Learning Quadruped Locomotion Using Differentiable Simulation
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Abstract (arXiv)
This work explores the potential of using differentiable simulation for learning quadruped locomotion. Differentiable simulation promises fast convergence and stable training by computing low-variance first-order gradients using robot dynamics. However, its usage for legged robots is still limited to simulation. The main challenge lies in the complex optimization landscape of robotic tasks due to discontinuous dynamics. This work proposes a new differentiable simulation framework to overcome these challenges. Our approach combines a high-fidelity, non-differentiable simulator for forward dynamics with a simplified surrogate model for gradient backpropagation. This approach maintains simulation accuracy by aligning the robot states from the surrogate model with those of the precise, non-differentiable simulator. Our framework enables learning quadruped walking in simulation in minutes without parallelization. When augmented with GPU parallelization, our approach allows the quadruped robot to master diverse locomotion skills on challenging terrains in minutes. We demonstrate that differentiable simulation outperforms a reinforcement learning algorithm (PPO) by achieving significantly better sample efficiency while maintaining its effectiveness in handling large-scale environments. Our method represents one of the first successful applications of differentiable simulation to real-world quadruped locomotion, offering a compelling alternative to traditional RL methods.
Key facts. Cited by 22 papers in the map (data through 7 Oct 2026). Builds on 34 of its 53 references that are in the map. First posted on arXiv 21 Mar 2024.
Builds on
34 of 53 references.
References · 34
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22 more
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Citing papers per year: 2024: 3; 2025: 14; 2026: 5.
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- 2025VLA-RFT: Vision-Language-Action Reinforcement Fine-tuning with Verified Rewards in World Simulatorscited by 65
- 2025Robotic World Model: A Neural Network Simulator for Robust Policy Optimization in Roboticscited by 47
- 2024Stabilizing Reinforcement Learning in Differentiable Multiphysics Simulationcited by 14
- 2025Differentiable Simulation of Hard Contacts with Soft Gradients for Learning and Controlcited by 5
- 2025Accelerating Visual-Policy Learning through Parallel Differentiable Simulationcited by 4
- 2025Symmetry-Guided Memory Augmentation for Efficient Locomotion Learningcited by 3
- 2025First Order Model-Based RL through Decoupled Backpropagationcited by 3
- 2026HydroShear: Hydroelastic Shear Simulation for Tactile Sim-to-Real Reinforcement Learningcited by 3
- 2024DiffSim2Real: Deploying Quadrupedal Locomotion Policies Purely Trained in Differentiable Simulationcited by 2
- 2025Learning to Walk With Less: A Dyna-Style Approach to Quadrupedal Locomotioncited by 2
- 2024Autonomous Vehicle Controllers From End-to-End Differentiable Simulationcited by 1
- 2025Unlocking Efficient Vehicle Dynamics Modeling via Analytic World Modelscited by 1
10 more
- 2025Leveraging Analytic Gradients in Provably Safe Reinforcement Learningcited by 1
- 2025When Is Diversity Rewarded in Cooperative Multi-Agent Learning?cited by 1
- 2025Reparameterization Proximal Policy Optimizationcited by 1
- 2025Learning Terrain-Specialized Policies for Adaptive Locomotion in Challenging Environmentscited by 1
- 2025Autonomous Vehicle Path Planning by Searching With Differentiable Simulationcited by 1
- 2026Efficient On-policy Visual-RL via Stochastic Decoupled Policy Gradientcited by 1
- 2025ABPT: Amended Backpropagation through Time with Partially Differentiable Rewardscited by 0
- 2026Open-DiffLoco: Open-Source Differentiable Learning for Deployable Blind Quadruped Locomotioncited by 0
- 2026Ostrich: Taking Large Strides Through Stiff Contact in Differentiable Dynamicscited by 0
- 2026Accelerating Visual Policy Learning with Sampling-Based Model Predictive Controlcited by 0
- 2026Accelerating Visual Policy Learning with Sampling-Based Model Predictive Control17 Sep 2026
- 2026Ostrich: Taking Large Strides Through Stiff Contact in Differentiable Dynamics8 Sep 2026
- 2026Open-DiffLoco: Open-Source Differentiable Learning for Deployable Blind Quadruped Locomotion3 Aug 2026
- 2026Efficient On-policy Visual-RL via Stochastic Decoupled Policy Gradient26 May 2026
