RL + Model-based Control: Using On-demand Optimal Control to Learn Versatile Legged Locomotion
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Abstract (arXiv)
This paper presents a control framework that combines model-based optimal control and reinforcement learning (RL) to achieve versatile and robust legged locomotion. Our approach enhances the RL training process by incorporating on-demand reference motions generated through finite-horizon optimal control, covering a broad range of velocities and gaits. These reference motions serve as targets for the RL policy to imitate, leading to the development of robust control policies that can be learned with reliability. Furthermore, by utilizing realistic simulation data that captures whole-body dynamics, RL effectively overcomes the inherent limitations in reference motions imposed by modeling simplifications. We validate the robustness and controllability of the RL training process within our framework through a series of experiments. In these experiments, our method showcases its capability to generalize reference motions and effectively handle more complex locomotion tasks that may pose challenges for the simplified model, thanks to RL's flexibility. Additionally, our framework effortlessly supports the training of control policies for robots with diverse dimensions, eliminating the necessity for robot-specific adjustments in the reward function and hyperparameters.
Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Builds on 25 of its 42 references that are in the map. First posted on arXiv 29 May 2023.
Builds on
25 of 42 references.
References · 25
- 2017Proximal Policy Optimization Algorithmscited by 14,441
- 2020Learning Quadrupedal Locomotion over Challenging Terraincited by 494
- 2021RMA: Rapid Motor Adaptation for Legged Robotscited by 430
- 2019Learning agile and dynamic motor skills for legged robotscited by 402
- 2021Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learningcited by 395
- 2022Learning robust perceptive locomotion for quadrupedal robots in the wildcited by 299
- 2020Learning Agile Robotic Locomotion Skills by Imitating Animalscited by 229
- 2022Rapid Locomotion via Reinforcement Learningcited by 130
- 2022Walk These Ways: Tuning Robot Control for Generalization with Multiplicity of Behaviorcited by 113
- 2022Adversarial Motion Priors Make Good Substitutes for Complex Reward Functionscited by 68
- 2019Policies Modulating Trajectory Generatorscited by 47
- 2020RLOC: Terrain-Aware Legged Locomotion using Reinforcement Learning and Optimal Controlcited by 46
13 more
- 2019Highly Dynamic Quadruped Locomotion via Whole-Body Impulse Control and Model Predictive Controlcited by 43
- 2022Perceptive Locomotion through Nonlinear Model Predictive Controlcited by 27
- 2022Learning Free Gait Transition for Quadruped Robots via Phase-Guided Controllercited by 23
- 2022Optimization-Based Control for Dynamic Legged Robotscited by 21
- 2022OPT-Mimic: Imitation of Optimized Trajectories for Dynamic Quadruped Behaviorscited by 19
- 2022Versatile Skill Control via Self-supervised Adversarial Imitation of Unlabeled Mixed Motionscited by 13
- 2020Motion Planning for Quadrupedal Locomotion: Coupled Planning, Terrain Mapping and Whole-Body Controlcited by 10
- 2022TAMOLS: Terrain-Aware Motion Optimization for Legged Systemscited by 10
- 2020Kinodynamic Motion Planning for Multi-Legged Robot Jumping via Mixed-Integer Convex Programcited by 4
- 2021Online Trajectory Optimization for Dynamic Aerial Motions of a Quadruped Robotcited by 4
- 2022Nonlinear Model Predictive Control for Quadrupedal Locomotion Using Second-Order Sensitivity Analysiscited by 2
- 2019Optimal control via second order sensitivity analysiscited by 1
- 2023Reinforcement Learning for Legged Robots: Motion Imitation from Model-Based Optimal Controlcited by 1
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Citing papers per year: 2023: 5; 2024: 4; 2025: 3; 2026: 2.
