Tech Briefs

Solving complex trajectory problems optimally is of vital importance to the success of future aerospace programs. Trajectory optimization research has been divided into two main categories: indirect methods and direct methods. Both methodologies have been tested and extensively applied to specific orbital trajectory problems.

Algorithm robustness is the ultimate aim. One approach to achieve this robustness is to modify current optimization approaches to handle complex problems without requiring meticulous tuning to obtain a solution. The algorithm developed in this work employs the direct method of trajectory optimization. The equations of motion that dictate the behavior of bodies in space have fixed constants. These may be invariable, but that does not mean they cannot be treated as optimization variables. The constants can be constrained to the fixed values, imparting a target error on known values and ensuring the final solution is feasible.

Taking advantage of a novel approach to the design of the orbital transfer optimization problem and advanced nonlinear programming algorithms, several optimal transfer trajectories are found for problems with and without known analytic solutions. The method treats the fixed known gravitational constants as optimization variables in order to reduce the need for an advanced initial guess.

Complex periodic orbits are targeted with very simple guesses, and the ability to find optimal transfers in spite of these bad guesses is successfully demonstrated. Impulsive transfers are considered for orbits in both the two-body frame as well as the circular restricted three-body problem (CRTBP). The results with this new approach demonstrate the potential for increasing robustness in finding solutions for all types of orbit transfer problems.

This work was done by Ryan Whitley of Johnson Space Center and Cesar Ocampo of the University of Texas at Austin. MSC-24748/95-1

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Direct Multiple Shooting Optimization with Variable Problem Parameters (reference MSC-24748-95-1) is currently available for download from the TSP library.

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