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Theory and computation of optimal low- and medium-thrust transfers

This report presents the formulation of the optimal low- and medium-thrust orbit transfer control problem and methods for numerical solution of the problem. The problem formulation is for final mass maximization and allows for second-harmonic oblateness, atmospheric drag, and three-dimensional, non-coplanar, non-aligned elliptic terminal orbits. We setup some examples to demonstrate the ability of two indirect methods to solve the resulting TPBVP's. The methods demonstrated are the multiple-point shooting method as formulated in H. J. Oberle's subroutine BOUNDSCO, and the minimizing boundary-condition method (MBCM). We find that although both methods can converge solutions, there are trade-offs to using either method. BOUNDSCO has very poor convergence for guesses that do not exhibit the correct switching structure. MBCM, however, converges for a wider range of guesses. However, BOUNDSCO's multi-point structure allows more freedom in quesses by increasing the node points as opposed to only quessing the initial state in MBCM. Finally, we note an additional drawback for BOUNDSCO: the routine does not supply information to the users routines for switching function polarity but only the location of a preset number of switching points.

Chuang, C.-H.

How the INCOSE Model-Based Capability Matrix Has Steered Model-Based Systems Engineering Transformation at NASA

The National Aeronautics and Space Administration (NASA) is embarking on new, complex, and diverse missions to accomplish its scientific and exploration objectives, and it views digital transformation as a key enabler for those missions. The NASA Model-Based Systems Engineering (MBSE) Lead-ership Team (MLT) is leading the charge in the digital transformation of the systems engineering domain at NASA, and it is using the INCOSE Model-Based Capability Matrix (MBCM) as a roadmap. This paper discusses the modifications and tailoring of the INCOSE MBCM (Hale & Hoheb, 2020) for use at NASA, the process the team has taken on multiple rounds of assessment, findings to date, and work products that have been generated as a result of the assessment. The paper will also discuss findings and potential changes that should be made to the original product.

MBSE

Computation of optimal low- and medium-thrust orbit transfers

This paper presents the formulation of the optimal low- and medium-thrust orbit transfer control problem, numerical methods for solution, and numerical solutions of the problem. The problem formulation is for final mass maximization and allows for second-harmonic oblateness, atmospheric drag, and 3D noncoplanar nonaligned elliptic terminal orbits. We set up examples to demonstrate the ability of two indirect methods to solve the resulting two point boundary value problems (TPBVP). The methods demonstrated are the multiple point shooting method as formulated in Oberle's (1987) subroutine BOUNDSCO, and the minimizing boundary-condition method (MBCM). We find that although both methods can converge solutions, there are tradeoffs to using either method. We present numerical solutions of planar transfers in which both the initial orbit exit and final orbit entry points have been optimized. These solutions include two- and three-burn transfers. The methods used show an ability to handle thrust down to at least T/W(o) = O(10 exp -3). They also show similar convergence abilities with or without the oblateness and drag terms. We discuss the issue of maximizing with respect to the final time and provide evidence that implies a local optimum at a maximum final time for a given number of burns.

Chuang, C.-H.

Theory and Computation of Optimal Low- and Medium- Thrust Orbit Transfers

This report presents new theoretical results which lead to new algorithms for the computation of fuel-optimal multiple-burn orbit transfers of low and medium thrust. Theoretical results introduced herein show how to add burns to an optimal trajectory and show that the traditional set of necessary conditions may be replaced with a much simpler set of equations. Numerical results are presented to demonstrate the utility of the theoretical results and the new algorithms. Two indirect methods from the literature are shown to be effective for the optimal orbit transfer problem with relatively small numbers of burns. These methods are the Minimizing Boundary Condition Method (MBCM) and BOUNDSCO. Both of these methods make use of the first-order necessary conditions exactly as derived by optimal control theory. Perturbations due to Earth's oblateness and atmospheric drag are considered. These perturbations are of greatest interest for transfers that take place between low Earth orbit altitudes and geosynchronous orbit altitudes. Example extremal solutions including these effects and computed by the aforementioned methods are presented. An investigation is also made into a suboptimal multiple-burn guidance scheme. The FORTRAN code developed for this study has been collected together in a package named ORBPACK. ORBPACK's user manual is provided as an appendix to this report.

Goodson, Troy D.