Abstract
Deep-space explorations have become dominant in current space programs, which presents an even higher demand on the deep-space trajectory design and orbit maintenance. To increase the availability of various interplanetary orbits and achieve higher accuracy in the orbit related research, the Circular Restricted Three-Body Problem (CRTBP) was investigated as the fundamental dynamics. However, due to its high non-linearity, most conclusions and methods related with the CRTBP are derived from linearised dynamics, which inevitably incurs limitations and inaccuracy in the correspond- ing applications.
In this work, by means of Differential Algebra (DA) techniques, high-order methods and strategies are explored and applied to the nonlinear problems related with the CRTBP. Specifically, two representative problems are targeted, including the computation of periodic/quasi-periodic orbits and the stationkeeping of these orbits. The classic Target Point Approach (TPA) is improved using the existing DA techniques and two nonlinear TPA methods are proposed for a more accurate calculation of stationkeeping manoeuvres. To incorporate the uncertainty from different sources, a stochastic optimisation scheme is devised to search for the error-robust and fuel-optimal stationkeeping parameters for a periodic orbit. After noticing the underperformance of TPA methods in the stationkeeping scenarios dominated by fast dynamics, a high-order Target Phase Approach (TPhA) is proposed using the Poincare mapping enabled by DA-based polynomial maps, with its performance being validated in multi-fidelity dynamics. The DA-enabled Poincare mapping technique is further adopted in the continuation of quasi-periodic orbits in the CRTBP and enhances the computing efficiency of the orbit family. Feasibility of the proposed TPhA method is explored for the stationkeeping of the acquired quasi-periodic orbits.