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 sub-optimal 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 (HOC). 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 (GA) and direct transcription with nonlinear programming (NLP) 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 NLP problems resulting from the use of a direct solver 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 NLP problem solver. Two new methods were developed for cases including low-thrust trajectories. The first method, based on GA, approximates optimal control histories by incorporating boundary conditions explicitly using a conditional penalty function. The second method, feasible region analysis, is based on GA and NLP; the GA approximates the optimal boundary points of low-thrust arcs while NLP finds the required control histories. The solution of two representative multiphase space mission design problems shows the effectiveness of the methods developed.