Abstract
Developing deployable locomotion policies through conventional reinforcement learning often requires complex reward engineering and expensive training times. While differentiable simulation offers a highly efficient alternative, open-source tools capable of end-to-end transfer of these policies to physical hardware remain limited. This paper introduces Open-DiffLoco, an open-source framework for training deployable blind quadruped locomotion policies with differentiable simulation. The framework implements the Short-Horizon Actor-Critic (SHAC) algorithm in MuJoCo XLA (MJX) and trains a proprioceptive policy that transfers to real-world hardware. The deployed policy removes privileged actor observations, including base linear velocity, and does not rely on reference trajectories. It also uses a substantially simplified reward function, enabling the robot to discover walking patterns without the complex auxiliary rewards typically used in conventional reinforcement learning pipelines. When deployed on physical hardware (a Unitree Go2 quadruped), the trained policy tracks omnidirectional velocity commands with root-mean-square error below 0.2 m/s, reaches speeds above 1 m/s, and remains robust to uneven terrain and external physical disturbances, such as lateral pushes. Across the reported configurations, training uses under 6 GB of VRAM on a single NVIDIA GeForce RTX 5080 GPU and completes in approximately 20-60 minutes. As an algorithmic extension to SHAC, we propose Jacobian-Augmented Value Estimation (JAVE), which supervises the critic Jacobians to improve early first-order policy-gradient training. To our knowledge, Open-DiffLoco is the first open-source framework for training deployable locomotion policies using differentiable simulation. Deployment videos and source code are available at: https://diffloco.martin-opat.com/
Explore similar work
Jul 20, 2026cs.RO
Learning-based approaches to locomotion have risen in popularity in recent years, showing the capability for complex legged locomotion and whole-body control. Reinforcement learning (RL), the primary learning-based approach for locomotion, often utilizes a high-performance simulation tool, providing a controlled and efficient training and development environment. However, policies that perform well in simulation frequently encounter unexpected challenges when deployed on a physical system, known as the sim-to-real gap. This work presents a robust RL locomotion framework capable of whole-body control. The proposed RL framework utilizes Nvidia's new set of simulation tools, Isaac Sim, and its companion RL framework, Isaac Lab, for training, achieving a zero-shot sim-to-real policy. The performance of our policy is validated on physical hardware using the Unitree Go1, with experimental results showing similar velocity tracking performance to the quadruped's integrated controller, with a greater ability to recover from large disturbances, and achieve linear velocities of 2.0 m/s and angular velocities of 1.8 rad/s.
Jordan Dowdy, Jean Chagas Vaz
Jun 23, 2026cs.RO
Universal quadrupedal locomotion remains limited by the difficulty of integrating perception across diverse robot morphologies. State-of-the-art controllers rely on single-robot training or blind policies that omit real-time perception, leading to poor cross-embodiment generalization. Designing locomotion policies that remain robust across related quadruped morphologies while incorporating perception is challenging. Moreover, fully perceptive policies are often sensitive to noise, whereas blind controllers lack terrain awareness. In this work, we study how perception should be integrated into morphology-aware reinforcement learning architectures for deployable quadrupedal control. Building on MorAL, we train morphology-specialized universal controllers on multiple reference quadrupeds using adaptive terrain curricula. We compare a blind baseline, a critic-perceptive variant (MorAL+), and a fully perceptive actor-critic (PPAL). Policies are evaluated in simulation on flat and rough terrains, and deployed on ANYmal hardware. Results show that critic-only perception improves robustness and tracking consistency over blind baselines while remaining more stable than fully perceptive policies under perception noise. These findings highlight that perception placement and curriculum design are key factors for scalable, morphology-aware locomotion.
David Rytz, Kim Tien Ly, Ioannis Havoutis
Jul 1, 2026cs.RO
Reinforcement learning (RL) for quadruped locomotion commonly depends on fixed, hand-crafted, and Markovian reward functions that limit both interpretability of learned policies and lack explicit control over gait behaviors. We introduce a framework where distinct gaits are specified using parameterized constraints expressed in Signal Temporal Logic (STL). These include safety bounds, gait synchronization constraints, command tracking, and actuation bounds. From these specifications, we develop a reward shaping mechanism that provides learning agents a dense, continuous reward landscape that encodes desired behavior. We define parametric STL templates for three speed regimes (walking-trot, trot, bound), calibrate their parameters from reference rollouts, and compute rewards from using smooth approximations of STL robustness over the rollouts. The generated rewards can be used to provide shaped gradients compatible with Proximal Policy Optimization (PPO). We instantiate the approach on Google's Barkour quadruped robot in MuJoCo XLA (MJX). We use parallelization within the simulator to improve training speeds and use domain randomization to robustify learned policies. We show that compared to a baseline of hand-crafted rewards, the STL-shaped rewards yield tighter velocity tracking and more stable training. Videos can be found on our project website: https://stl-locomotion.github.io/.
Merve Atasever, Cagan Bakirci, Alfredo Reina Corona +2