A Novel Indirect Scheme for Optimal Lunar Soft Landing at a Target Site

The problem of precise and soft lunar landing in a pre-specified target location is solved using a numerical scheme based on indirect approach. In indirect approach, the problem is transformed into a two-point boundary value problem using Pontryagin’s principle and solved. The challenge in the indirect approach lies in finding suitable initial co-states with no prior knowledge available about them. In the proposed numerical scheme, the differential transformation (DT) technique is employed to determine the unknown initial co-states using the information on the target site and the flight time. The flight time, the only unknown, is handled by differential evolution, an optimization technique. The novel computational scheme combines differential transformation and differential evolution techniques and uses differential transformation in multi-steps, to ensure the precise landing at the target site. The guidelines that help fixing the bounds for the flight time are provided. The proposed scheme is uniformly valid for various performance measures such as minimum fuel, minimum control and minimum time. Also, it is capable of introducing coasting during descent while maximizing the landing mass. © 2021, The Institution of Engineers (India).