Robotscited by 54
- 2023Not Only Rewards But Also Constraints: Applications on Legged Robot Locomotioncited by 47
- 2023Robust and Versatile Bipedal Jumping Control through Reinforcement Learningcited by 36
- 2022Machine Learning for Microcontroller-Class Hardware: A Reviewcited by 28
- 2023A Survey on Physics Informed Reinforcement Learning: Review and Open Problemscited by 24
- 2023Trust Region-Based Safe Distributional Reinforcement Learning for Multiple Constraintscited by 21
- 2022Learning Low-Frequency Motion Control for Robust and Dynamic Robot Locomotioncited by 12
- 2021OstrichRL: A Musculoskeletal Ostrich Simulation to Study Bio-mechanical Locomotioncited by 10
12 most cited of 28 All 28 (JSON)
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- 2025MASH: Cooperative-Heterogeneous Multi-Agent Reinforcement Learning for Single Humanoid Robot Locomotion14 Aug 2025
- 2025Optimizing Bipedal Locomotion for The 100m Dash With Comparison to Human Running5 Aug 2025
- 2024Data Augmentation for Automated Adaptive Rodent Training23 Oct 2024
- 2024HumanPlus: Humanoid Shadowing and Imitation from Humans15 Jun 2024
- 2024TRANSIC: Sim-to-Real Policy Transfer by Learning from Online Correction16 May 2024
- 2023MPC-Inspired Reinforcement Learning for Verifiable Model-Free Control8 Dec 2023
- 2023A Survey on Physics Informed Reinforcement Learning: Review and Open Problems5 Sep 2023
- 2023Not Only Rewards But Also Constraints: Applications on Legged Robot Locomotion24 Aug 2023
- 2023Characterization of Human Balance through a Reinforcement Learning-based Muscle Controller8 Aug 2023
- 2023Real-World Humanoid Locomotion with Reinforcement Learning6 Mar 2023
- 2023Robust and Versatile Bipedal Jumping Control through Reinforcement Learning19 Feb 2023
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