Low-Thrust Fuel-Optimal Guidance with Automatic Control Sequence Detection and Separation

This paper develops a novel fuel-optimal guidance scheme using differential algebraic techniques that is capable of handling changes in the optimal thrust sequence, in addition to a large domain of uncertainty. Taylor polynomials of the solution flow exhibit large approximation errors when the control sequence changes within the domain of operation. This property is leveraged through automatic domain splitting, a technique that tracks the approximation error and splits the domain into smaller subdomains when high errors are observed. After multiple splits, the domain is autonomously separated along the boundaries between different optimal control sequences. Crucially, each resulting subdomain encompasses only a single control sequence, ensuring that any guidance updates obtained from the final polynomial map provide the corresponding optimal control sequence. To ensure high accuracy of the guidance updates, this work also develops an efficient and iterative-less differential-algebra-based refinement algorithm, which is applied to the outputs of the polynomial map. The overall guidance scheme provides highly accurate guidance updates in response to large trajectory deviations, including new optimal control sequences, as demonstrated in an Earth–Psyche transfer.