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GLiDE: Generalizable Quadrupedal Locomotion in Diverse Environments with a Centroidal Model

arXiv 2104.09771 ↗First posted 20 Apr 2021cs.RO cs.LGcited by 23

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Abstract (arXiv)

Model-free reinforcement learning (RL) for legged locomotion commonly relies on a physics simulator that can accurately predict the behaviors of every degree of freedom of the robot. In contrast, approximate reduced-order models are commonly used for many model predictive control strategies. In this work we abandon the conventional use of high-fidelity dynamics models in RL and we instead seek to understand what can be achieved when using RL with a much simpler centroidal model when applied to quadrupedal locomotion. We show that RL-based control of the accelerations of a centroidal model is surprisingly effective, when combined with a quadratic program to realize the commanded actions via ground contact forces. It allows for a simple reward structure, reduced computational costs, and robust sim-to-real transfer. We show the generality of the method by demonstrating flat-terrain gaits, stepping-stone locomotion, two-legged in-place balance, balance beam locomotion, and direct sim-to-real transfer.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). Builds on 37 of its 59 references that are in the map. First posted on arXiv 20 Apr 2021.

Builds on

37 of 59 references.

References · 37

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2017Proximal Policy Optimization Algorithmscited by 14,441
  3. 2020Learning Quadrupedal Locomotion over Challenging Terraincited by 494
  4. 2019Learning agile and dynamic motor skills for legged robotscited by 402
  5. 2018Sim-to-Real: Learning Agile Locomotion For Quadruped Robotscited by 277
  6. 2020Learning Agile Robotic Locomotion Skills by Imitating Animalscited by 229
  7. 2017Preparing for the Unknown: Learning a Universal Policy with Online System Identificationcited by 129
  8. 2020Conservative Safety Critics for Explorationcited by 107
  9. 2020NeuralSim: Augmenting Differentiable Simulators with Neural Networkscited by 77
  10. 2020Multi-expert learning of adaptive legged locomotioncited by 62
  11. 2019Data Efficient Reinforcement Learning for Legged Robotscited by 60
  12. 2019Variable Impedance Control in End-Effector Space: An Action Space for Reinforcement Learning in Contact-Rich Taskscited by 56
25 more
  1. 2020Dynamics Randomization Revisited:A Case Study for Quadrupedal Locomotioncited by 54
  2. 2020RLOC: Terrain-Aware Legged Locomotion using Reinforcement Learning and Optimal Controlcited by 46
  3. 2019DeepGait: Planning and Control of Quadrupedal Gaits using Deep Reinforcement Learningcited by 45
  4. 2021LASER: Learning a Latent Action Space for Efficient Reinforcement Learningcited by 32
  5. 2019MPC-Net: A First Principles Guided Policy Searchcited by 28
  6. 2020Guided Constrained Policy Optimization for Dynamic Quadrupedal Robot Locomotioncited by 24
  7. 2020Learning a Contact-Adaptive Controller for Robust, Efficient Legged Locomotioncited by 22
  8. 2020Multi-Layered Safety for Legged Robots via Control Barrier Functions and Model Predictive Controlcited by 20
  9. 2020From Pixels to Legs: Hierarchical Learning of Quadruped Locomotioncited by 20
  10. 2020Learning Task Space Actions for Bipedal Locomotioncited by 15
  11. 2018Progressive Reinforcement Learning with Distillation for Multi-Skilled Motion Controlcited by 12
  12. 2020Planning in Learned Latent Action Spaces for Generalizable Legged Locomotioncited by 11
  13. 2020Motion Planning for Quadrupedal Locomotion: Coupled Planning, Terrain Mapping and Whole-Body Controlcited by 10
  14. 2018Using Deep Reinforcement Learning to Learn High-Level Policies on the ATRIAS Bipedcited by 8
  15. 2020Learning Spring Mass Locomotion: Guiding Policies with a Reduced-Order Modelcited by 8
  16. 2019Learning Hierarchical Control for Robust In-Hand Manipulationcited by 6
  17. 2020Robust Quadrupedal Locomotion on Sloped Terrains: A Linear Policy Approachcited by 6
  18. 2018Frequency-Aware Model Predictive Controlcited by 5
  19. 2017Combining Trajectory Optimization, Supervised Machine Learning, and Model Structure for Mitigating the Curse of Dimensionality in the Control of Bipedal Robotscited by 4
  20. 2020Learning a Centroidal Motion Planner for Legged Locomotioncited by 4
  21. 2020Angular Momentum about the Contact Point for Control of Bipedal Locomotion: Validation in a LIP-based Controllercited by 3
  22. 2020DeepQ Stepper: A framework for reactive dynamic walking on uneven terraincited by 3
  23. 20213D Underactuated Bipedal Walking via H-LIP based Gait Synthesis and Stepping Stabilizationcited by 3
  24. 2020Line Walking and Balancing for Legged Robots with Point Feetcited by 2
  25. 2018Efficient Humanoid Contact Planning using Learned Centroidal Dynamics Predictioncited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 6; 2022: 3; 2023: 8; 2024: 1; 2025: 4; 2026: 1.

