# MULE: Multi-terrain and Unknown Load Adaptation for Effective Quadrupedal Locomotion

arXiv: https://arxiv.org/abs/2505.00488 · HTML: https://mlsanity.com/paper/2505.00488/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 22 references that are in the map.
- First posted on arXiv 1 May 2025.

## Builds on (most cited first, 15 of 15)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learning](https://mlsanity.com/paper/2109.11978/) (2021)
- [RMA: Rapid Motor Adaptation for Legged Robots](https://mlsanity.com/paper/2107.04034/) (2021)
- [Learning agile and dynamic motor skills for legged robots](https://mlsanity.com/paper/1901.08652/) (2019)
- [Walk These Ways: Tuning Robot Control for Generalization with Multiplicity of Behavior](https://mlsanity.com/paper/2212.03238/) (2022)
- [DreamWaQ: Learning Robust Quadrupedal Locomotion With Implicit Terrain Imagination via Deep Reinforcement Learning](https://mlsanity.com/paper/2301.10602/) (2023)
- [RLOC: Terrain-Aware Legged Locomotion using Reinforcement Learning and Optimal Control](https://mlsanity.com/paper/2012.03094/) (2020)
- [Hybrid Internal Model: Learning Agile Legged Locomotion with Simulated Robot Response](https://mlsanity.com/paper/2312.11460/) (2023)
- [Domain Randomization via Entropy Maximization](https://mlsanity.com/paper/2311.01885/) (2023)
- [Safe Reinforcement Learning with Dual Robustness](https://mlsanity.com/paper/2309.06835/) (2023)
- [Learning Agile Locomotion and Adaptive Behaviors via RL-augmented MPC](https://mlsanity.com/paper/2310.09442/) (2023)
- [Adaptive CLF-MPC With Application To Quadrupedal Robots](https://mlsanity.com/paper/2112.04536/) (2021)
- [PIP-Loco: A Proprioceptive Infinite Horizon Planning Framework for Quadrupedal Robot Locomotion](https://mlsanity.com/paper/2409.09441/) (2024)
- [Adaptive Force-based Control for Legged Robots](https://mlsanity.com/paper/2011.06236/) (2020)
- [Online Optimization of Central Pattern Generators for Quadruped Locomotion](https://mlsanity.com/paper/2410.16417/) (2024)

## Built on by (most cited first, 1 of 1)

- [Transporting Unsecured Stacked Payloads with a Quadrupedal Robot via Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2610.05819/) (2026)

## Abstract (arXiv)

Quadrupedal robots are increasingly deployed for load-carrying tasks across diverse terrains. While Model Predictive Control (MPC)-based methods can account for payload variations, they often depend on predefined gait schedules or trajectory generators, limiting their adaptability in unstructured environments. To address these limitations, we propose an Adaptive Reinforcement Learning (RL) framework that enables quadrupedal robots to dynamically adapt to both varying payloads and diverse terrains. The framework consists of a nominal policy responsible for baseline locomotion and an adaptive policy that learns corrective actions to preserve stability and improve command tracking under payload variations. We validate the proposed approach through large-scale simulation experiments in Isaac Gym and real-world hardware deployment on a Unitree Go1 quadruped. The controller was tested on flat ground, slopes, and stairs under both static and dynamic payload changes. Across all settings, our adaptive controller consistently outperformed the controller in tracking body height and velocity commands, demonstrating enhanced robustness and adaptability without requiring explicit gait design or manual tuning.