The solution of some difficult problems in low-thrust interplanetary trajectory optimization†

This paper deals with an approach to the problem of spacecraft trajectory optimization that has been successful on a wide range of practical examples. A particular group of missions involving low-thrust solar-powered vehicles has presented difficulties for the method, however, and these are described and discussed. In particular the problems seem to reveal weaknesses in some current algorithms for constrained minimization, and we therefore consider some new optimization routines. We also derive a new formulation of the problem using eccentricity and momentum vectors as state variables rather than the more usual Cartesian co-ordinates. This reformulation allows us to make some simplifying assumptions which make the problem easier to solve while still furnishing good estimates of the true optimum.