A model of reaching via subriemannian geodesics in Engel-type group

TL;DR

This paper models arm reaching movements as geodesics in a sub-Riemannian space, linking neural activity to geometric trajectories, and extends the model to include movement direction for task-specific analysis.

Contribution

It introduces a novel geometric model of reaching movements based on sub-Riemannian geodesics, incorporating neural selectivity and movement direction.

Findings

Revealed a geometric interpretation of reaching trajectories.

Extended the model to include movement direction.

Provided a framework linking neural activity to movement geometry.

Abstract

In this paper, we propose a model of arm reaching movements expressed in terms of geodesics in a sub-Riemannian space. We will choose a set of kinematic variables to which motor cortical cells are selective with the purpose of modelling the specific task of reaching. Minimizing trajectories will be recovered as suitable geodesics of the geometric spaces arising from the selective behaviour of M1 neurons. We will then extend this model by including the direction of arm movement. On this set, we will define a suitable sub-Riemannian metric able to provide a geometric interpretation of two-dimensional task-dependent arm reaching movements.