State Estimation With Nonlinear Inequality Constraints for Small Celestial Body Flexible Landing

Compared to rigid landers, a flexible lander can reduce the landing risks in small celestial body missions by taking advantage of its soft structure. In this article, we focus on the autonomous navigation problem of the flexible lander. Particularly, we consider the utilization of the additional information provided by the inherent state constraints of the landing system, i.e., the flexible deformation constraints, into the design of the navigation filter. To involve such nonlinear inequality constraints, we develop a constrained filtering algorithm with theoretically guaranteed performance. By exploiting the geometrical relationship between the state estimates and the constraint region, we establish the estimation refinement theorem. This theorem presents the sufficient condition for improving estimation accuracy through the inclusion of constraints. Guided by this theorem, we devise a constrained filter where a maximum margin separating hyperplane is optimized to refine the state estimate. Further, we demonstrate that the constrained estimation error is exponentially bounded. At last, we validate the proposed filter through a 433 Eros-based flexible landing simulation.