Earth-to-Mars End-to-End Mission Design – SNOPT

Design and optimize a trajectory from Earth park orbit to encounter at Mars using the SNOPT nonlinear programming algorithm.

This submission is a MATLAB script named e2m_matlab_snopt that can be used to design and optimize ballistic interplanetary missions from a Earth park orbit to encounter at Mars. The software assumes that interplanetary injection occurs impulsively from a circular park orbit. The type of final Mars-centered (areocentric) mission “targeting” and the target values are defined by the user.

The first part of this MATLAB script solves for the minimum delta-v using a zero-sphere-of-influence (ZSOI), two-body Lambert solution for the heliocentric transfer trajectory from Earth to Mars. Using this solution as an initial guess, the second part implements a simple shooting method that attempts to optimize the characteristics of the geocentric injection hyperbola while numerically integrating the spacecraft’s geocentric and heliocentric equations of motion and targeting to user-defined mission constraints at Mars.

The spacecraft motion within the Earth’s sphere-of-influence (SOI) includes the Earth’s J2 oblate gravity effect and the point-mass perturbations of the sun and moon. The heliocentric equations of motion include the point-mass gravity of the sun and the first seven planets of the solar system.

The user can select one of the following delta-v optimization options for the two-body solution of the interplanetary transfer trajectory;

1. minimize departure delta-v
2. minimize arrival delta-v
3. minimize total delta-v

The user also selects the type of final mission constraints from the following script options;

1. B-plane (B dot T and B dot R)
2. orbital elements (radius and inclination)
3. EI conditions (altitude and flight path angle)
4. grazing flyby
5. node/apse alignment

The characteristics of the final user-defined areoocentric (Mars-centered) mission constraints can be calculated in one of the following coordinate systems;

1. Earth mean equator and equinox of J2000
2. Mars mean equator and IAU node of epoch

This MATLAB script reads JPL DE421 lunar and solar ephemerides in a machine-independent binary format (kernels) which are available from the SPICE web site and by anonymous ftp from ftp://ssd.jpl.nasa.gov/pub/eph/planets/bsp. These *.bsp ephemeris files are IEEE-Little Endian style of binary kernel. This is the binary form native to PC/Linux, PC/Windows and MAC/Intel machines. Additional information about JPL ephemerides can be found at http://naif.jpl.nasa.gov/naif/.

The e2m_matlab_snoptscript uses routines from the MICE software suite to read and evaluate the JPL ephemeris file. Platform-specific MICE mex files, support functions and the binary ephemeris file (de421.bsp) are available at naif.jpl.nasa.gov/naif/toolkit_MATLAB.html. MICE is a MATLAB implementation of the SPICE library created by JPL.

MATLAB versions of SNOPT for several computer platforms can be purchase/requested at Professor Philip Gill’s web site which is located at http://scicomp.ucsd.edu/~peg/. Professor Gill’s web site also includes a PDF version of the SNOPT software user’s guide.