Fuel-Optimal Low-Thrust Trajectory Design under High-Fidelity Dynamics: A State Transition Matrix-Based Sensitivity Approach

Abstract

A straightforward and computationally efficient indirect method based on STM sensitivity analysis is introduced for designing fuel-optimal low-thrust transfers under high-fidelity dynamics. Conventional indirect approaches require explicit expressions for the partial derivatives of the system dynamics to formulate the costate equations, making the derivation process complex for high-fidelity trajectory design. In this work, the costate equations are reformulated as ordinary differential equations involving only the state variables and their time derivatives. High-order dynamical effects are treated as black-box components, avoiding the need to derive partial derivatives of the system dynamics. A standard gradient-based or interior-point optimizer is used to determine the optimal costates and transfer parameters. The equivalence between the proposed method and conventional approaches is demonstrated through a classic Earth-Mars transfer scenario. An Earth-Mars transfer under high-fidelity dynamics is then presented, including perturbations from solar radiation pressure, solar J2 oblateness, Jupiter third-body gravity, and relativistic effects. Finally, the method is applied to a multiple-revolution Earth-Venus transfer under high-fidelity dynamics.