Generation of optimal trajectories for soft landing on the lunar surface, with optimal control approach using Particle Swarm Programming

In this article, the optimal path for the soft landing on the lunar surface is generated. Path planning is defined as an optimization problem that aims to achieve the optimal control function for the spacecraft. The thrust value of the device is fixed and the thrust angle is considered as a control variable. The objective function is to minimize the landing time and actually maximize the mass of the device at the moment of landing. The speed constraints related to the soft landing of the vehicle are also included in the objective function in the form of a cost function. Due to the unstructured and infinite search space, a new meta-heuristic algorithm called Particle Swarm Programming is used to find the optimal controller function. This algorithm is based on the Particle Swarm Optimization algorithm and has a favorable performance in the simultaneous optimization of the structure and parameters. The design of the controller was done in two types: open-loop, time-dependent, and closed-loop, time-independent, and in both types, it was able to find the optimal solution for the controller function. The resulting numerical results show a very high agreement of the controller function with the response of other optimization methods. Finally, to make the simulation more realistic, the turbulence conditions are applied to the spacecraft thrust force and the results prove the superiority of the closed-loop, time-independent controller.