OPTIMAL LANDING TRAJECTORIES ON THE MOON USING LAMBERT TARGETING AND PARTICLE SWARM OPTIMIZATION
Open Access
- Author:
- Patel, Khushboo
- Graduate Program:
- Aerospace Engineering
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- July 20, 2019
- Committee Members:
- David Bradley Spencer, Thesis Advisor/Co-Advisor
Robert Graham Melton, Thesis Advisor/Co-Advisor
Amy Ruth Pritchett, Committee Member - Keywords:
- Multiple precision landings
Optimal trajectories - Abstract:
- This thesis presents a trajectory optimization problem for a lunar lander using Lambert’s solution with a Particle Swarm Optimization method. The goal of this thesis is to look for optimal and repeatable transfers, starting from a circular orbit to land at a desired location on the lunar surface. The Particle Swarm Optimization method, inspired by the motion of birds swarming, has been used to find acceptable and appropriate solutions for spacecraft trajectories. The purpose of this thesis is to determine the best location to start the descent to the Moon for multiple landings corresponding to the pre-selected landing site location. A constant starting altitude of 100 km above the lunar surface is used. This research presents two cases where the cost function of the optimization problem with respect to various transfer variables of the trajectories is considered. These cases represent two landing scenarios where the number of decision variables is either 1 or 3. The elements investigated are the semi-major axis and eccentricity which define the shape of the trajectory, inclination of the transfer orbit with respect to the Moon’s equatorial plane, right ascension of ascending node, true anomaly, the argument of periapsis and the time to land. The cost function for the optimization problem comprises the Δv, in the form of engine burns. Using Particle Swarm Optimization on Lambert’s solution for a swarm of 100 trajectories, the ten local best trajectories are selected at each stage of the generation. The particle swarm optimization method was modified with the inclusion of simple genetic algorithm operators, crossover and mutation to increase interdependence between generations. These ten trajectories contain an effective combination of the decision variables that produces the lowest total Δv. This information is then utilized to generate the next swarm of 100 trajectories which is evaluated for fitness through Lambert targeting by Particle Swarm Optimization. Once the best solution does not change from generation to generation for around 20 generations, the ten best transfer trajectory characteristics with the lowest total Δv and thereby minimum propellant are recorded. The ten trajectories obtained are then used to generate ground tracks with respect to the lunar surface and appropriate downrange data are analyzed. Sensitivity analysis on the first attempt solution and the initial conditions used for the two cases is presented. In summary, with the Particle Swarm Optimization, optimal results with minimum propellant usage and via a Pareto frontier convergence curve for the cost function were obtained through many generations. The ten final trajectories obtained through this process can pave a way for multiple-precision landings on the Moon or a planetary surface.