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

arXiv: https://arxiv.org/abs/2104.09771 · HTML: https://mlsanity.com/paper/2104.09771/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 59 references that are in the map.
- First posted on arXiv 20 Apr 2021.

## Builds on (most cited first, 30 of 37)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Learning Quadrupedal Locomotion over Challenging Terrain](https://mlsanity.com/paper/2010.11251/) (2020)
- [Learning agile and dynamic motor skills for legged robots](https://mlsanity.com/paper/1901.08652/) (2019)
- [Sim-to-Real: Learning Agile Locomotion For Quadruped Robots](https://mlsanity.com/paper/1804.10332/) (2018)
- [Learning Agile Robotic Locomotion Skills by Imitating Animals](https://mlsanity.com/paper/2004.00784/) (2020)
- [Preparing for the Unknown: Learning a Universal Policy with Online System Identification](https://mlsanity.com/paper/1702.02453/) (2017)
- [Conservative Safety Critics for Exploration](https://mlsanity.com/paper/2010.14497/) (2020)
- [NeuralSim: Augmenting Differentiable Simulators with Neural Networks](https://mlsanity.com/paper/2011.04217/) (2020)
- [Variable Impedance Control in End-Effector Space: An Action Space for Reinforcement Learning in Contact-Rich Tasks](https://mlsanity.com/paper/1906.08880/) (2019)
- [Multi-expert learning of adaptive legged locomotion](https://mlsanity.com/paper/2012.05810/) (2020)
- [Data Efficient Reinforcement Learning for Legged Robots](https://mlsanity.com/paper/1907.03613/) (2019)
- [Dynamics Randomization Revisited:A Case Study for Quadrupedal Locomotion](https://mlsanity.com/paper/2011.02404/) (2020)
- [RLOC: Terrain-Aware Legged Locomotion using Reinforcement Learning and Optimal Control](https://mlsanity.com/paper/2012.03094/) (2020)
- [DeepGait: Planning and Control of Quadrupedal Gaits using Deep Reinforcement Learning](https://mlsanity.com/paper/1909.08399/) (2019)
- [MPC-Net: A First Principles Guided Policy Search](https://mlsanity.com/paper/1909.05197/) (2019)
- [LASER: Learning a Latent Action Space for Efficient Reinforcement Learning](https://mlsanity.com/paper/2103.15793/) (2021)
- [Guided Constrained Policy Optimization for Dynamic Quadrupedal Robot Locomotion](https://mlsanity.com/paper/2002.09676/) (2020)
- [Multi-Layered Safety for Legged Robots via Control Barrier Functions and Model Predictive Control](https://mlsanity.com/paper/2011.00032/) (2020)
- [Learning a Contact-Adaptive Controller for Robust, Efficient Legged Locomotion](https://mlsanity.com/paper/2009.10019/) (2020)
- [Learning Task Space Actions for Bipedal Locomotion](https://mlsanity.com/paper/2011.04741/) (2020)
- [From Pixels to Legs: Hierarchical Learning of Quadruped Locomotion](https://mlsanity.com/paper/2011.11722/) (2020)
- [Learning Spring Mass Locomotion: Guiding Policies with a Reduced-Order Model](https://mlsanity.com/paper/2010.11234/) (2020)
- [Progressive Reinforcement Learning with Distillation for Multi-Skilled Motion Control](https://mlsanity.com/paper/1802.04765/) (2018)
- [Planning in Learned Latent Action Spaces for Generalizable Legged Locomotion](https://mlsanity.com/paper/2008.11867/) (2020)
- [Motion Planning for Quadrupedal Locomotion: Coupled Planning, Terrain Mapping and Whole-Body Control](https://mlsanity.com/paper/2003.05481/) (2020)
- [Using Deep Reinforcement Learning to Learn High-Level Policies on the ATRIAS Biped](https://mlsanity.com/paper/1809.10811/) (2018)
- [3D Underactuated Bipedal Walking via H-LIP based Gait Synthesis and Stepping Stabilization](https://mlsanity.com/paper/2101.09588/) (2021)
- [Learning Hierarchical Control for Robust In-Hand Manipulation](https://mlsanity.com/paper/1910.10985/) (2019)
- [Robust Quadrupedal Locomotion on Sloped Terrains: A Linear Policy Approach](https://mlsanity.com/paper/2010.16342/) (2020)

## Built on by (most cited first, 25 of 25)

- [Orbit: A Unified Simulation Framework for Interactive Robot Learning Environments](https://mlsanity.com/paper/2301.04195/) (2023)
- [Learning Vision-Guided Quadrupedal Locomotion End-to-End with Cross-Modal Transformers](https://mlsanity.com/paper/2107.03996/) (2021)
- [DTC: Deep Tracking Control](https://mlsanity.com/paper/2309.15462/) (2023)
- [BeamDojo: Learning Agile Humanoid Locomotion on Sparse Footholds](https://mlsanity.com/paper/2502.10363/) (2025)
- [Learning to Jump from Pixels](https://mlsanity.com/paper/2110.15344/) (2021)
- [Prompt a Robot to Walk with Large Language Models](https://mlsanity.com/paper/2309.09969/) (2023)
- [Neural Volumetric Memory for Visual Locomotion Control](https://mlsanity.com/paper/2304.01201/) (2023)
- [Learning Torque Control for Quadrupedal Locomotion](https://mlsanity.com/paper/2203.05194/) (2022)
- [Model-free Reinforcement Learning for Robust Locomotion using Demonstrations from Trajectory Optimization](https://mlsanity.com/paper/2107.06629/) (2021)
- [Learning to Brachiate via Simplified Model Imitation](https://mlsanity.com/paper/2205.03943/) (2022)
- [Learning to Walk by Steering: Perceptive Quadrupedal Locomotion in Dynamic Environments](https://mlsanity.com/paper/2209.09233/) (2022)
- [Continuous Versatile Jumping Using Learned Action Residuals](https://mlsanity.com/paper/2304.08663/) (2023)
- [An Adaptable Approach to Learn Realistic Legged Locomotion without Examples](https://mlsanity.com/paper/2110.14998/) (2021)
- [Puppeteer and Marionette: Learning Anticipatory Quadrupedal Locomotion Based on Interactions of a Central Pattern Generator and Supraspinal Drive](https://mlsanity.com/paper/2302.13378/) (2023)
- [Learning Coordinated Terrain-Adaptive Locomotion by Imitating a Centroidal Dynamics Planner](https://mlsanity.com/paper/2111.00262/) (2021)
- [LocoMamba: Vision-Driven Locomotion via End-to-End Deep Reinforcement Learning with Mamba](https://mlsanity.com/paper/2508.11849/) (2025)
- [DeepTransition: Viability Leads to the Emergence of Gait Transitions in Learning Anticipatory Quadrupedal Locomotion Skills](https://mlsanity.com/paper/2306.07419/) (2023)
- [QuadKAN: KAN-Enhanced Quadruped Motion Control via End-to-End Reinforcement Learning](https://mlsanity.com/paper/2508.19153/) (2025)
- [PM-FSM: Policies Modulating Finite State Machine for Robust Quadrupedal Locomotion](https://mlsanity.com/paper/2109.12696/) (2021)
- [The Role of Domain Randomization in Training Diffusion Policies for Whole-Body Humanoid Control](https://mlsanity.com/paper/2411.01349/) (2024)
- [Mind Your Steps: A General Learning Framework for Accurate Humanoid Foothold Tracking](https://mlsanity.com/paper/2606.08253/) (2026)
- [Adaptive Tracking of a Single-Rigid-Body Character in Various Environments](https://mlsanity.com/paper/2308.07491/) (2023)
- [Learning Generic and Dynamic Locomotion of Humanoids Across Discrete Terrains](https://mlsanity.com/paper/2405.17227/) (2024)
- [Vision-Proprioception Fusion with Mamba2 in End-to-End Reinforcement Learning for Motion Control](https://mlsanity.com/paper/2509.07593/) (2025)
- [HybridMimic: Hybrid RL-Centroidal Control for Humanoid Motion Mimicking](https://mlsanity.com/paper/2603.06775/) (2026)

## 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.