/algodiff

Code to generate trajectory optimization of human movement using OpenSim

Primary LanguageC

Algorithmic differentiation (AD - algodiff) in OpenSim

This repository contains code and data to generate OpenSim-based trajectory optimization of human movement while exploiting algorithmic differentiation (AD) as described in: Falisse A, Serrancoli G, Dembia C, Gillis J, De Groote F, (2019). Algorithmic differentiation improves the computational efficiency of OpenSim-based trajectory optimization of human movement. PLoS ONE 14(10): e0217730, https://doi.org/10.1371/journal.pone.0217730.

We enabled the use of AD in OpenSim through a custom source code transformation tool named Recorder and through the operator overloading tool ADOL-C. For this purpose, we modified the source code of OpenSim and Simbody: https://github.com/antoinefalisse/opensim-core/tree/AD-recorder.

We then developed an interface between OpenSim and CasADi to solve trajectory optimization problems. CasADi is a tool for nonlinear optimization and algorithmic differentiation.

We compared the computational efficiency of using standard finite differences (FD) versus AD, implemented through Recorder (AD-Recorder) and ADOL-C (AD-ADOLC), when solving a series of trajectory optimization problems. These problems consisted of simulations of perturbed balance, two-dimensional predictive simulations of walking, and three-dimensional tracking simulations of walking. We found that using AD through Recorder was between 1.8 ± 0.1 and 17.8 ± 4.9 times faster than using FD, and between 3.6 ± 0.3 and 12.3 ± 1.3 times faster than using AD through ADOL-C. The larger the problem the larger the computational benefit of using AD instead of FD.

In this repository, we provide code necessary to re-produce the simulations with AD-Recorder and FD. We also provide code for analyzing the results and reproducing the figures presented in the associated paper.

Brief overview of the repository

  • Predictive simulations of walking with a 2D musculoskeletal model

    • The main script is PredSim_2D.m in the folder predictiveSimulations_2D/OCP. Running this script will solve the trajectory optimization problem / optimal control problem (OCP) underlying a predictive simulation of walking. This script calls several functions saved in the other folders of predictiveSimulations_2D. The best way to get started is therefore to run this script and look at the different steps. When the optimization has converged, the results will be saved in the folder predictiveSimulations_2D/Results/PredSim_2D. Among the saved results is a motion file that can be loaded in the OpenSim GUI using the musculoskeletal model saved as predictiveSimulations_2D/OpenSimModel/subject1/subject1_scaled.osim. You can observe the details of your optimal solution with the script observeResults_2D.m in predictiveSimulations_2D/ResultsAnalysis.

  • Tracking simulations of walking with a 3D musculoskeletal model

    • The main script is TrackSim_3D.m in the folder trackingSimulations_3D/OCP. Running this script will solve the trajectory optimization problem / optimal control problem (OCP) underlying a tracking simulation of walking. This script calls several functions saved in the other folders of trackingSimulations_3D. The best way to get started is therefore to run this script and look at the different steps. When the optimization has converged, the results will be saved in the folder trackingSimulations_3D/Results/PredSim_2D. Among the saved results is a mot file that can be loaded in the OpenSim GUI using the musculoskeletal model saved as trackingSimulations_3D/OpenSimModel/subject1/subject1.osim. You can observe the details of your optimal solution with the script observeResults_3D.m in trackingSimulations_3D/ResultsAnalysis.

  • Simulations of perturbed balance with inverted pendulums of varying complexities (between 2 and 10 degrees of freedom)

    • The main scripts are OCP_pendulum_<#>dofs in the folders pendulumSimulations/Pendulum_<#>dofs, where # is the number of degrees of freedom. Note that we ran those scripts from batch_OCP_pendulum_<#>dofs to investigate different cases (e.g., derivative scenarios).

  • Scripts for analyzing results

    • The scripts in the folder analysisResultsForPaper enable analyzing the results and reproducing the figures presented in the paper.

Brief overview of the framework

A detailed description of our framework to solve trajectory optimization problems with OpenSim is provided in Figure 2 of the paper. In brief, our framework enables making an OpenSim function F and its derivatives available within the CasADi environment for use by the NLP solver during an optimization. In more detail:

  • the function F is described in a C++ code (e.g., predictiveSimulations_2D/ExternalFunctions/PredSim_2D.cpp).
  • the Recorder tool is used to provide the expression graph of F as MATLAB source code.
  • the CasADi’s C-code generator tool is used to generate, from the MATLAB code, C-code containing F and expressions for its derivatives.
  • the C-code is compiled as a Dynamic-link Library (DLL) and imported as an external function within the CasADi environment.

In our application, F represents the multi-body dynamics and is called when formulating the optimal control problem. The latter is then composed into a differentiable optimal control transcription using CasADi. During the optimization, CasADi provides the NLP solver with evaluations of the NLP objective function, constraints, objective function gradient, constraint Jacobian, and Hessian of the Lagrangian. CasADi efficiently queries F and its derivatives to construct the full derivative matrices.

You can find more information about how to build this pipeline in this repository: https://github.com/antoinefalisse/opensim-core/tree/AD-recorder.

Thanks for citing our work in any derived publication. Feel free to reach us for any questions: antoine.falisse@kuleuven.be | antoinefalisse@gmail.com | friedl.degroote@kuleuven.be | gil.serrancoli@upc.edu.

This code has been developed on Windows using MATLAB2017b. There is no guarantee that it runs smooth on other platforms. Please let us know if you run into troubles.