Development of non-linear guidance algorithms for asteroids close-proximity operations

In this paper, we discuss non-linear methodologies that can be employed to devise real-time algorithms suitable for guidance and control of spacecrafts during asteroid close-proximity operations. Combination of optimal and sliding control theory provide the theoretical framework for the development of guidance laws that generates thrust commands as function of the estimated spacecraft state. Using a Lyapunov second theorem one can design non-linear guidance laws that are proven to be globally stable against perturbations with known upper bound. Such algorithms can be employed for autonomous targeting of points of the asteroid surface (soft landing, Touch-And-Go (TAG) maneuvers). Here, we theoretically derived and tested the Optimal Sliding Guidance (OSG) for close-proximity operations. The guidance algorithm has its root in the generalized ZEM/ZEV feedback guidance and its mathematical equations are naturally derived by properly defining a sliding surface as function of Zero-Effort-Miss and Zero-Effort-Velocity. The latter enables the augmentation of the energy-optimal guidance law by a sliding mode that ensures global stability for the proposed algorithm. A set of Monte Carlo simulations in realistic environments are executed to assess the guidance performance in typical operational scenarios found during asteroids close-proximity operations. OSG is shown to satisfy stringent requirements for asteroid pinpoint landing and sampling accuracy.