# Geometry-aware Dynamic Movement Primitives

arXiv: https://arxiv.org/abs/2003.06061 · HTML: https://mlsanity.com/paper/2003.06061/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Mar 2020.

## Built on by (most cited first, 4 of 4)

- [A Survey on Imitation Learning for Contact-Rich Tasks in Robotics](https://mlsanity.com/paper/2506.13498/) (2025)
- [ManiDP: Manipulability-Aware Diffusion Policy for Posture-Dependent Bimanual Manipulation](https://mlsanity.com/paper/2510.23016/) (2025)
- [Fusion Dynamical Systems with Machine Learning in Imitation Learning: A Comprehensive Overview](https://mlsanity.com/paper/2403.19916/) (2024)
- [Guided Learning from Demonstration for Robust Transferability](https://mlsanity.com/paper/2302.03901/) (2023)

## Abstract (arXiv)

In many robot control problems, factors such as stiffness and damping matrices and manipulability ellipsoids are naturally represented as symmetric positive definite (SPD) matrices, which capture the specific geometric characteristics of those factors. Typical learned skill models such as dynamic movement primitives (DMPs) can not, however, be directly employed with quantities expressed as SPD matrices as they are limited to data in Euclidean space. In this paper, we propose a novel and mathematically principled framework that uses Riemannian metrics to reformulate DMPs such that the resulting formulation can operate with SPD data in the SPD manifold. Evaluation of the approach demonstrates that beneficial properties of DMPs such as change of the goal during operation apply also to the proposed formulation.