Using genetic algorithms for the construction of a space mission automaton

Abstract

Many interesting problems in numerical optimization are hybrid optimal control problems. Hybrid optimal control (HOC) problems include both continuous-valued variables and categorical variables in the problem formulation. For the types of problems envisioned here the categorical variables will specify the structure or sequence of events that qualitatively describes the trajectory or mission. Continuous variables are used in the modeling of the continuous dynamics. In this work, the mission planning problem is of interest. The problem is qualitatively different from the typical interception of multiple targets as the discrete variables now represent events like impulses, coast and thrust arcs that change the structure of the problem. In addition, the number of events in the categorical sequence is not fixed. For the dynamical assembly of events required for the solution of the mission planning problem, a scheme that defines events as modules consisting of parameters and constraints is presented. The method assembles the respective events one next to the other in time according to the given mission structure. For the generation of the initial guess, two new methods were developed that approximate optimal low-thrust trajectories. The first method, based on genetic algorithms (GA), handles the rendezvous constraints explicitly using a conditional penalty function. The second method, feasible region analysis (FRA), is based on GA and nonlinear programming (NLP), which allows taking advantage of the GA capabilities in finding a global optimum and NLP ability in handling constraints. A rendezvous problem with known solution is solved.