From brain to motion: harnessing higher-derivative mechanics for neural control

Abstract

Optimal Feedback Control provides a theoretical framework for goal-directed movements, where the nervous system adjusts actions based on sensory feedback. This theory assumes that there exists a cost function that is optimized throughout one's movement. It is natural to assume that mechanical quantities should be involved in cost functions, but this does not imply that the mechanical principles that govern human voluntary movements are necessarily Newtonian. We argue that integrating principles from Lagrangian and Hamiltonian higher-derivative mechanics, i.e. dynamical models relying on a Lagrangian of the form $L\left(\vec x,\dot{\vec x},\ddot{\vec x},\dots,\vec x^{\, (N)}\right)$, with $N\geq 2$ and where $\vec x^{\, (i)}$ denotes the $i^{\rm th}$ time-derivative of the position $\vec x$, provides a more natural framework to study the constraints hidden in human voluntary movement within Optimal Feedback Control theory.