Analytical Uncertainty Propagation and Robust Trajectory Optimization for Continuous-Thrust Relative Motion

Analytical continuous-thrust uncertainty propagation is derived under the control error and the initial navigation error for the linear relative motion near elliptic orbits. Two continuous-thrust control error models are considered: control-linear error model and thrust-magnitude-direction error model. The analytical uncertainty propagation expression is obtained by using the thrust series expansion with respect to eccentric anomaly. Based on the derived analytical uncertainty propagation, the robust energy-optimum and fuel-optimum orbital rendezvous problems are formulated as nonlinear programming ones. In particular, the robust energy-optimum rendezvous problem under the control-linear error model is converted into solving a one-dimensional equation. Several numerical examples indicate that the derived analytical uncertainty propagation is accurate and that the developed robust trajectory optimization approach is computationally efficient.