Robust mission design using invariant manifolds

Uncertainties in the dynamical system affect all real-life applications in astrodynamics. This is particularly true for satellites orbiting about small bodies owing to their irregular shapes and to the difficulties in characterizing their physical properties at the early stages of a dedicated spacecraft mission. Hence, accommodating uncertainty in the orbital design process may be extremely beneficial for the success of the mission. Here, in a Lyapunov stability perspective, the properties of the invariant manifolds are exploited to generate regions of the phase space where the motion is guaranteed to evolve despite the uncertainties in the system parameters and navigation errors. Specifically, the scenario approach is applied to tackle a semi-infinite optimization problem that locates these robust regions. The methodology is illustrated with the robust design of a inner retrograde orbit about the primary of (65803) Didymos as well as with a ballistic landing on the smaller secondary body.