- 2026HydroShear: Hydroelastic Shear Simulation for Tactile Sim-to-Real Reinforcement Learning28 Feb 2026
- 2025Autonomous Vehicle Path Planning by Searching With Differentiable Simulation14 Nov 2025
- 2025VLA-RFT: Vision-Language-Action Reinforcement Fine-tuning with Verified Rewards in World Simulators1 Oct 2025
- 2025Learning Terrain-Specialized Policies for Adaptive Locomotion in Challenging Environments25 Sep 2025
- 2025Learning to Walk With Less: A Dyna-Style Approach to Quadrupedal Locomotion8 Sep 2025
- 2025First Order Model-Based RL through Decoupled Backpropagation29 Aug 2025
- 2025Reparameterization Proximal Policy Optimization8 Aug 2025
- 2025Differentiable Simulation of Hard Contacts with Soft Gradients for Learning and Control17 Jun 2025
10 more
- 2025When Is Diversity Rewarded in Cooperative Multi-Agent Learning?11 Jun 2025
- 2025Leveraging Analytic Gradients in Provably Safe Reinforcement Learning2 Jun 2025
- 2025Accelerating Visual-Policy Learning through Parallel Differentiable Simulation15 May 2025
- 2025Unlocking Efficient Vehicle Dynamics Modeling via Analytic World Models14 Feb 2025
- 2025Symmetry-Guided Memory Augmentation for Efficient Locomotion Learning3 Feb 2025
- 2025ABPT: Amended Backpropagation through Time with Partially Differentiable Rewards24 Jan 2025
- 2025Robotic World Model: A Neural Network Simulator for Robust Policy Optimization in Robotics17 Jan 2025
- 2024Stabilizing Reinforcement Learning in Differentiable Multiphysics Simulation16 Dec 2024
- 2024DiffSim2Real: Deploying Quadrupedal Locomotion Policies Purely Trained in Differentiable Simulation4 Nov 2024
- 2024Autonomous Vehicle Controllers From End-to-End Differentiable Simulation12 Sep 2024
- 2025VLA-RFT: Vision-Language-Action Reinforcement Fine-tuning with Verified Rewards in World Simulatorscited by 65
- 2025Robotic World Model: A Neural Network Simulator for Robust Policy Optimization in Roboticscited by 47
- 2025Unlocking Efficient Vehicle Dynamics Modeling via Analytic World Modelscited by 1
- 2025VLA-RFT: Vision-Language-Action Reinforcement Fine-tuning with Verified Rewards in World Simulators1 Oct 2025
- 2025Unlocking Efficient Vehicle Dynamics Modeling via Analytic World Models14 Feb 2025
- 2025Robotic World Model: A Neural Network Simulator for Robust Policy Optimization in Robotics17 Jan 2025
- 2024Stabilizing Reinforcement Learning in Differentiable Multiphysics Simulationcited by 14
- 2025Differentiable Simulation of Hard Contacts with Soft Gradients for Learning and Controlcited by 5
- 2025Accelerating Visual-Policy Learning through Parallel Differentiable Simulationcited by 4
- 2025Symmetry-Guided Memory Augmentation for Efficient Locomotion Learningcited by 3
- 2025First Order Model-Based RL through Decoupled Backpropagationcited by 3
- 2026HydroShear: Hydroelastic Shear Simulation for Tactile Sim-to-Real Reinforcement Learningcited by 3
- 2024DiffSim2Real: Deploying Quadrupedal Locomotion Policies Purely Trained in Differentiable Simulationcited by 2
- 2025Learning to Walk With Less: A Dyna-Style Approach to Quadrupedal Locomotioncited by 2
- 2025Leveraging Analytic Gradients in Provably Safe Reinforcement Learningcited by 1
- 2025When Is Diversity Rewarded in Cooperative Multi-Agent Learning?cited by 1
- 2025Reparameterization Proximal Policy Optimizationcited by 1
- 2025Learning Terrain-Specialized Policies for Adaptive Locomotion in Challenging Environmentscited by 1
12 most cited of 17 All 17 (JSON)
- 2026Accelerating Visual Policy Learning with Sampling-Based Model Predictive Control17 Sep 2026
- 2026Ostrich: Taking Large Strides Through Stiff Contact in Differentiable Dynamics8 Sep 2026
- 2026Open-DiffLoco: Open-Source Differentiable Learning for Deployable Blind Quadruped Locomotion3 Aug 2026
- 2026Efficient On-policy Visual-RL via Stochastic Decoupled Policy Gradient26 May 2026
- 2026HydroShear: Hydroelastic Shear Simulation for Tactile Sim-to-Real Reinforcement Learning28 Feb 2026
- 2025Learning Terrain-Specialized Policies for Adaptive Locomotion in Challenging Environments25 Sep 2025
- 2025Learning to Walk With Less: A Dyna-Style Approach to Quadrupedal Locomotion8 Sep 2025
- 2025First Order Model-Based RL through Decoupled Backpropagation29 Aug 2025
- 2025Reparameterization Proximal Policy Optimization8 Aug 2025
- 2025Differentiable Simulation of Hard Contacts with Soft Gradients for Learning and Control17 Jun 2025
- 2025When Is Diversity Rewarded in Cooperative Multi-Agent Learning?11 Jun 2025
- 2025Leveraging Analytic Gradients in Provably Safe Reinforcement Learning2 Jun 2025
12 newest of 17 All 17 (JSON)