Hovering in asteroid dynamical environments using higher-order sliding control

Close-proximity operations around small bodies in general and asteroids in particular are extremely challenging. In this paper, we apply the higher-order sliding modes theory to devise a class of discontinuous two-sliding homogeneous controllers for hovering in highly uncertain dynamical environments typically found around asteroids. The class of controllers that can be constructed using the higher-order sliding modes theory is shown to be globally finite-time stable against perturbations with a known upper bound. The behavior of the proposed two-sliding controller as a function of the design parameters has been analyzed via a set of closed-loop simulations around 433 Eros and 1999 RQ36 Bennu. For all cases, the controller is demonstrated to be highly effective in achieving and maintaining the hovering state in spite of perturbing accelerations as well as navigation errors. Moreover, it has been demonstrated that the two-sliding controller can be implemented in a bang-off-bang fashion for propellant saving while maintaining the desired performances (i.e., robustness and good accuracy).