Aircraft trajectory optimization using nonlinear programming

Abstract

We describe two discretization methods, direct collocation and a scheme based on differential inclusion, that enable the solution of optimal control problems by nonlinear programming. We apply the methods in calculating optimal trajectories for a modern fighter aircraft. Unlike collocation, the differential inclusion scheme converges robustly even in the presence of singular controls.

VIATO-visual interactive aircraft trajectory optimization

“…The elimination of the control variables might be beneficial in problems involving singular control arcs [33]. The direct collocation and differential inclusion schemes are compared in [28].…”

“…The optimization server is an independent program that is implemented with Fortran 77. The server discretizes the problems using direct collocation [19] or a scheme based on differential inclusions [28], [33]. The finite dimensional approximation of the original optimal control problem is solved by utilizing a nonlinear programming package NPSOL [16], an implementation of sequential quadratic programming (SQP), (e.g., [3]).…”

“…In VIATO's optimization server, the original optimal control problem is converted into a finite dimensional optimization problem that is solved using nonlinear programming [19], [28], [33]. For a recent review of different discretization schemes, see [21].…”

The unmanned aerial vehicle routing and trajectory optimisation problem, a taxonomic review

“…For instance, Schultz & Zagalsky (1972) present solutions for several fixed endpoint aircraft TOPs using calculus of variations. In Raivio et al (1996), a nonlinear programming-based method is proposed to compute optimal trajectories for a descending aircraft. Fisch (2011) presents a high fidelity optimisation framework for the computation of air race trajectories under safety requirements.…”

“…The books by Tsourdos et al (2010) and Beard & McLain (2012) provide good overviews of PP algorithms for UAVs. On the other hand, high fidelity TO models (i.e., using more accurate physical models) have been developed for aircraft and spacecraft (Raivio et al, 1996;Conway, 2010;Fisch, 2011;García-Heras et al, 2014;Colasurdo et al, 2014). These models are currently solved by OC techniques.…”