Desensitized Optimal Trajectory for Multi-phase Lunar Landing

Lunar landing problem has been formulated as desensitized optimal control problem and solved by Legendre Pseudospectral method. The problem has been split into three phases to account for mission constraints, namely the braking with rough navigation stage (from 18km to 7km), attitude hold stage (holding the attitude for 35sec) for a typical mission scenario. In presence of uncertainties, following the open loop reference trajectory using the closed loop linear quadratic regulator contribute greatly in trajectory dispersions. The goal is to desensitize this multi-phase optimal trajectory with reduced error in presence of initial state error, thrust error, Moon's gravity uncertainty. To achieve this, the fuel minimization cost function is augmented with closed loop covariance to generate the open loop reference trajectory. Following this reference trajectory using closed loop linear quadratic regulator, shows significant reduction in landing error. The amount of extra fuel consumed by desensitizing optimal trajectory is less significant when compared to improvement in landing accuracy to meet mission constraints assuring the desensitized optimal control a viable technique for lunar landing trajectory design. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved