Tisserand-Leveraging Lambert Problem: Formulation, Solution, and Applications

Abstract

Tisserand-leveraging transfers (TILTs) were proposed as techniques to achieve an endgame tour with small orbit insertion maneuvers and short flight times in low-energy regions of the planar, circular, restricted three-body problem. This paper presents a new formulation of TILTs with a framework similar to the classical Lambert problem. The developed algorithm searches for trajectories of TILTs with constraints on boundary values and time of flight by solving a one-dimensional root-finding problem. Compared to the traditional algorithm for TILTs, the developed algorithm enhances its generality by removing the restriction on the initial and final phases of the transfer. Additionally, the algorithm can achieve trajectory patching that includes TILTs without reoptimization and tour redesign based on the actual position of the spacecraft due to the Lambert-like input–output design. The algorithm uses existing neural network tools for fast and broad search in the solution space. Simulation results indicate that the algorithm can explicitly find TILT solutions and families satisfying boundary value constraints. Furthermore, the algorithm is applied to design a new endgame trajectory from Ganymede to Europa, demonstrating the potential of integrating the new algorithms with other trajectory design tools.