# Towards Orientation Learning and Adaptation in Cartesian Space

arXiv: https://arxiv.org/abs/1907.03918 · HTML: https://mlsanity.com/paper/1907.03918/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Placed in Robot learning from demonstration, one of 13 directions in Offline RL and imitation learning from data.
- First posted on arXiv 9 Jul 2019.

## Placed in

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

## Built on by (most cited first, 12 of 12)

- [Residual Learning from Demonstration: Adapting DMPs for Contact-rich Manipulation](https://mlsanity.com/paper/2008.07682/) (2020)
- [Learning Stable Vector Fields on Lie Groups](https://mlsanity.com/paper/2110.11774/) (2021)
- [Continual Learning from Demonstration of Robotics Skills](https://mlsanity.com/paper/2202.06843/) (2022)
- [Orientation Probabilistic Movement Primitives on Riemannian Manifolds](https://mlsanity.com/paper/2110.15036/) (2021)
- [Scalable and Efficient Continual Learning from Demonstration via a Hypernetwork-generated Stable Dynamics Model](https://mlsanity.com/paper/2311.03600/) (2023)
- [Unraveling the Single Tangent Space Fallacy: An Analysis and Clarification for Applying Riemannian Geometry in Robot Learning](https://mlsanity.com/paper/2310.07902/) (2023)
- [Gaussian-Process-based Robot Learning from Demonstration](https://mlsanity.com/paper/2002.09979/) (2020)
- [PUMA: Deep Metric Imitation Learning for Stable Motion Primitives](https://mlsanity.com/paper/2310.12831/) (2023)
- [Periodic DMP formulation for Quaternion Trajectories](https://mlsanity.com/paper/2110.10510/) (2021)
- [Non-parametric regression for robot learning on manifolds](https://mlsanity.com/paper/2310.19561/) (2023)
- [Constrained Equation Learner Networks for Precision-Preserving Extrapolation of Robotic Skills](https://mlsanity.com/paper/2311.02475/) (2023)
- [Imitation Learning-based Direct Visual Servoing using the Large Projection Formulation](https://mlsanity.com/paper/2406.09120/) (2024)

## Abstract (arXiv)

As a promising branch of robotics, imitation learning emerges as an important way to transfer human skills to robots, where human demonstrations represented in Cartesian or joint spaces are utilized to estimate task/skill models that can be subsequently generalized to new situations. While learning Cartesian positions suffices for many applications, the end-effector orientation is required in many others. Despite recent advances in learning orientations from demonstrations, several crucial issues have not been adequately addressed yet. For instance, how can demonstrated orientations be adapted to pass through arbitrary desired points that comprise orientations and angular velocities? In this paper, we propose an approach that is capable of learning multiple orientation trajectories and adapting learned orientation skills to new situations (e.g., via-points and end-points), where both orientation and angular velocity are considered. Specifically, we introduce a kernelized treatment to alleviate explicit basis functions when learning orientations, which allows for learning orientation trajectories associated with high-dimensional inputs. In addition, we extend our approach to the learning of quaternions with angular acceleration or jerk constraints, which allows for generating smoother orientation profiles for robots. Several examples including experiments with real 7-DoF robot arms are provided to verify the effectiveness of our method.