# PA-LOCO: Learning Perturbation-Adaptive Locomotion for Quadruped Robots

arXiv: https://arxiv.org/abs/2407.04224 · HTML: https://mlsanity.com/paper/2407.04224/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 34 of its 40 references that are in the map.
- First posted on arXiv 5 Jul 2024.

## Placed in

- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Builds on (most cited first, 30 of 34)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learning](https://mlsanity.com/paper/2108.10470/) (2021)
- [Sim-to-Real Transfer of Robotic Control with Dynamics Randomization](https://mlsanity.com/paper/1710.06537/) (2017)
- [Learning Quadrupedal Locomotion over Challenging Terrain](https://mlsanity.com/paper/2010.11251/) (2020)
- [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)
- [Learning robust perceptive locomotion for quadrupedal robots in the wild](https://mlsanity.com/paper/2201.08117/) (2022)
- [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)
- [Rapid Locomotion via Reinforcement Learning](https://mlsanity.com/paper/2205.02824/) (2022)
- [Extreme Parkour with Legged Robots](https://mlsanity.com/paper/2309.14341/) (2023)
- [Legged Locomotion in Challenging Terrains using Egocentric Vision](https://mlsanity.com/paper/2211.07638/) (2022)
- [Robot Parkour Learning](https://mlsanity.com/paper/2309.05665/) (2023)
- [Deep Whole-Body Control: Learning a Unified Policy for Manipulation and Locomotion](https://mlsanity.com/paper/2210.10044/) (2022)
- [Adversarial Motion Priors Make Good Substitutes for Complex Reward Functions](https://mlsanity.com/paper/2203.15103/) (2022)
- [Concurrent Training of a Control Policy and a State Estimator for Dynamic and Robust Legged Locomotion](https://mlsanity.com/paper/2202.05481/) (2022)
- [Multi-expert learning of adaptive legged locomotion](https://mlsanity.com/paper/2012.05810/) (2020)
- [Not Only Rewards But Also Constraints: Applications on Legged Robot Locomotion](https://mlsanity.com/paper/2308.12517/) (2023)
- [Learning to Jump from Pixels](https://mlsanity.com/paper/2110.15344/) (2021)
- [Learning Agile Skills via Adversarial Imitation of Rough Partial Demonstrations](https://mlsanity.com/paper/2206.11693/) (2022)
- [DribbleBot: Dynamic Legged Manipulation in the Wild](https://mlsanity.com/paper/2304.01159/) (2023)
- [Legs as Manipulator: Pushing Quadrupedal Agility Beyond Locomotion](https://mlsanity.com/paper/2303.11330/) (2023)
- [Hierarchical Reinforcement Learning for Precise Soccer Shooting Skills using a Quadrupedal Robot](https://mlsanity.com/paper/2208.01160/) (2022)
- [Advanced Skills through Multiple Adversarial Motion Priors in Reinforcement Learning](https://mlsanity.com/paper/2203.14912/) (2022)
- [Learning and Adapting Agile Locomotion Skills by Transferring Experience](https://mlsanity.com/paper/2304.09834/) (2023)
- [Creating a Dynamic Quadrupedal Robotic Goalkeeper with Reinforcement Learning](https://mlsanity.com/paper/2210.04435/) (2022)
- [Versatile Skill Control via Self-supervised Adversarial Imitation of Unlabeled Mixed Motions](https://mlsanity.com/paper/2209.07899/) (2022)
- [Cat-like Jumping and Landing of Legged Robots in Low-gravity Using Deep Reinforcement Learning](https://mlsanity.com/paper/2106.09357/) (2021)
- [Circus ANYmal: A Quadruped Learning Dexterous Manipulation with Its Limbs](https://mlsanity.com/paper/2011.08811/) (2020)

## Built on by (most cited first, 8 of 8)

- [FACET: Force-Adaptive Control via Impedance Reference Tracking for Legged Robots](https://mlsanity.com/paper/2505.06883/) (2025)
- [TAR: Teacher-Aligned Representations via Contrastive Learning for Quadrupedal Locomotion](https://mlsanity.com/paper/2503.20839/) (2025)
- [GRAM: Generalization in Deep RL with a Robust Adaptation Module](https://mlsanity.com/paper/2412.04323/) (2024)
- [Disturbance-Aware Adaptive Compensation in Hybrid Force-Position Locomotion Policy for Legged Robots](https://mlsanity.com/paper/2506.00472/) (2025)
- [Flexible Locomotion Learning with Diffusion Model Predictive Control](https://mlsanity.com/paper/2510.04234/) (2025)
- [Scoop-and-Toss: Dynamic Object Collection for Quadrupedal Systems](https://mlsanity.com/paper/2506.09406/) (2025)
- [Knowledge-Distilled End-to-End Reinforcement Learning for Smooth 6-DOF Thrust Control and Rapid Adaptation to Ocean Currents in Remotely Operated Vehicles](https://mlsanity.com/paper/2608.08598/) (2026)
- [PILOT: Privileged Imitation Learning for End-to-End Motion Planning of Autonomous UAVs under Partial Observability](https://mlsanity.com/paper/2608.14082/) (2026)

## Abstract (arXiv)

Numerous locomotion controllers have been designed based on Reinforcement Learning (RL) to facilitate blind quadrupedal locomotion traversing challenging terrains. Nevertheless, locomotion control is still a challenging task for quadruped robots traversing diverse terrains amidst unforeseen disturbances. Recently, privileged learning has been employed to learn reliable and robust quadrupedal locomotion over various terrains based on a teacher-student architecture. However, its one-encoder structure is not adequate in addressing external force perturbations. The student policy would experience inevitable performance degradation due to the feature embedding discrepancy between the feature encoder of the teacher policy and the one of the student policy. Hence, this paper presents a privileged learning framework with multiple feature encoders and a residual policy network for robust and reliable quadruped locomotion subject to various external perturbations. The multi-encoder structure can decouple latent features from different privileged information, ultimately leading to enhanced performance of the learned policy in terms of robustness, stability, and reliability. The efficiency of the proposed feature encoding module is analyzed in depth using extensive simulation data. The introduction of the residual policy network helps mitigate the performance degradation experienced by the student policy that attempts to clone the behaviors of a teacher policy. The proposed framework is evaluated on a Unitree GO1 robot, showcasing its performance enhancement over the state-of-the-art privileged learning algorithm through extensive experiments conducted on diverse terrains. Ablation studies are conducted to illustrate the efficiency of the residual policy network.