# Learning from Demonstration via Spatiotemporal Tubes for Unknown Euler-Lagrange Systems

arXiv: https://arxiv.org/abs/2607.00534 · HTML: https://mlsanity.com/paper/2607.00534/

## 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 10 of its 23 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## 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, 10 of 10)

- [Learning Control Barrier Functions from Expert Demonstrations](https://mlsanity.com/paper/2004.03315/) (2020)
- [Interactive Imitation Learning in Robotics: A Survey](https://mlsanity.com/paper/2211.00600/) (2022)
- [Control Barrier Functions for Unknown Nonlinear Systems using Gaussian Processes](https://mlsanity.com/paper/2010.05818/) (2020)
- [Uncertainty-Aware Imitation Learning using Kernelized Movement Primitives](https://mlsanity.com/paper/1903.02114/) (2019)
- [Learning Complex Motion Plans using Neural ODEs with Safety and Stability Guarantees](https://mlsanity.com/paper/2308.00186/) (2023)
- [Gaussian-Process-based Robot Learning from Demonstration](https://mlsanity.com/paper/2002.09979/) (2020)
- [Funnel Control Under Hard and Soft Output Constraints (extended version)](https://mlsanity.com/paper/2208.02006/) (2022)
- [Spatiotemporal Tubes for Temporal Reach-Avoid-Stay Tasks in Unknown Systems](https://mlsanity.com/paper/2411.13834/) (2024)
- [Safe and Stable Neural Network Dynamical Systems for Robot Motion Planning](https://mlsanity.com/paper/2511.20593/) (2025)
- [Real-Time Spatiotemporal Tubes for Dynamic Unsafe Sets](https://mlsanity.com/paper/2512.06151/) (2025)

## Abstract (arXiv)

We present STT-LfD, a unified Learning from Demonstration (LfD) framework that integrates motion learning with control for unknown Euler-Lagrange systems. Unlike traditional decoupled approaches that track a fixed reference, the proposed method treats demonstrations as a data-driven safety specification. Using heteroscedastic Gaussian Processes, STT-LfD learns Spatiotemporal Tubes (STTs) as an intent envelope that capture time-varying precision requirements of a task. A closed-form feedback controller then enforces these learned constraints while respecting actuator limits, without requiring explicit system identification. The approach preserves the temporal structure of demonstrations, remains computationally efficient, and avoids explicit system identification. Hardware experiments on a mobile robot and a 7-DOF manipulator show that it outperforms baselines in robustness to disturbances and computational speed.