Modeling musculoskeletal kinematic and dynamic redundancy using null space projection

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[![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.2000421.svg)](https://doi.org/10.5281/zenodo.2000421)

`git lfs install`

`git lfs clone https://github.com/mitkof6/musculoskeletal-redundancy.git`

Description

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This project contains the source code related to the following publication:

D. Stanev and Konstantinos Moustakas, Modeling musculoskeletal kinematic and 

dynamic redundancy using null space projection, PLoS ONE, 14(1): e0209171, 

Jan. 2019, DOI: https://doi.org/10.1371/journal.pone.0209171

The coordination of the human musculoskeletal system is deeply influenced by its

redundant nature, in both kinematic and dynamic terms. Noticing a lack of a

relevant, thorough treatment in the literature, we formally address the issue in

order to understand and quantify factors affecting the motor coordination. We

employed well-established techniques from linear algebra and projection

operators to extend the underlying kinematic and dynamic relations by modeling

the redundancy effects in null space. We found that there are three operational

spaces, namely task, joint and muscle space, which are directly associated with

the physiological factors of the system. A method for consistently quantifying

the redundancy on multiple levels in the entire space of feasible solutions is

also presented. We evaluate the proposed muscle space projection on segmental

level reflexes and the computation of the feasible muscle space forces for

arbitrary movement. The former proves to be a convenient representation for

interfacing with segmental level models or implementing controllers for tendon

driven robots, while the latter enables the identification of force variability

and correlations between muscle groups, attributed to the system's

redundancy. Furthermore, the usefulness of the proposed framework is

demonstrated in the context of estimating the bounds of the joint reaction

loads, where we show that misinterpretation of the results is possible if the

null space forces are ignored. This work presents a theoretical analysis of the

redundancy problem, facilitating application in a broad range of fields related

to motor coordination, as it provides the groundwork for null space

characterization. The proposed framework rigorously accounts for the effects of

kinematic and dynamic redundancy, incorporating it directly into the underlying

equations using the notion of null space projection, leading to a complete

description of the system.

Repository Overview

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- arm_model: simulation of simple arm model

- feasible_joint_reaction_loads: calculation of the feasible reaction loads, by

  accounting for musculoskeletal redundancy effects

- docker: a self contained docker setup file, which installs all dependencies

  related to the developed algorithms

Demos

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The user can navigate into the corresponding folders and inspect the source

code. The following case studies are provided in the form of interactive Jupyter

notebooks:

- [Arm Model](arm_model/model.ipynb) presents a case study using muscle space

  projection to study the response of segmental level reflexes

- [Muscle Space Projection](arm_model/muscle_space_projection.ipynb)

  demonstrates muscle space projection in the context of segmental level

  (reflex) modeling

- [Feasible Muscle Forces](arm_model/feasible_muscle_forces.ipynb) uses

  task space projection to simulate a simple hand movement, where the feasible

  muscle forces that satisfy this task are calculated and analyzed

- [Feasible Joint Reaction Loads](feasible_joint_reaction_loads/python/feasible_joint_reaction_loads.ipynb)

  demonstrates the utilization of the feasible muscle forces to calculate the

  bounds of the joint reaction loads during walking

The .html files corresponding to the .ipynb notebooks included in the folders

contain the pre-executed results of the demos.

<a rel="license" href="http://creativecommons.org/licenses/by/4.0/"><img

alt="Creative Commons License" style="border-width:0"

src="https://i.creativecommons.org/l/by/4.0/88x31.png" /></a><br />This work is

licensed under a <a rel="license"

href="http://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution

4.0 International License</a>.