Optimal control approach to solving the muscle redundancy problem. Code expanded on from the original SimTK project by Freidl De Groote, B.J. Fregly, Antoine Falisse, and Maarten Afschrift (located here: https://simtk.org/projects/optcntrlmuscle.) Additional software required as described in the included Manual. For a more detailed description of the general problem being solved, please refer to the associated paper:
Authors: Nick Bianco, Rachel Troutman, Chris Dembia
All examples within the Examples/SoftExosuitDesign subdirectory were created for the Stanford course ME485: Modeling and Simulation of Human Movement. A webpage containing results and analysis of this project can be found on the OpenSim documentation site: http://simtk-confluence.stanford.edu:8080/display/OpenSim/Simulation-based+soft+exosuit+design.
For this project, the following MATLAB m-files were either created or modified:
- Problem files These files call SolveMuscleRedundancy_lMtildeState to execute a particular predefined optimal control problem. If the examples included with the SimTK project run on your machine (i.e. OpenSim downloaded, GPOPS-II/Adigator installed, etc.), these examples should run out of the box.
Quinlivan2017.m -- This problem attempts to replicate the study in [2] using the Gait2354 default model and data set that is packaged with the OpenSim distribution.
HipAnkle.m -- This problem modifies the Quinlivan2017.m problem by optimizing for both the tradeoff between assistive moments at the hip and ankle and for the device control signal.
HipKneeAnkle.m -- This problem is similar to the HipAnkle.m problem, where now the optimization is free to choose assistive knee flexion or extension moments.
HipExtHipAbd.m -- This problem is similar to the HipAnkle.m problem, except now the tradeoff is optimized between hip extension and hip abduction assistance.
HipAnkleMass.m -- This problem is similar to the HipAnkle.m problem, except now assisting a particular joint incurs a mass penalty associated with the relationship presented in [3]. This problem is currently a work-in-progress.
Each one of these files is contained within a subdirectory of the same name (i.e. Examples/SoftExosuitDesign/). Folders within each of these directories contain results obtained by using different integrated cost functions:
Exc_Act -- Excitations and activations squared. (Results from our project utilized only this cost function, but we have included our other results as well.)
MinAlex -- Metabolic rate (Minetti and Alexander 1997 [4]).
Exc_Act_MinAlex -- Excitations and activations squared + metabolic rate
Note: all of the problems under the HipAnkleMass subdirectory include the device mass penalty in the cost, even though the result folder names do not reflect this.
Various plotting scripts exist in many of the subdirectories. These were used to generate the plots of our project results.
- SolveMuscleRedundancy_lMtildeState.m
This file serves as the "main" function for solving the muscle redundancy problem. Different problem files call this function to execute a particular predefined optimal control problem. The optimal control problems called by this file introduce normalized muscle fiber length as a state variable for solving the implicit muscle dynamics formulation described in [1]. (Another similar file called SolveMuscleRedundancy_FtildeState solves the same problem, but introduces normalized tendon force as a state variable instead, see [1]. No changes were made to this file, as we only considered problems using normalized fiber length as a state.)
The section labeled "PART II: OPTIMAL CONTROL PROBLEM FORMULATION", is where most code modifications are located. Based on the choice of problem in section 1), the structure, bounds, and initial guesses of the controls and parameters are modified. Data structures containing force and moment data from the Quinlivan et al. 2017 study [2] are created as necessary for each problem. All of this information is passed on to the continous and endpoint functions, see section 3).
- Continous and Endpoint Functions
In the subdirectory Optimization\lMtildeState, there are multiple folders containing m-files that define the continous and endpoint functions needed by GPOPS-II to solve the optimal control problem. The continous function defines any path constraints, dynamics constraints, or integrated objectives for a given optimal control problem. For our project, this is where we modified the inverse dynamics moment tracking constraint (see the PATH CONSTRAINTS section in each continous function file). The endpoint function defines any endpoints contraints or bounds, including initial or final state values or periodicity. For more details on continous and endpoint functions in general, please refer to the GPOPS-II instruction manual.
References:
[1] F. De Groote, A. L. Kinney, A. V. Rao, and B.J. Fregly, "Evaluation of Direct Collocation Optimal Control Problem Formulations for Solving the Muscle Redundancy Problem," Annals of Biomedical Engineering, 2016, DOI: 10.1007/s10439-016-1591-9
[2] B.T. Quinlivan et al., "Assistance magnitude versus metabolic cost reductions for a tethered multiarticular soft exosuit," Science Robotics, 2017, Vol. 2, eaah4416
[3] R.C. Browning et al., "The Effects of Adding Mass to the Legs on the Energetics and Biomechanics of Walking," Medicine & Science in Sports & Exercise, 2007 DOI: 10.1249/mss.0b013e31802b3562
[4] A.E. Minetti and R. McN. Alexander, "A Theory of Metabolic Costs for Bipedal Gaits," Journal of Theoretical Biology, 1997, Vol. 186, pgs. 467-476