Mission design using low-thrust propulsion requires a method for approximating the spacecraft's trajectory and its cost. This can be for the purpose of evaluating a large search space or for providing a suitable initial guess to be used with more accurate trajectory optimizers. Such optimizers (for example, direct transcription methods in which the continuous problem is converted into a nonlinear programming problem) are more likely to converge when given an initial guess satisfying the equation of motion constraints and the terminal boundary conditions. A shape-based method is derived here that is capable of determining such trajectories for both time-free and time-fixed cases. When combined with a genetic algorithm, it is possible to find solutions by adjusting the free parameters of the problem within a few percent of optimal solutions found with a very exact optimizer. The method is intended for the rendezvous case but, with small modifications, it is able to solve for the less constrained cases of interception, orbit transfer, and escape.
ASJC Scopus subject areas
- Control and Systems Engineering
- Aerospace Engineering
- Space and Planetary Science
- Electrical and Electronic Engineering
- Applied Mathematics