Earth-to-Mars Interplanetary TCM Optimization - OTB

Optimization Toolbox version of the MATLAB script that determines optimal Earth-to-Mars impulsive TCM maneuvers.

This submission is a MATLAB script called e2m_tcm_otb which can be used to solve the classic one impulse, Earth-to-Mars interplanetary trajectory correction maneuver (TCM) optimization problem. The software implements a simple shooting method that attempts to minimize the scalar magnitude of the TCM delta-v while numerically integrating the n-body heliocentric equations of motion and solving for user-defined final orbit conditions at Mars. With the implementation of proper planet-centered coordinate transformations, the software can be used for other planets.

The final conditions of the spacecraft at closest approach at Mars can be determined using one of the following user-defined options;

• flight path angle, radius and orbital inclination
• user-defined B-plane coordinates
• grazing flyby; user-defined B-plane angle

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

This MATLAB script uses the fmincon (minimization with constraints) algorithm of the Mathworks® Optimization Toolbox (OTB) to solve this optimization problem. The numerical method is the ‘interior-point’ algorithm.