design space pruning heuristics and global optimization method for ...

Prior to the LTTT effort, the primary low-thrust trajectory analysis tools for most
of NASA’s preliminary design studies were CHEBYTOP, VARITOP, SEPTOP, and
SAIL. 34
CHEBYTOP uses Chebychev polynomials to represent state variables, which
are then differentiated and integrated in closed form to solve a variable-thrust trajectory.
This solution can then be used to approximate a constant thrust trajectory. While it is
considered a low-fidelity program, it is highly valued for its ability to rapidly assess large
trade spaces. It cannot, however, analyze multi-leg missions and is limited to the
heliocentric sphere of influence. VARITOP, SEPTOP, and SAIL all use calculus of
variations in the formulation of the state and co-state equations, which are integrated
numerically to solve the two-point boundary value problem. The programs differ in their
solar electric propulsion, nuclear electric propulsion, and solar sail models. These tools
can also only handle heliocentric trajectories, and are considered to be medium-fidelity.
The tools developed under the LTTT effort are all considered to be medium- to
high-fidelity trajectory tools. 34
MALTO was developed at JPL based on the method by
Sims and Flanagan described in Section 1.2.2. It is considered to be medium fidelity.
This tool has been used for numerous trajectory design studies, including the trajectories
for the Jupiter Icy Moons Orbiter. The remaining LTTT tools are all considered to be
high-fidelity. COPERNICUS, developed at the University of Texas at Austin, is an n-
body tool with a high degree of flexibility. The user can model a number of different
missions, with varying gravitational bodies, objective functions, optimization variables,
constraint options, and levels of fidelity. Additionally, it can model multiple spacecraft,
as well as optimize for both constant and variable specific impulse trajectories.
COPERNICUS employs multiple shooting and direct integration for targeting and state
propagation. 41
Mystic was developed by Greg Whiffen at JPL, and implements
Static/Dynamic Optimal Control (SDC), which was developed by Whiffen. SDC is a
nonlinear optimal control method designed to optimize both static variables and dynamic
variables (functions of time) simultaneously. 42
The program is robust enough to take
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