Indirect Optimization of Two Dimensional Finite-Burning Interplanetary Transfers Including Spiral Dynamics

Paper number

IAC-06-C1.P.4.03

Author

Mr. Christopher Ranieri, The University of Texas at Austin, United States

Coauthor

Dr. Cesar Ocampo, The University of Texas at Austin, United States

Year

2006

Abstract

Using algorithms previously developed for accurately estimating the unknown co-states for escape and capture spirals, the indirect optimization problem for a two-dimensional simplification of the Low Earth Orbit (LEO) to Low Mars Orbit (LMO) transfer is solved.  The goal of the optimization is to compute minimum propellant trajectories for finite-burning engines.  Solutions are considered with and without limits on specific impulse and compared with previous research.   While this indirect optimization problem has been approached previously, this work makes significant improvements to the process, opening a much greater solution space of numerically achievable missions.   

A regimented, step-by-step process is developed that allows the analyst to relatively easily create LEO to LMO missions in two dimensions, especially considering the typical difficulty of using indirect methods for optimizing challenging trajectories.  The iterative process used in prior research to reduce the final capture orbit size (from an initial solution of 300 Mars Radii (DUM) to 6 DUM) is found to be inefficient and limited in the achievable complexity of the capture sequence.  The iterative approach is therefore removed by the new derivation of relationships between the co-states and by integrating the capture sequence backwards.  The derivations allow the co-states in a Martian coordinate frame to be expressed as the equivalent set of co-states in an Earth coordinate frame or vice versa.  This allows the entire LEO-LMO trajectory to be integrated in a single coordinate frame, bypassing the optimality corner conditions normally associated with the patch point when coordinate frames are switched.  

Using the newly developed derivations, the new approach does not tediously iterate but rather directly targets low final orbits on the initial solution step.  This allows a much greater range of functionality as solutions are found with final Martian circular orbits as low as 1.32 - 1.77 DUM (4500-6000 km) compared to the 6 DUM (20382 km) orbits achieved previously.   In direct comparison to 6 DUM solutions of past research, more fuel efficient trajectories are found.  The importance of local versus global optimal solutions is also explored, particularly in relationship with the optimal escape and capture times.  The behavior of the thrust for the globally optimal escapes and captures is found to be distinctly different than for nearby locally optimal solutions.  This work forms the stepping stone for analysis of 3-D interplanetary transfers and may be used to optimize powered gravity assists. This work has not been presented at other conferences.

Abstract document

IAC-06-C1.P.4.03.pdf

Manuscript document

IAC-06-C1.P.4.03.pdf (🔒 authorized access only).

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