Fuel-Efficient Powered Descent Guidance on Large Planetary Bodies via Theory of Functional Connections
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Fuel-Efficient Powered Descent Guidance on Large Planetary Bodies via Theory of Functional Connections Hunter Johnston1 · Enrico Schiassi2 · Roberto Furfaro2,3
· Daniele Mortari1
© American Astronautical Society 2020
Abstract In this paper we present a new approach to solve the fuel-efficient powered descent guidance problem on large planetary bodies with no atmosphere (e.g., Moon or Mars) using the recently developed Theory of Functional Connections. The problem is formulated using the indirect method which casts the optimal guidance problem as a system of nonlinear two-point boundary value problems. Using the Theory of Functional Connections, the problem’s linear constraints are analytically embedded into a functional, which maintains a free-function that is expanded using orthogonal polynomials with unknown coefficients. The constraints are always analytically satisfied regardless of the values of the unknown coefficients (e.g., the coefficients of the free-function) which converts the two-point boundary value problem into an unconstrained optimization problem. This process reduces the whole solution space into the admissible solution subspace satisfying the constraints and, therefore, simpler, more accurate, and faster numerical techniques can be used to solve it. In this paper a nonlinear least-squares method is used. In addition to the derivation of this technique, the method is validated in two scenarios and the results are compared to those obtained by the general purpose optimal control software, GPOPS-II. In general, the proposed technique produces solutions of O(10−10 ) accuracy. Additionally, for the proposed test cases, it is reported that each individual TFC-based inner-loop iteration converges within 6 iterations, each iteration exhibiting a computational time between 72 and 81 milliseconds, with a total execution time of 2.1 to 2.6 seconds using MATLAB. Consequently, the proposed methodology is potentially suitable for real-time computation of optimal trajectories.
This work was partially supported by a NASA Space Technology Research Fellowship, Johnston [NSTRF 2019] Grant #: 80NSSC19K1149. Roberto Furfaro
[email protected]
Extended author information available on the last page of the article.
The Journal of the Astronautical Sciences
Keywords Fuel optimal pinpoint landing · Theory of functional connections · Optimal control · Indirect method · Least-squares · Constraint embedding
Introduction Precision landing on large planetary bodies is a technology of utmost importance for future human and robotic exploration of the solar system. Over the past two decades, landing systems for robotic Mars missions have been developed and successfully deployed robotic assets on the Martian surface (e.g. rovers [1], landers [2]). Considering the strong interest in sending humans to Mars within the next few decades, as well as the renewed interest in building infrastructure in the Earth-Moon system for easy access to the Lunar surface, the landing system technology will need to progress to satisf
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