git lfs install
git lfs clone https://github.com/mitkof6/musculoskeletal-redundancy.git
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.
- 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
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:
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Arm Model presents a case study using muscle space projection to study the response of segmental level reflexes
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Muscle Space Projection demonstrates muscle space projection in the context of segmental level (reflex) modeling
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Feasible Muscle Forces uses task space projection to simulate a simple hand movement, where the feasible muscle forces that satisfy this task are calculated and analyzed
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Feasible Joint Reaction Loads 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.
This work is
licensed under a Creative Commons Attribution
4.0 International License.
