Asteroid Landing Trajectory Optimization Based on Stability Robustness Criterion

Dynamical environments of asteroids are uncertain, leading to the spacecraft deviating from the designed reference trajectory in the landing process, thus reducing the landing accuracy. To improve the landing accuracy of the spacecraft under disturbances, this paper proposes a closed-loop trajectory optimization method considering the stability robustness of the system. First, the nominal landing dynamics of the spacecraft are analyzed, and the landing motion with the fuel-optimal control sequence is unstable. Replacing the traditional open-loop control, a control policy is included in the trajectory optimization to improve the landing accuracy, including feedforward control and linear feedback control. Then, a stability performance index is designed based on the short-time stability theory to assist the control policy design under disturbances. To reduce the computational burden, the feedback gain is designed by the linear quadratic regulator (LQR) method and only optimizes the control parameters. Finally, the stability robustness index is augmented onto the minimum fuel cost function through penalty factors, and SNOPT is used to solve the closed-loop trajectory optimization. Monte Carlo simulations are conducted with consideration of uncertain asteroid parameters, initial errors, and thrust errors. Results show that the trajectory obtained by this method has a better landing performance than the fuel-optimal trajectory. The proposed method increases the landing accuracy by improving the robustness of the closed-loop system to disturbance, which indicates that the proposed method can be successfully applied in asteroid landing missions in uncertain environments.