A survey of numerical algorithms for trajectory optimization of flight vehicles

As one of the important components of computational flight mechanics and control,numerical algorithms of trajectory optimization for flight vehicles are currently studied by many researchers in aerospace engineering to completely solve these difficult problems,but few papers on the survey of this research field have been published recently.Based on the investigation of more than one hundred literatures,considering the application perspectives of computational flight mechanics and recent developments of trajectory optimization,the numerical algorithms of trajectory optimizations for aerospace vehicles are summarized and systematically analyzed.This paper summarized the basic principle,characteristics and application for all kinds of current trajectory optimization algorithms;and introduced some new methods and theories appearing in recent years.Finally,collaborative trajectory optimization for many flight vehicles,and hypersonic vehicle trajectory optimization were mainly reviewed in this paper.In the conclusion of this paper,the future research properties are presented regarding to numerical algorithms of trajectory optimization and control for flight vehicles as follows:collaboration and antagonization for many flight vehicles and multiple targets,global,real-time online,high accuracy of 7-D trajectory,considering all kinds of unknown random disturbances in trajectory optimization,and so on.

New reference trajectory optimization algorithm for a flight management system inspired in beam search

With the objective of reducing the flight cost and the amount of polluting emissions released in the atmosphere, a new optimization algorithm considering the climb, cruise and descent phases is presented for the reference vertical flight trajectory. The selection of the reference vertical navigation speeds and altitudes was solved as a discrete combinatory problem by means of a graphtree passing through nodes using the beam search optimization technique. To achieve a compromise between the execution time and the algorithm＇s ability to find the global optimal solution, a heuristic methodology introducing a parameter called ‘‘optimism coefficient was used in order to estimate the trajectory＇s flight cost at every node. The optimal trajectory cost obtained with the developed algorithm was compared with the cost of the optimal trajectory provided by a commercial flight management system（FMS）. The global optimal solution was validated against an exhaustive search algorithm（ESA）, other than the proposed algorithm. The developed algorithm takes into account weather effects, step climbs during cruise and air traffic management constraints such as constant altitude segments, constant cruise Mach, and a pre-defined reference lateral navigation route. The aircraft fuel burn was computed using a numerical performance model which was created and validated using flight test experimental data.