Optimal Low-Thrust and Gravity Assist Trajectory Design for Ultra-Distant Gas Giant Exploration

The exploration of gas giant planets in the Solar System has long been a key challenge for deep space missions. Due to the vast distance between gas giants and Earth, even with the assistance of Jupiter, exploring the outer gas giants still necessitates high launch velocities and precise timing windows. The combination of Optimal Low Thrust and Gravity Assist (OLTGA) is an ideal model for exploring ultra-distant gas giants. However, both the optimal low-thrust trajectory design and the gravity assist sequence are complex problems that are not easily solved. The integration of these two factors poses a challenge for traditional methods to compute appropriate OLTGA trajectories due to its long control durations, strict boundary constraints, and multi-loop transfers. This work proposes a two-layer optimization strategy to solve the OLTGA trajectory problem using sequential convex programming in a low-dimensional space, which can be an efficient framework for solving ultra-distant exploration trajectory. First, for the inner low-thrust transfer, we introduce a sequential convex programming algorithm to solve the optimal two-point boundary value problem under low-thrust conditions. By convexifying the optimal transfer dynamics and corresponding nonlinear constraints, the problem is transformed into a convex optimization problem, which can be efficient solved using self-dual minimization theory. A sequential convex programming procedure is constructed to make this trajectory converge to the feasible optimal. This method greatly reduces the computation time for a single low-thrust trajectory to just seconds. Second, for the outer gravity assist sequence, we develop a differential evolution global search strategy. This strategy utilizes a smaller search dimension to stitch together different gravity assist sequences compared with the high dimension B-plane shooting. For each gravity assist, only one additional dimension is required, which significantly reduces the computational complexity caused by the increasing number of gravity assists. For the Neptune exploration scenario, we search for a low-launch-energy, low-thrust Jupiter gravity assist window for a mission to Neptune between 2036 and 2046. Compared to simple Jupiter gravity assist or multiple assist sequences, the small-thrust Jupiter gravity assist allows for exploration of Neptune’s orbit within a longer time window and at extremely low launch energy. Even with zero launching C₃, it is possible to reach Neptune within 20 years. This method can serve as a preliminary reference for OLTGA trajectory in future deep space missions in terms of orbital design and launch windows.