Trajectory design for comet 67P/Churyumov–Gerasimenko mission: Multiple gravity assist analysis using Tisserand Graph

Optimizing interplanetary trajectories is critical for advancing deep space exploration, as it minimizes energy requirements and facilitates efficient orbital insertions. This study presents a mission trajectory model to comet 67P/Churyumov–Gerasimenko, employing a two-step approach that combines the Tisserand Graph (TG) method with a Genetic Algorithm (GA). In the first step, the complex mixed-integer nonlinear programming (MINLP) problem is simplified into a combinatorial search using a TG-based Depth-Limited Tree Search (DLTS) algorithm, significantly narrowing the search space for initial guesses. Subsequently, the solution is refined through accelerated optimization with a GA. To address the fixed terminal phase constraint at comet 67P, a reverse-search strategy for launch windows reformulates the problem into a non-linear programming framework with one fixed and one free endpoint. As a result, 11 feasible trajectory scenarios to comet 67P within the next 15 years were found, validated across four launch vehicle options. To further minimize fuel consumption, the study adopts fuel consumption as the performance index and applies a continuation method to verify the feasibility of these transfers under various Hall thruster models for low-thrust propulsion. The proposed approach thus provides a validated, fuel-efficient set of trajectory options, significantly enhancing planning flexibility for comet 67P exploration in upcoming decades.