# PUMA: Deep Metric Imitation Learning for Stable Motion Primitives

arXiv: https://arxiv.org/abs/2310.12831 · HTML: https://mlsanity.com/paper/2310.12831/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Robot manipulation imitation learning, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 12 of its 67 references that are in the map.
- First posted on arXiv 19 Oct 2023.

## Placed in

- Offline RL and imitation learning from data / [Robot manipulation imitation learning](https://mlsanity.com/offlinerl/robot-manipulation-imitation-learning/)

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

- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Neural Dynamic Policies for End-to-End Sensorimotor Learning](https://mlsanity.com/paper/2012.02788/) (2020)
- [ImitationFlow: Learning Deep Stable Stochastic Dynamic Systems by Normalizing Flows](https://mlsanity.com/paper/2010.13129/) (2020)
- [Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systems](https://mlsanity.com/paper/2005.13143/) (2020)
- [ProDMPs: A Unified Perspective on Dynamic and Probabilistic Movement Primitives](https://mlsanity.com/paper/2210.01531/) (2022)
- [Geometric Fabrics: Generalizing Classical Mechanics to Capture the Physics of Behavior](https://mlsanity.com/paper/2109.10443/) (2021)
- [Learning Riemannian Stable Dynamical Systems via Diffeomorphisms](https://mlsanity.com/paper/2211.03169/) (2022)
- [Towards Orientation Learning and Adaptation in Cartesian Space](https://mlsanity.com/paper/1907.03918/) (2019)
- [Learning Stable Vector Fields on Lie Groups](https://mlsanity.com/paper/2110.11774/) (2021)
- [Learning Stable Robotic Skills on Riemannian Manifolds](https://mlsanity.com/paper/2208.13267/) (2022)
- [Gaussian-Process-based Robot Learning from Demonstration](https://mlsanity.com/paper/2002.09979/) (2020)

## Built on by (most cited first, 3 of 3)

- [The Duality of Generative AI and Reinforcement Learning in Robotics: A Review](https://mlsanity.com/paper/2410.16411/) (2024)
- [TamedPUMA: safe and stable imitation learning with geometric fabrics](https://mlsanity.com/paper/2503.17432/) (2025)
- [Let the Dynamics Flow: Stable Flow Matching Dynamical Systems](https://mlsanity.com/paper/2606.03834/) (2026)

## Abstract (arXiv)

Imitation Learning (IL) is a powerful technique for intuitive robotic programming. However, ensuring the reliability of learned behaviors remains a challenge. In the context of reaching motions, a robot should consistently reach its goal, regardless of its initial conditions. To meet this requirement, IL methods often employ specialized function approximators that guarantee this property by construction. Although effective, these approaches come with a set of limitations: 1) they are unable to fully exploit the capabilities of modern Deep Neural Network (DNN) architectures, 2) some are restricted in the family of motions they can model, resulting in suboptimal IL capabilities, and 3) they require explicit extensions to account for the geometry of motions that consider orientations. To address these challenges, we introduce a novel stability loss function, drawing inspiration from the triplet loss used in the deep metric learning literature. This loss does not constrain the DNN's architecture and enables learning policies that yield accurate results. Furthermore, it is not restricted to a specific state space geometry; therefore, it can easily incorporate the geometry of the robot's state space. We provide a proof of the stability properties induced by this loss and empirically validate our method in various settings. These settings include Euclidean and non-Euclidean state spaces, as well as first-order and second-order motions, both in simulation and with real robots. More details about the experimental results can be found in: https://youtu.be/ZWKLGntCI6w.