# Learning Emergent Gaits with Decentralized Phase Oscillators: on the role of Observations, Rewards, and Feedback

arXiv: https://arxiv.org/abs/2402.08662 · HTML: https://mlsanity.com/paper/2402.08662/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 35 references that are in the map.
- First posted on arXiv 13 Feb 2024.

## Builds on (most cited first, 12 of 12)

- [Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learning](https://mlsanity.com/paper/2109.11978/) (2021)
- [Learning robust perceptive locomotion for quadrupedal robots in the wild](https://mlsanity.com/paper/2201.08117/) (2022)
- [Walk These Ways: Tuning Robot Control for Generalization with Multiplicity of Behavior](https://mlsanity.com/paper/2212.03238/) (2022)
- [Sim-to-Real Learning of All Common Bipedal Gaits via Periodic Reward Composition](https://mlsanity.com/paper/2011.01387/) (2020)
- [Dynamics Randomization Revisited:A Case Study for Quadrupedal Locomotion](https://mlsanity.com/paper/2011.02404/) (2020)
- [Highly Dynamic Quadruped Locomotion via Whole-Body Impulse Control and Model Predictive Control](https://mlsanity.com/paper/1909.06586/) (2019)
- [Fast and Efficient Locomotion via Learned Gait Transitions](https://mlsanity.com/paper/2104.04644/) (2021)
- [GenLoco: Generalized Locomotion Controllers for Quadrupedal Robots](https://mlsanity.com/paper/2209.05309/) (2022)
- [CPG-RL: Learning Central Pattern Generators for Quadruped Locomotion](https://mlsanity.com/paper/2211.00458/) (2022)
- [Learning Free Gait Transition for Quadruped Robots via Phase-Guided Controller](https://mlsanity.com/paper/2201.00206/) (2022)
- [Quadruped Capturability and Push Recovery via a Switched-Systems Characterization of Dynamic Balance](https://mlsanity.com/paper/2201.11928/) (2022)
- [Hybrid iLQR Model Predictive Control for Contact Implicit Stabilization on Legged Robots](https://mlsanity.com/paper/2207.04591/) (2022)

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

- [Symmetry-Guided Memory Augmentation for Efficient Locomotion Learning](https://mlsanity.com/paper/2502.01521/) (2025)

## Abstract (arXiv)

We present a minimal phase oscillator model for learning quadrupedal locomotion. Each of the four oscillators is coupled only to itself and its corresponding leg through local feedback of the ground reaction force, which can be interpreted as an observer feedback gain. We interpret the oscillator itself as a latent contact state-estimator. Through a systematic ablation study, we show that the combination of phase observations, simple phase-based rewards, and the local feedback dynamics induces policies that exhibit emergent gait preferences, while using a reduced set of simple rewards, and without prescribing a specific gait. The code is open-source, and a video synopsis available at https://youtu.be/1NKQ0rSV3jU.