Fuel-optimal space-flight transfer solutions through a redundant adjoint variable transformation

Abstract

A transformation between minimum dimension adjoint variables and redundant adjoint variables is derived in this dissertation. The transformation is then applied between the adjoint variables associated with Cartesian position and velocity vectors and a set of redundant adjoint variables associated with certain regularized variables (Schumacher variables). This transformation proves to be very beneficial when it is applied to minimum-fuel space rendezvous and intercept problems. It facilitates using attributes from the two systems simultaneously; a new necessary condition in Schumacher adjoints is derived in this dissertation, and this together with classical necessary conditions for fuel-optimal transfer (existing in the position and velocity space) leads to a numerical algorithm which seems to be quite robust in finding candidate optimal control solutions for space transfer problems.