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- 2023Robot Parkour Learningcited by 115
- 2025Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classificationcited by 19
- 2024RobotKeyframing: Learning Locomotion with High-Level Objectives via Mixture of Dense and Sparse Rewardscited by 12
- 2025Design and Control of a Bipedal Robotic Charactercited by 12
- 2024Guided Reinforcement Learning for Robust Multi-Contact Loco-Manipulationcited by 9
- 2023Tuning Legged Locomotion Controllers via Safe Bayesian Optimizationcited by 8
- 2024Helpful DoggyBot: Open-World Object Fetching using Legged Robots and Vision-Language Modelscited by 8
- 2023Learning Diverse Skills for Local Navigation under Multi-constraint Optimalitycited by 7
- 2025A roadmap for AI in roboticscited by 7
- 2023DeepTransition: Viability Leads to the Emergence of Gait Transitions in Learning Anticipatory Quadrupedal Locomotion Skillscited by 2
- 2024Reinforcement Learning Compensated Model Predictive Control for Off-road Driving on Unknown Deformable Terraincited by 1
- 2026Agile perceptive multi-skill locomotion for quadrupedal robots in the wildcited by 1
- 2026Guided Riemannian Optimization (GuRO): Bridging Model Predictive Control and Decision Transformers24 Aug 2026
- 2026Agile perceptive multi-skill locomotion for quadrupedal robots in the wild15 Jul 2026
- 2025A roadmap for AI in robotics26 Jul 2025
- 2025Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classification4 Feb 2025
- 2025Design and Control of a Bipedal Robotic Character9 Jan 2025
- 2024Guided Reinforcement Learning for Robust Multi-Contact Loco-Manipulation17 Oct 2024
- 2024Helpful DoggyBot: Open-World Object Fetching using Legged Robots and Vision-Language Models30 Sep 2024
- 2024Reinforcement Learning Compensated Model Predictive Control for Off-road Driving on Unknown Deformable Terrain17 Aug 2024
- 2024RobotKeyframing: Learning Locomotion with High-Level Objectives via Mixture of Dense and Sparse Rewards16 Jul 2024
- 2023Learning Diverse Skills for Local Navigation under Multi-constraint Optimality3 Oct 2023
- 2023Robot Parkour Learning11 Sep 2023
- 2023Learning to Navigate from Scratch using World Models and Curiosity: the Good, the Bad, and the Ugly30 Aug 2023
- 2023Robot Parkour Learningcited by 115
- 2025Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classificationcited by 19
- 2024RobotKeyframing: Learning Locomotion with High-Level Objectives via Mixture of Dense and Sparse Rewardscited by 12
- 2025Design and Control of a Bipedal Robotic Charactercited by 12
- 2024Guided Reinforcement Learning for Robust Multi-Contact Loco-Manipulationcited by 9
- 2023Tuning Legged Locomotion Controllers via Safe Bayesian Optimizationcited by 8
- 2024Helpful DoggyBot: Open-World Object Fetching using Legged Robots and Vision-Language Modelscited by 8
- 2023Learning Diverse Skills for Local Navigation under Multi-constraint Optimalitycited by 7
- 2025A roadmap for AI in roboticscited by 7
- 2023DeepTransition: Viability Leads to the Emergence of Gait Transitions in Learning Anticipatory Quadrupedal Locomotion Skillscited by 2
- 2026Agile perceptive multi-skill locomotion for quadrupedal robots in the wildcited by 1
- 2026Agile perceptive multi-skill locomotion for quadrupedal robots in the wild15 Jul 2026
- 2025A roadmap for AI in robotics26 Jul 2025
- 2025Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classification4 Feb 2025
- 2025Design and Control of a Bipedal Robotic Character9 Jan 2025
- 2024Guided Reinforcement Learning for Robust Multi-Contact Loco-Manipulation17 Oct 2024
- 2024Helpful DoggyBot: Open-World Object Fetching using Legged Robots and Vision-Language Models30 Sep 2024
- 2024RobotKeyframing: Learning Locomotion with High-Level Objectives via Mixture of Dense and Sparse Rewards16 Jul 2024
- 2023Learning Diverse Skills for Local Navigation under Multi-constraint Optimality3 Oct 2023
- 2023Robot Parkour Learning11 Sep 2023
- 2023DeepTransition: Viability Leads to the Emergence of Gait Transitions in Learning Anticipatory Quadrupedal Locomotion Skills12 Jun 2023
- 2023Tuning Legged Locomotion Controllers via Safe Bayesian Optimization12 Jun 2023