A Sequential Convex Programming Chance-Constrained Covariance-Steering Approach to Robust Low-Thrust Trajectory Optimization

Abstract

This dissertation reviews and presents a computational framework for robust spacecraft trajectory optimization under uncertainty, advancing beyond deterministic methods to ensure mission reliability in low-thrust interplanetary flights. At the core of the framework are two iterative Covariance Steering (iCS) algorithms that convexify the stochastic optimal control problem through complementary approaches: factorized-covariance formulation that jointly optimizes feedforward and feedback policies, and a computationally efficient covariance-variable formulation that directly manipulates state statistics via linear matrix inequalities resulting in semi-definite programs. Both methods handle nonlinear dynamics through successive linearization and convex programming while explicitly enforcing probabilistic constraints.

The considered solution formulations are validated through high-fidelity numerical simulations, progressing from linear verification to complex interplanetary transfers. A double-integrator case demonstrates precise uncertainty regulation and constraint satisfaction. Subsequent planar and three-dimensional (3D) Earth-Mars rendezvous maneuvers are considered to showcase scalability to nonlinear orbital dynamics, with the covariance-variable method solving 7-state problems in under 12 iterations. Crucially, the 3D analysis provides the first quantitative demonstration that neglecting propellant mass uncertainty leads to significant performance miscalculation, underestimating trajectory dispersion by up to 35\% and required control authority by 6\%, thereby quantifying a critical source of mission risk.

This research provides practical, scalable tools for robust trajectory optimization of astrodynamics problems, successfully transitioning covariance steering from theory to implementable strategy. By enabling autonomous systems to guarantee performance under uncertainty while satisfying safety constraints, the work advances robust trajectory optimization and guidance capabilities for next-generation deep-space exploration missions.