Predictive Simulation of Musculoskeletal Models Using Direct Collocation

Brockie, Samuel 

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Applications of biomechanical predictive simulation are wide ranging, with the technique used to provide insights into movement disorders, sports performance, and injury prevention. However, current software provision has limitations. Users are restricted from leveraging state-of-the-art methods and algorithms. Alternatively, they are required to develop bespoke implementations of direct collocation, or laboriously manually link multiple software packages. In order to address these limitations, this research aims to develop and critically evaluate a software suite that enables both expert and non-expert users to construct and solve predictive simulation optimal control problems (OCPs) involving musculoskeletal models.

Solving OCPs is a critical part of predictive simulation. Algorithms for transcription, scaling, mesh refinement, and derivative generation are presented, along with their implementations in an open-source software package for numerically solving OCPs, Pycollo. Benchmarking of Pycollo against an industry-standard commercial software package, GPOPS-II, by solving five known OCPs from the literature demonstrates comparable convergence and computational performance, with Pycollo requiring fewer mesh iterations and sparser discretisation meshes to meet defined error tolerances in four out of five cases.

Biomechanical predictive simulations also require the ability to derive multibody dynamics and implement musculotendon models. Furthermore, these need to be formulated in a way suitable for OCPs. Two software packages, Pynamics and Pyomechanics, which formulate multibody dynamics and musculoskeletal OCPs respectively, are presented. Comparison of explicit and implicit formulations of multibody dynamics shows that solution accuracies, solve times, convergence rates, and discretisation errors are improved when implicit dynamics are used. Similarly, comparison of multiple musculotendon formulations and their numerical sensitivity finds that implicit musculotendon equations offer the best numerical properties for OCPs and should be preferred. Testing of solution sensitivity to the sigmoidal smoothing coefficient in continuous activation dynamics suggests a value of 100 should be preferred over the previously published recommendation of 10.

Cole, David
biomechanics, optimal control, multibody dynamics, trajectory optimisation, predictive simulation, musculoskeletal modelling, direct collocation, biomechanical modelling, nonlinear programming
Doctor of Philosophy (PhD)
Awarding Institution
University of Cambridge
Engineering and Physical Sciences Research Council (1931100)
EPSRC (1643407)