design space pruning heuristics and global optimization method for ...
design space pruning heuristics and global optimization method for ...
design space pruning heuristics and global optimization method for ...
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Prior to the LTTT ef<strong>for</strong>t, the primary low-thrust trajectory analysis tools <strong>for</strong> most<br />
of NASA’s preliminary <strong>design</strong> studies were CHEBYTOP, VARITOP, SEPTOP, <strong>and</strong><br />
SAIL. 34<br />
CHEBYTOP uses Chebychev polynomials to represent state variables, which<br />
are then differentiated <strong>and</strong> integrated in closed <strong>for</strong>m to solve a variable-thrust trajectory.<br />
This solution can then be used to approximate a constant thrust trajectory. While it is<br />
considered a low-fidelity program, it is highly valued <strong>for</strong> its ability to rapidly assess large<br />
trade <strong>space</strong>s. It cannot, however, analyze multi-leg missions <strong>and</strong> is limited to the<br />
heliocentric sphere of influence. VARITOP, SEPTOP, <strong>and</strong> SAIL all use calculus of<br />
variations in the <strong>for</strong>mulation of the state <strong>and</strong> co-state equations, which are integrated<br />
numerically to solve the two-point boundary value problem. The programs differ in their<br />
solar electric propulsion, nuclear electric propulsion, <strong>and</strong> solar sail models. These tools<br />
can also only h<strong>and</strong>le heliocentric trajectories, <strong>and</strong> are considered to be medium-fidelity.<br />
The tools developed under the LTTT ef<strong>for</strong>t are all considered to be medium- to<br />
high-fidelity trajectory tools. 34<br />
MALTO was developed at JPL based on the <strong>method</strong> by<br />
Sims <strong>and</strong> Flanagan described in Section 1.2.2. It is considered to be medium fidelity.<br />
This tool has been used <strong>for</strong> numerous trajectory <strong>design</strong> studies, including the trajectories<br />
<strong>for</strong> the Jupiter Icy Moons Orbiter. The remaining LTTT tools are all considered to be<br />
high-fidelity. COPERNICUS, developed at the University of Texas at Austin, is an n-<br />
body tool with a high degree of flexibility. The user can model a number of different<br />
missions, with varying gravitational bodies, objective functions, <strong>optimization</strong> variables,<br />
constraint options, <strong>and</strong> levels of fidelity. Additionally, it can model multiple <strong>space</strong>craft,<br />
as well as optimize <strong>for</strong> both constant <strong>and</strong> variable specific impulse trajectories.<br />
COPERNICUS employs multiple shooting <strong>and</strong> direct integration <strong>for</strong> targeting <strong>and</strong> state<br />
propagation. 41<br />
Mystic was developed by Greg Whiffen at JPL, <strong>and</strong> implements<br />
Static/Dynamic Optimal Control (SDC), which was developed by Whiffen. SDC is a<br />
nonlinear optimal control <strong>method</strong> <strong>design</strong>ed to optimize both static variables <strong>and</strong> dynamic<br />
variables (functions of time) simultaneously. 42<br />
The program is robust enough to take<br />
16