Automated Design of Multiphase Space Missions Using Hybrid Optimal Control

摘要

A modern space mission is assembled from multiple phases or events such as impulsive maneuvers, coast arcs, thrust arcs, and planetary flybys. Traditionally, a mission planner would resort to intuition and experience to develop a sequence of events for the multiphase mission and to find the space trajectory that minimizes propellant use by solving the associated continuous optimal control problem. This strategy, however, will most likely yield a suboptimal solution, as the problem is sophisticated for several reasons. For example, the number of events in the optimal mission structure is not known a priori, and the system equations of motion change depending on what event is current. In this work a framework for the automated design of multiphase space missions is presented using hybrid optimal control. The method developed uses two nested loops: an outer-loop that handles the discrete dynamics and finds the optimal mission structure in terms of the categorical variables, and an inner-loop that performs the optimization of the corresponding continuous-time dynamical system and obtains the required control history. Genetic algorithms and direct transcription with nonlinear programming are introduced as methods of solution for the outer-loop and inner-loop problems, respectively. Automation of the inner-loop, continuous optimal control problem solver required two new technologies. The first is a method for the automated construction of the nonlinear programming problems resulting from the use of a transcription method for systems with different structures, including different numbers of categorical events. The method assembles modules, consisting of parameters and constraints appropriate to each event, sequentially according to the given mission structure. The other new technology is for a robust initial guess generator required by the inner-loop nonlinear programming problem solver. The method, based on a real genetic algorithm, approximates optimal control histories by incorporating boundary conditions explicitly using a conditional penalty function. The solution of representative multiphase mission design problems shows the effectiveness of the methods developed.