Real-time optimal guidance via the Theory of Functional Connections

The proposed research looks to develop the mathematical framework and algorithm for real-time, on-board optimal guidance using the Theory of Connections (a newly established technique to solve differential equations). Current publications on the Theory of Connections provide machine-level accurate solutions in milliseconds. This provides a foundation for the computation of dynamical equations of motion in real-time in order to make control decisions. Moreover, a preliminary study of this technique applied to optimal guidance type problems has already been conducted validating further work in this area. While the main goal of this proposal is to develop a real-time optimal guidance architecture, it will also further the development of the Theory of Connections as a robust mathematical tool. In general, this has potential to be applied across all fields of engineering where machine level accuracy is necessary in the solution of problems. In all, research in real-time optimal guidance and control is the building block for reduced reliance on Earth based systems for spaceflight and ultimately full spacecraft autonomy.

While the main goal of this proposal is to develop a real-time optimal guidance architecture, it will also further the development of the Theory of Connections as a robust mathematical tool. In general, this has potential to be applied across all fields of engineering where machine level accuracy is necessary in the solution of problems. In all, research in real-time optimal guidance and control is the building block for reduced reliance on Earth based systems for spaceflight and ultimately full spacecraft autonomy.

This is early/mid-stage (TRL 3) — the most realistic path in is NASA SBIR/STTR, which funds small businesses and research institutions to develop technology aligned with NASA's needs (equity-free, phased funding). Check whether a current SBIR/STTR solicitation topic overlaps with this project's technology area, or contact the project directly (above) to ask.

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