# Benchmark of optimal control problems - Comparison of coordinate and dynamic formulations

## Description

These folders contain the optimal control problems to predict the swing movement from an initial to a final state. They were solved using 8 models of different complexity (from 3 to 10 degrres of freedom - DoF), with 4 types of coordinates (absolute, natural, relative from hip and relative from ankle), and with two dynamic formulations (implicit and explicit). Each folder contains the files needed to run the optimal control problems for each DoF model. In each folder, one can find four files starting with "main_...", which contains the optimal control problems for each type of coordinate. The user can run the optimal control problems running the files starting with "main_...". At the beginning of these files, the user can choose either solving the optimal control problems using an implicit dynamic formulation (Options.Implicit=1) or using an explicit dynamic formulation (Options.Implicit=0). The files starting with "Equations_" contain the equations of motion and the user does not need to modify them. The results of these optimal control problems show that the number of iterations needed to find an optimal solution is related to the conditioning of the Hessian of the NLP problem and mass matrices simultaneously.

## Files

## Steps to reproduce

Requirements: - MATLAB installed - CasADi installed. Casadi can be downloaded from https://web.casadi.org/ Instructions to use the code: - Choose the folder corresponding to the model you want to use. Run one of the four MATLAB files starting with "main_" acoording to the type of coordinate you want to use. Modify the Options.Implicit depending on you want to use an implicit (Options.Implicit=1) or an explicit (Options.Implicit=0) formulation. Run the code.