# Predicting Rigid Body Dynamics using Dual Quaternion Recurrent Neural Networks with Quaternion Attention

arXiv: https://arxiv.org/abs/2011.08734 · HTML: https://mlsanity.com/paper/2011.08734/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2020.

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

- [Dual Quaternion Ambisonics Array for Six-Degree-of-Freedom Acoustic Representation](https://mlsanity.com/paper/2204.01851/) (2022)
- [Dual Quaternion Rotational and Translational Equivariance in 3D Rigid Motion Modelling](https://mlsanity.com/paper/2310.07623/) (2023)
- [Time Series Compression using Quaternion Valued Neural Networks and Quaternion Backpropagation](https://mlsanity.com/paper/2403.11722/) (2024)
- [PHYDI: Initializing Parameterized Hypercomplex Neural Networks as Identity Functions](https://mlsanity.com/paper/2310.07612/) (2023)

## Abstract (arXiv)

We propose a novel neural network architecture based on dual quaternions which allow for a compact representation of informations with a main focus on describing rigid body movements. To cover the dynamic behavior inherent to rigid body movements, we propose recurrent architectures in the neural network. To further model the interactions between individual rigid bodies as well as external inputs efficiently, we incorporate a novel attention mechanism employing dual quaternion algebra. The introduced architecture is trainable by means of gradient based algorithms. We apply our approach to a parcel prediction problem where a rigid body with an initial position, orientation, velocity and angular velocity moves through a fixed simulation environment which exhibits rich interactions between the parcel and the boundaries.