Effect of navigation and maneuver execution errors on optimal RPO trajectory design

A robust trajectory optimization approach for rendezvous and proximity operations (RPO) in elliptical perturbed orbits with uncertainties is presented. The linearized dynamics are used to formulate a stochastic optimization problem that takes into account navigation errors, maneuver execution errors, and trajectory dispersion. A stochastic optimization problem is then defined based on a performance index equal to the sum of the expected maneuver delta-v and the 3-sigma delta-v dispersion, subject to a 3-sigma constraint on the final state dispersion. A genetic algorithm is used to solve the stochastic optimization problem, and a series of simulations are carried out to show that the stochastic optimal RPO trajectories can be significantly different than the corresponding deterministic optimal trajectories.