Time-Optimal and Fuel-Optimal Trajectories for Asteroid Landing via Indirect Optimization

This paper presents an efficient indirect optimization method to solve time- and fuel-optimal asteroid landing trajectory design problems. The gravitational field of the target asteroid is approximated with two methods: 1) a simple two-body (point-mass) model, and 2) a high-fidelity polyhedral model. A homotopy approach, at the level of the gravity-model, is considered to solve the resulting boundary-value problems. Moreover, in fuel-optimal trajectories, the difficulties associated with control discontinuities (i.e., the so-called bang-off-bang profile of thrust) are overcome by employing a recently introduced hyperbolic tangent smoothing method. We generate time- and fuel-optimal trajectories for spacecraft landing on asteroid (101955) Bennu with low-thrust propulsion. The trajectories are validated through comparison with the trajectories obtained by other methods. The results indicate that the two-body gravity model can be used for generating high-quality solutions to "warm-start" numerical methods when a high-fidelity gravity model is used.