# A CPG-Based Agile and Versatile Locomotion Framework Using Proximal Symmetry Loss

arXiv: https://arxiv.org/abs/2103.00928 · HTML: https://mlsanity.com/paper/2103.00928/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2021.

## Built on by (most cited first, 6 of 6)

- [One Policy to Run Them All: an End-to-end Learning Approach to Multi-Embodiment Locomotion](https://mlsanity.com/paper/2409.06366/) (2024)
- [CPG-RL: Learning Central Pattern Generators for Quadruped Locomotion](https://mlsanity.com/paper/2211.00458/) (2022)
- [Leveraging Symmetry in RL-based Legged Locomotion Control](https://mlsanity.com/paper/2403.17320/) (2024)
- [Towards Embodiment Scaling Laws in Robot Locomotion](https://mlsanity.com/paper/2505.05753/) (2025)
- [Gait in Eight: Efficient On-Robot Learning for Omnidirectional Quadruped Locomotion](https://mlsanity.com/paper/2503.08375/) (2025)
- [Addressing imperfect symmetry: A novel symmetry-learning actor-critic extension](https://mlsanity.com/paper/2309.02711/) (2023)

## Abstract (arXiv)

Humanoid robots are made to resemble humans but their locomotion abilities are far from ours in terms of agility and versatility. When humans walk on complex terrains, or face external disturbances, they combine a set of strategies, unconsciously and efficiently, to regain stability. This paper tackles the problem of developing a robust omnidirectional walking framework, which is able to generate versatile and agile locomotion on complex terrains. The Linear Inverted Pendulum Model and Central Pattern Generator concepts are used to develop a closed-loop walk engine, which is then combined with a reinforcement learning module. This module learns to regulate the walk engine parameters adaptively, and generates residuals to adjust the robot's target joint positions (residual physics). Additionally, we propose a proximal symmetry loss function to increase the sample efficiency of the Proximal Policy Optimization algorithm, by leveraging model symmetries and the trust region concept. The effectiveness of the proposed framework was demonstrated and evaluated across a set of challenging simulation scenarios. The robot was able to generalize what it learned in unforeseen circumstances, displaying human-like locomotion skills, even in the presence of noise and external pushes.