Optimal Multiple-Impulse Direct Ascent Fixed-Time Rendezvous

Minimum-fuel, impulsive, direct ascent rendezvous trajectories are obtained for the fixed transfer time case. The terminal orbit is circular about a spherical nonrotating planet. The inclination and radius of the terminal orbit, the target position at launch, and the transfer time are independent parameters in the problem. Two- and three-impulse optimal solutions are obtained. The primer vector evaluated along a nonoptimal trajectory provides a gradient of the cost with respect to impulse times and locations. The Davidon-Fletcher-Powell algorithm is used to perform the minimization. For certain rendezvous geometries and transfer times the optimal three-impulse timefixed fuel cost is lower than the optimal two-impulse time-open cost.