An end-to-end data-driven optimization framework for constrained trajectories

Abstract

Many real-world problems require to optimize trajectories under constraints. Classical approaches are often based on optimal control methods but require an exact knowledge of the underlying dynamics and constraints, which could be challenging or even out of reach. In view of this, we leverage data-driven approaches to design a new end-to-end framework which is dynamics-free for optimized and realistic trajectories. Trajectories are here decomposed on function basis, trading the initial infinite dimension problem on a multivariate functional space for a parameter optimization problem. Then a maximum a posteriori approach which incorporates information from data is used to obtain a new penalized optimization problem. The penalized term narrows the search on a region centered on data and includes estimated features of the problem. We apply our data-driven approach to two settings in aeronautics and sailing routes optimization. The developed approach is implemented in the Python library PyRotor.

Keywords

• Constrained optimization
• functional data
• statistical modeling