Robust Spacecraft Low-Thrust Trajectory Design: A Chance-Constrained Covariance-Steering Approach

TL;DR

This work develops a sequential convex programming framework for robust low-thrust interplanetary trajectory design under uncertainty by solving a chance-constrained covariance-steering problem. It explicitly models spacecraft mass dynamics and couples mass variation to stochastic disturbance intensity, enabling a mass-aware control synthesis with a piecewise affine policy $\boldsymbol{u}_t = \boldsymbol{v}_t + \boldsymbol{K}_t(\boldsymbol{x}_t - \bar{\boldsymbol{x}}_t)$ and a $p$-quantile objective. Covariance propagation is convexified using auxiliary variables $U_k$ and $Y_k$ with Schur complement LMIs, while chance constraints are convexified via an upper-bounded standard deviation $\tau_k$ and SOC constraints; the objective is augmented with a regularization term to preserve convexity. Numerical studies on planar and 3D Earth-to-Mars transfers show that incorporating mass dynamics significantly affects state dispersion and control effort, with Monte Carlo simulations validating the covariance propagation. The results demonstrate that the proposed framework can generate robust, high-fidelity interplanetary guidance solutions under realistic mass-uncertainty and disturbance conditions.

Abstract

This paper proposes a systematic method for generating practical and robust low-thrust spacecraft trajectories. One contribution is to consider the change in mass of the spacecraft at two levels: a) the propulsive acceleration and b) the intensity of the stochastic disturbances. A covariance variable formulation is considered, which is computationally more efficient than the factorized covariance implementation. The proposed approach is applied to two- (i.e., planar) and three-dimensional heliocentric phases of spacecraft flight from Earth to Mars under the restricted two-body dynamics. The results highlight the importance of keeping track of mass change to generate more realistic, robust solutions for interplanetary space missions to avoid underestimation of mission risks.

Figures (14)

• Figure 1: Position covariances.
• Figure 2: Position covariances (scaled 10x).
• Figure 3: Control mean and covariance evolution.
• Figure 4: Mass and its standard deviation vs. time.
• Figure 5: Velocity standard deviation along first principle component with (black) and without (red) mass uncertainty.