Robust trajectory design for rendezvous and proximity operations with uncertainties

A robust trajectory optimization approach for rendezvous and proximity operations in perturbed elliptical orbits with uncertainties is proposed. For robust trajectory design, a new discrete-time linear dynamics model describing the relative equations of motion for powered flight in perturbed elliptical orbits is developed. The linear dynamics model is used to formulate a stochastic trajectory optimization problem that takes into account navigation sensor errors, maneuver execution errors, and trajectory and control dispersion. The objective of the stochastic optimization problem is to minimize the sum of the expected maneuver and the maneuver dispersion subject to a 3-σ constraint on the final state dispersion. A genetic algorithm is used to solve the stochastic trajectory optimization problem, and a series of examples demonstrate that the stochastic maneuver solution can be significantly better than the solution corresponding deterministic trajectory optimization problem. Nonlinear Monte Carlo simulations are used to validate the results.