23 papers.

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  1. 2023Orbit: A Unified Simulation Framework for Interactive Robot Learning Environmentscited by 239
  2. 2021Learning Vision-Guided Quadrupedal Locomotion End-to-End with Cross-Modal Transformerscited by 71
  3. 2023Prompt a Robot to Walk with Large Language Modelscited by 44
  4. 2023Neural Volumetric Memory for Visual Locomotion Controlcited by 40
  5. 2021Learning to Jump from Pixelscited by 39
  6. 2023DTC: Deep Tracking Controlcited by 37
  7. 2025BeamDojo: Learning Agile Humanoid Locomotion on Sparse Footholdscited by 32
  8. 2022Learning Torque Control for Quadrupedal Locomotioncited by 22
  9. 2021Model-free Reinforcement Learning for Robust Locomotion using Demonstrations from Trajectory Optimizationcited by 16
  10. 2022Learning to Brachiate via Simplified Model Imitationcited by 7
  11. 2022Learning to Walk by Steering: Perceptive Quadrupedal Locomotion in Dynamic Environmentscited by 7
  12. 2023Puppeteer and Marionette: Learning Anticipatory Quadrupedal Locomotion Based on Interactions of a Central Pattern Generator and Supraspinal Drivecited by 5
11 more
  1. 2023Continuous Versatile Jumping Using Learned Action Residualscited by 5
  2. 2021An Adaptable Approach to Learn Realistic Legged Locomotion without Examplescited by 4
  3. 2021Learning Coordinated Terrain-Adaptive Locomotion by Imitating a Centroidal Dynamics Plannercited by 4
  4. 2025LocoMamba: Vision-Driven Locomotion via End-to-End Deep Reinforcement Learning with Mambacited by 3
  5. 2023DeepTransition: Viability Leads to the Emergence of Gait Transitions in Learning Anticipatory Quadrupedal Locomotion Skillscited by 2
  6. 2025QuadKAN: KAN-Enhanced Quadruped Motion Control via End-to-End Reinforcement Learningcited by 2
  7. 2024The Role of Domain Randomization in Training Diffusion Policies for Whole-Body Humanoid Controlcited by 1
  8. 2021PM-FSM: Policies Modulating Finite State Machine for Robust Quadrupedal Locomotioncited by 0
  9. 2023Adaptive Tracking of a Single-Rigid-Body Character in Various Environmentscited by 0
  10. 2025Vision-Proprioception Fusion with Mamba2 in End-to-End Reinforcement Learning for Motion Controlcited by 0
  11. 2026Mind Your Steps: A General Learning Framework for Accurate Humanoid Foothold Trackingcited by 0