Trajectory optimization of mechanical hybrid systems using SUMT

The aim of this report is to propose a unified framework for the determination of non-smooth trajectories for structure-variant mechanical systems along with a computational scheme. The benefits to represent the dynamics as a measure-differential inclusion will be presented. The optimal control problem will be transcribed into a Nonlinear Programming Problem (NLP) and transformed from the infinite dimensional representation into a finite dimensional representation. The relation to bilevel programming will be established. A numerical scheme will be proposed for the determination of the state and costate trajectories, which can bear discontinuities and set-valuedness.