A homotopy method for space flight rendezvous problems
Abstract
The fueloptimal rendezvous problem which assumes a finite number of Keplarian coasting arcs, each one separated from a previous one by a velocity impulse, can be approached from the point of view of a nonlinear programming problem with the components of the velocity impusle and the change of true anomaly along the coasting arcs as the parameters. A homotopy approach to the solution of this problem is presented which includes a summary of the supporting theory and a novel method for dealing with inequality constraints. As a result, two homotopy maps are proposed. The first map has the property that all solutions along the homotopy path are optimal solutions to some rendezvous problem, the final point being the solution of interest, and the second map provides a means to bridge the point where the inequality constraint set changes. Some discussion of implementing the method is given including the selection of a convenient set of variables. Selected results are presented.
 Publication:

Astrodynamics 1989
 Pub Date:
 1990
 Bibcode:
 1990asdy.conf..533L
 Keywords:

 Homotopy Theory;
 Space Rendezvous;
 Trajectory Optimization;
 Fuel Consumption;
 Thrust Programming;
 Astrodynamics