Predicting Rigid Body Dynamics Using Dual Quaternion Recurrent Neural Networks With Quaternion Attention

Abstract

We propose a novel neural network architecture based on dual quaternions which allow for a compact representation of information with a main focus on describing rigid body movements. After introducing the underlying dual quaternion math, we derive dual quaternion valued neural network layer which are generally applickable to all sorts of problems which can benefit from a mathematical description in dual quaternion space. To cover the dynamic behavior inherent to rigid body movements, we propose recurrent architectures in the neural network. To further model the rigid bodies interactions 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. There we can show that the dual quaternion valued models outperform their counterparts operation on the real numbers, confirming the successful introduction of an inductive bias through the usage of dual quaternion math. Furthermore, we used an advantageous custom data augmentation technique specifically tailored for the usage with our dual quaternion valued input data. INDEX TERMSdual quaternion attention, dual duaternion neural networks, hypercomplex neural networks, rigid body dynamics

Dual Quaternion Rotational and Translational Equivariance in 3D Rigid Motion Modelling

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Dual Attitude Representations and Kinematics for Six-Degree-of-Freedom Spacecraft Dynamics

“…Moreover, control laws based on the dual quaternion involving combined position and attitude intrinsically account for the natural coupling between the rotational and translational motion [1]. The widespread use of dual quaternions can be found in robotics systems [2] [3], rigid body dynamics [4] [5] [6], and in relative spacecraft system dynamics [7] [8]. They are also utilized in field of aerospace engineering involving dual quaternions for powered descent [9] and satellite autonomous rendezvous control [10] [11].…”

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