Application of Particle Swarm Optimization to Lyapunov Periodic Orbits

Open Access
Author:
Caldwell, Cory
Area of Honors:
Aerospace Engineering
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Robert Graham Melton, Thesis Supervisor
  • David Bradley Spencer, Honors Advisor
  • George A Lesieutre, Faculty Reader
Keywords:
  • particle
  • swarm
  • optimization
  • method
  • Lyapunov
  • orbit
  • periodic
  • Langrange
Abstract:
The particle swarm optimization (PSO) technique is a stochastic population-based method motivated by the unpredictable behavior of bird flocks searching for food. This method utilizes information sharing within the population to influence the swarm in finding the optimal solution for the unknown parameters of the problem being considered. PSO has various applications; this research applies the optimization method to space trajectories. Specifically, PSO is applied to find the unknown parameters for the Lyapunov periodic orbits around the collinear interior and exterior Lagrange points in the context of the Circular Restricted Three-Body Problem (CR3BP) in the Earth-Moon system. In this problem, the unknown parameters are represented by the initial position and period which define these orbits. The research starts with application of PSO to the interior Lagrange point of the Earth-Moon system to predict the planar periodic orbits in a synodic reference frame. The orbits for the exterior Lagrange point are examined with PSO in a similar manner. This research concludes PSO is effective in finding Lyapunov periodic orbits defined by low values of the Jacobi constant (the only integral of the motion in the CR3BP).