Onboard targeting law for finite-time orbital maneuver in cislunar orbit

This study addresses a new onboard targeting law used for finite-time orbital maneuvers in cislunar orbits, and is motivated by international discussion regarding the design architecture of future space stations in cislunar orbits. The current concept study focuses on a subset of the halo families specified as Near Rectilinear Halo Orbits (NRHOs) of the Earth-Moon system. According to the mission sequence identified in literature, the transfer sequence from Low Earth Orbit (LEO) to NRHO requires orbital maneuvers with large delta-V of about 250 m/s, which is significantly larger than the delta-V required in rendezvous missions to the International Space Station in LEO. A spacecraft used for a cislunar transfer mission must be designed with the capability to execute large orbital maneuvers using the limited thrust force of its own engines. Moreover, the unique conditions of orbital dynamics dominated by the features of the multibody problem must be considered. Previous work proposed a new guidance logic that achieves precise execution accuracy used for finite-time orbital maneuvers of the cislunar transfer sequence. The logic basically utilizes a trajectory optimization technique, and derives the time series of thrust angles during a finite-time maneuver. In practical application, navigation and control errors prior to the orbital maneuver induce deviations of orbital states from that of the nominal maneuver arc. Real-time updates of the guidance profile must be made to compensate for these deviations. This paper presents an onboard targeting law to achieve this compensation with sufficient accuracy. The targeting law generates an updated guidance arc in the form of a polynomial. Coefficients of the polynomial are calculated by solving simultaneous equations that are derived from equality constraints of the two-point boundary value problem with updated orbital states. The control profile is calculated by the first and second derivatives of the polynomial combined with an equation of motion linearized around states of the nominal guidance arc. The proposed onboard targeting law is evaluated by means of simulations. It is therefore concluded that the proposed targeting law can derive an updated guidance arc and a control profile with sufficient accuracy. The guidance law in the form of a polynomial is simple and appropriate in terms of onboard software implementation.