# Chapter 8

# Chapter 8: Feasible Neural Commands with Mechanical Constraints (*under construction*)

*Last updated Dec. 26 2015 by Francisco Valero-Cuevas*

**Abstract:**

In this chapter I refine the notion of feasible neural commands by introducing the concept of functional constraints. Chapter 7 presented the geometric principles that allow us to find the structure of the sets of all feasible neural commands and feasible mechanical outputs as a function of the natural bounds on muscle activations, strengths of the muscles, routing of the tendons, and mechanics of the limb. From that perspective it is clear that producing maximal mechanical output—shown for the case of static force production—can only be achieved by a unique muscle activation pattern (i.e., there is no muscle redundancy). But producing sub-maximal mechanical outputs can be done by multiple muscle activation patterns (i.e., there is muscle redundancy). This chapter explores the nature of those multiple muscle activation patterns, and the relationships among them. I emphasize that considering the properties of the limb plus the functional constraints of the task (which can be mechanical, metabolic, physiological, etc.) allows us to define and find families of valid and related solutions—instead of unique solutions in isolation. These concepts continue to challenge the classical notion of muscle redundancy but, most importantly, provide perspective and computational tools to explore mechanisms by which the nervous system controls the limbs for specific tasks. That is, muscle redundancy is a function of both the limb and the task. This is directly relevant to the central questions of motor control such as optimization, learning, adaptation, dimensionality reduction, synergistic control, etc. More generally, these concepts build a case to argue that exploring and exploiting feasible activation sets is likely a more biologically tenable way in which the nervous system operates in the context of muscle redundancy and multifaceted real-world tasks.

**Forum and commentary:**

*Coming soon!*

**Exercises:**

*Coming soon!*

**Additional references and suggested reading:**

*Coming soon!*

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**Code:**

ncube.m: Download

**Note:** *This .m file is only required for matlab users since python has a more clever way of creating generator vectors.*

zonotope_multi_N_2D.m: Download

zonotope_multi_N_2D.py: Download

© Francisco Valero-Cuevas 2015