ASTOS Orbit Generator - rapid creation of quasi-optimal orbital transfers in the 2BP, CR3BP and BCR4BP
Authors:   Astos Solutions GmbH, Stuttgart, Germany, Walther Maximilian , Wiegand Andreas 
Published: January 2024

The design of optimal orbital transfer trajectories is a crucial but not always straightforward task in spaceflight mission planning. Transferring spacecraft into their target orbits as efficiently as possible enables greater payload masses or operational duration for their missions. In the design process, however, mission planners require a good overview of various trajectory possibilities before moving on to in-depth optimization and analyses.
The Orbit Generator tool as part of the ASTOS software aims to support this process by rapidly creating and simulating a variety of quasi-optimal solutions to different orbital transfers for spacecraft and therefore supports mission designers in their trade-off studies of favorable transfers. Its primary use will be for mission planners and engineers in the aerospace industry, but it can also be used for academic research and education.
The software addresses transfer trajectories at Earth, between Earth and Moon, or to/from their libration point orbits, such as near-rectilinear halo orbits (NRHOs) or distant retrograde orbits (DROs). In addition, transfers to libration point orbits in the Sun-Earth system are also supported. To manage these requirements, the tool designs the orbits in circular restricted dynamic systems, like the circular restricted three-body problem (CR3BP) or the bi-circular restricted four-body problem (BCR4BP).
The user is asked to specify the transfer approach by a sequence of maneuver types, flight arcs and single state conditions. This allows them to choose between high- and low-thrust propulsion systems, short- and long-time transfers with impact on the required delta-V, and between more complex transfers concerning navigation and guidance. The tool utilizes a combination of different methods, such as a multiple-shooting differential corrections method to solve Lambert’s problem for impulsive orbital transfers and a modified version of Petropoulos’ Q-Law to analytically determine thrust directions in every time-instance of (continuous or intermittent) low-thrust orbital transfers.
Each transfer is subdivided into a number of trajectory sections of different types. The goal is to connect the initial and final orbit, which can both either be a Keplerian orbit or e.g. a NRHO. They are connected via a Lambert arc section in the case of impulsive maneuvers or a continuous or intermittent low-thrust phase for electric propulsion. Special trajectory sections, such as fly-bys, invariant manifolds, or weak stability boundary transfers, can be incorporated by the user to exploit the features of the 3BP or 4BP dynamic systems. Each trajectory section is defined by several characteristic parameters, whose optimization is the tool’s objective considering additional constraints, such as launch date as well as fuel and transfer duration limitations. Using the ant colony optimizer MIDACO, the tool optimizes those parameters and outputs the Pareto front of the most fuel- or time-efficient trajectories that meet the defined constraints.
After selecting a trajectory from the Pareto front, it can then be imported into an ASTOS scenario for further optimization or mission analysis. Integrated in the ASTOS software, its graphical user interface allows for easy input and visualization of the orbital transfers, as well as further optimization in higher-fidelity models and mission analysis in deeper detail. An important aspect here is the transformation from the circular restricted dynamics system to perturbed n-body dynamics system using ephemeris data.
To validate and classify the Orbit Generator tool‘s performance, the optimized trajectories obtained are compared with transfer trajectories from other sources using different optimization approaches. For all kinds of different transfer types, the results are at least competitive if not favorable. Therefore, it poses a versatile and powerful tool to quickly create a variety of quasi-optimal orbital transfers in the cislunar space. It lays the groundwork for the possibility of subsequent detailed analysis in a perturbed 2BP using ASTOS including the capability to consider navigation, guidance and control aspects in the process.
This paper outlines the architecture of the Orbit Generator tool, gives an insight into the algorithms used, and presents a set of reference solutions in the CR3BP and BCR4BP including the comparison to solutions from other sources.