Controllable cone for horizontal landing on asteroids using a flexible probe

The recently proposed flexible probe for asteroids provides a novel scheme for landing on low-gravity surface. To understand the feasible initial condition of the flexible probe's horizontal landing trajectory under multiple constraints, a controllable cone is defined and investigated. The boundary of the controllable cone is calculated using a double-layer optimization method. In the inner-layer, the switching time of the thrust profile is fixed, and the boundary point is solved through a multi-constraint trajectory optimization problem that considers the influence caused by the flexible deformation. In the outer-layer, the switching time of the thrust profile is optimized to maximize the cone boundary. To improve the optimization efficiency, an adaptive interval is used to search the switching time. With the double-layer optimization method, the controllable cone boundaries can be generated for both a specific height and a three-dimensional space. The controllable cone of the flexible probe is simulated for the landing on asteroid 433 Eros, and the influence of the flexible deformation is also analyzed.