Siro Moreno Martin, PhD candidate, visiting PhD presso DICI
Institut del Robotica i Informatica Industrial, Universitat Politècnica de Catalunya (BarcelonaTech)
Abstract: Collocation methods are a way to discretize a continuous problem in order to solve it numerically. They are based on building interpolating polynomials to connect certain points, on which equations are imposed. This approach can be applied to solve very different problems, such as simulations or trajectory optimization. On the other hand, lots of systems can have their dynamics described by second order differential equations. The usual practice is to reduce the order of these equations by working on the so called space state, but doing so can have some unintended effects on the solutions found. However, that is not the only way: our work is to demonstrate that collocation methods can be adapted to take advantage of that second order underlying structure.