# TamedPUMA: safe and stable imitation learning with geometric fabrics

arXiv: https://arxiv.org/abs/2503.17432 · HTML: https://mlsanity.com/paper/2503.17432/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Robot learning from demonstration, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 23 of its 43 references that are in the map.
- First posted on arXiv 21 Mar 2025.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018)
- [Riemannian Motion Policies](https://mlsanity.com/paper/1801.02854/) (2018)
- [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)
- [Learning Model Predictive Controllers with Real-Time Attention for Real-World Navigation](https://mlsanity.com/paper/2209.10780/) (2022)
- [ProDMPs: A Unified Perspective on Dynamic and Probabilistic Movement Primitives](https://mlsanity.com/paper/2210.01531/) (2022)
- [Bayesian Optimization Meets Riemannian Manifolds in Robot Learning](https://mlsanity.com/paper/1910.04998/) (2019)
- [Neural Contractive Dynamical Systems](https://mlsanity.com/paper/2401.09352/) (2024)
- [Learning Stable Robotic Skills on Riemannian Manifolds](https://mlsanity.com/paper/2208.13267/) (2022)
- [Geometric Fabrics for the Acceleration-based Design of Robotic Motion](https://mlsanity.com/paper/2010.14750/) (2020)
- [Model Predictive Control via On-Policy Imitation Learning](https://mlsanity.com/paper/2210.09206/) (2022)
- [Efficient Deep Learning of Robust Policies from MPC using Imitation and Tube-Guided Data Augmentation](https://mlsanity.com/paper/2306.00286/) (2023)
- [Optimization Fabrics](https://mlsanity.com/paper/2008.02399/) (2020)
- [CollisionIK: A Per-Instant Pose Optimization Method for Generating Robot Motions with Environment Collision Avoidance](https://mlsanity.com/paper/2102.13187/) (2021)
- [Deep Probabilistic Movement Primitives with a Bayesian Aggregator](https://mlsanity.com/paper/2307.05141/) (2023)
- [Geometric Fabrics: a Safe Guiding Medium for Policy Learning](https://mlsanity.com/paper/2405.02250/) (2024)
- [PUMA: Deep Metric Imitation Learning for Stable Motion Primitives](https://mlsanity.com/paper/2310.12831/) (2023)
- [Fusion Dynamical Systems with Machine Learning in Imitation Learning: A Comprehensive Overview](https://mlsanity.com/paper/2403.19916/) (2024)
- [Dynamic Optimization Fabrics for Motion Generation](https://mlsanity.com/paper/2205.08454/) (2022)
- [A Riemannian Take on Human Motion Analysis and Retargeting](https://mlsanity.com/paper/2208.01372/) (2022)
- [Avoidance of Concave Obstacles through Rotation of Nonlinear Dynamics](https://mlsanity.com/paper/2306.16160/) (2023)
- [Imitation Learning via Simultaneous Optimization of Policies and Auxiliary Trajectories](https://mlsanity.com/paper/2105.03019/) (2021)
- [Fabrics: A Foundationally Stable Medium for Encoding Prior Experience](https://mlsanity.com/paper/2309.07368/) (2023)

## Abstract (arXiv)

Using the language of dynamical systems, Imitation learning (IL) provides an intuitive and effective way of teaching stable task-space motions to robots with goal convergence. Yet, IL techniques are affected by serious limitations when it comes to ensuring safety and fulfillment of physical constraints. With this work, we solve this challenge via TamedPUMA, an IL algorithm augmented with a recent development in motion generation called geometric fabrics. As both the IL policy and geometric fabrics describe motions as artificial second-order dynamical systems, we propose two variations where IL provides a navigation policy for geometric fabrics. The result is a stable imitation learning strategy within which we can seamlessly blend geometrical constraints like collision avoidance and joint limits. Beyond providing a theoretical analysis, we demonstrate TamedPUMA with simulated and real-world tasks, including a 7-DoF manipulator.