Efficient trajectory optimization for curved running using a 3D musculoskeletal model with implicit dynamics

Marlies Nitschke,Anne D Koelewijn,Dieter Heinrich,Eva Dorschky,Heiko Schlarb,Bjoern M Eskofier,Antonie J Van Den Bogert

doi:10.1038/s41598-020-73856-w

Marlies Nitschke, Anne D Koelewijn + Show 5 more

Open Access

https://doi.org/10.1038/s41598-020-73856-w

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Abstract

Trajectory optimization with musculoskeletal models can be used to reconstruct measured movements and to predict changes in movements in response to environmental changes. It enables an exhaustive analysis of joint angles, joint moments, ground reaction forces, and muscle forces, among others. However, its application is still limited to simplified problems in two dimensional space or straight motions. The simulation of movements with directional changes, e.g. curved running, requires detailed three dimensional models which lead to a high-dimensional solution space. We extended a full-body three dimensional musculoskeletal model to be specialized for running with directional changes. Model dynamics were implemented implicitly and trajectory optimization problems were solved with direct collocation to enable efficient computation. Standing, straight running, and curved running were simulated starting from a random initial guess to confirm the capabilities of our model and approach: efficacy, tracking and predictive power. Altogether the simulations required 1 h 17 min and corresponded well to the reference data. The prediction of curved running using straight running as tracking data revealed the necessity of avoiding interpenetration of body segments. In summary, the proposed formulation is able to efficiently predict a new motion task while preserving dynamic consistency. Hence, labor-intensive and thus costly experimental studies could be replaced by simulations for movement analysis and virtual product design.

Highlights

Trajectory optimization with musculoskeletal models can be used to reconstruct measured movements and to predict changes in movements in response to environmental changes
The tracking of straight running using standing as initial guess required more iterations than the prediction of curved running using straight running as initial guess since standing is quite a different task than running
Joint angles and ground reaction force (GRF) of straight running were close to the reference data of straight running, since the difference was generally less than one standard deviation (SD) (Fig. 5)

Summary

Introduction

Trajectory optimization with musculoskeletal models can be used to reconstruct measured movements and to predict changes in movements in response to environmental changes. Since either the motion or the forces are not simulated but prescribed, these methods cannot be applied to predict novel movements These limitations can be overcome by solving an open-loop optimal control problem, known as trajectory optimization. Human motion can be simulated using a neuromuscular model with a controller based on reflexes[15,16] or central pattern g enerators[17] Because of their relevance to daily activities and sports, it is important to simulate movements with changes in direction additional to straight walking and running. We need the capability to find solutions from an initial guess that is far from the solution, the solution should be found in a reasonable amount of time, and the solutions should exactly satisfy task requirements, such as a specified running speed and change of direction The latter is of critical importance for sports applications

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