Trajectory Optimization Method for Small Body Landing Integrated with Observability

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