# Phase-Amplitude Reduction-Based Imitation Learning

arXiv: https://arxiv.org/abs/2406.03735 · HTML: https://mlsanity.com/paper/2406.03735/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 6 of its 38 references that are in the map.
- First posted on arXiv 6 Jun 2024.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

## Builds on (most cited first, 6 of 6)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [dm_control: Software and Tasks for Continuous Control](https://mlsanity.com/paper/2006.12983/) (2020)
- [Dynamic Movement Primitives in Robotics: A Tutorial Survey](https://mlsanity.com/paper/2102.03861/) (2021)
- [On the Utility of Koopman Operator Theory in Learning Dexterous Manipulation Skills](https://mlsanity.com/paper/2303.13446/) (2023)

## Abstract (arXiv)

In this study, we propose the use of the phase-amplitude reduction method to construct an imitation learning framework. Imitating human movement trajectories is recognized as a promising strategy for generating a range of human-like robot movements. Unlike previous dynamical system-based imitation learning approaches, our proposed method allows the robot not only to imitate a limit cycle trajectory but also to replicate the transient movement from the initial or disturbed state to the limit cycle. Consequently, our method offers a safer imitation learning approach that avoids generating unpredictable motions immediately after disturbances or from a specified initial state. We first validated our proposed method by reconstructing a simple limit-cycle attractor. We then compared the proposed approach with a conventional method on a lemniscate trajectory tracking task with a simulated robot arm. Our findings confirm that our proposed method can more accurately generate transient movements to converge on a target periodic attractor compared to the previous standard approach. Subsequently, we applied our method to a real robot arm to imitate periodic human movements.