# Task-Parameterized Imitation Learning with Time-Sensitive Constraints

arXiv: https://arxiv.org/abs/2312.03506 · HTML: https://mlsanity.com/paper/2312.03506/

## 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 4 of its 34 references that are in the map.
- First posted on arXiv 6 Dec 2023.

## 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, 4 of 4)

- [Kernelized Movement Primitives](https://mlsanity.com/paper/1708.08638/) (2017)
- [Memory of Motion for Warm-starting Trajectory Optimization](https://mlsanity.com/paper/1907.01474/) (2019)
- [Learning Stable Robotic Skills on Riemannian Manifolds](https://mlsanity.com/paper/2208.13267/) (2022)
- [Learning from Few Demonstrations with Frame-Weighted Motion Generation](https://mlsanity.com/paper/2303.14188/) (2023)

## Abstract (arXiv)

Programming a robot manipulator should be as intuitive as possible. To achieve that, the paradigm of teaching motion skills by providing few demonstrations has become widely popular in recent years. Probabilistic versions thereof take into account the uncertainty given by the distribution of the training data. However, precise execution of start-, via-, and end-poses at given times can not always be guaranteed. This limits the technology transfer to industrial application. To address this problem, we propose a novel constrained formulation of the Expectation Maximization algorithm for learning Gaussian Mixture Models (GMM) on Riemannian Manifolds. Our approach applies to probabilistic imitation learning and extends also to the well-established TP-GMM framework with Task-Parameterization. It allows to prescribe end-effector poses at defined execution times, for instance for precise pick & place scenarios. The probabilistic approach is compared with state-of-the-art learning-from-demonstration methods using the KUKA LBR iiwa robot. The reader is encouraged to watch the accompanying video available at https://youtu.be/JMI1YxtN9C0