Hierarchical Dual Quaternion-Based Recurrent Neural Network as a Flexible Internal Body Model

Abstract

Internal models of the body are assumed to serve a multitude of different functions. Forward and inverse models are important concepts in motor control. Usually, it is distinguished between these function and there are different models for each individual function or there are even models that are specific to individual behaviors. Here, we present a concept of a core internal model of the body which can act both as an inverse and forward model. In addition, it provides a mechanism for integration of sensory data and can be in this way grounded in the continuous interaction with the environment. In this article, a hierarchical Mean of Multiple Computations neural network is presented that is based on an axis-angle representation of joint movements using dual quaternions. It is shown in detail how the network provides a solution for the forward kinematic problem applied for the case of a seven degrees of freedom robotic arm. Furthermore, it is used in a complex scenario of a bimanual movement task. This demonstrates how the MMC approach can be easily scaled up from a representation of a single arm to a complex model of a complete body.