Trajectory Optimization Method for Small Body Landing Integrated with Observability

Aiming at the problem of degradation of state estimation accuracy caused by insufficient perception ability of navigation system during the landing of small bodies, a trajectory optimization method integrated with observability is proposed. First, the optical navigation performance is quantified based on the Fisher information matrix. An analytical expression for the observability is derived. The observability, as a new performance index, is introduced into the trajectory optimization framework. In this way, an engineering trade-off between fuel consumption and navigation accuracy is achieved. Secondly, the homotopy coefficients are used to associate the fuel-observability optimal control problem with the energy optimal control problem. By adjusting homotopy coefficients and observability weight coefficient, the iterative solution of the optimal control problem is realized. Finally, simulation studies are conducted on 101955 Bennu. The simulation results demonstrate that the proposed method can effectively enhance the navigation performance of the landing trajectory while maintaining reasonable fuel consumption.