Fuel-Efficient Powered Descent Guidance on Large Planetary Bodies via Theory of Functional Connections
Affiliation
Univ Arizona, Syst & Ind EngnUniv Arizona, Aerosp & Mech Engn
Issue Date
2020-09-25Keywords
Fuel optimal pinpoint landingTheory of functional connections
Optimal control
Indirect method
Least-squares
Constraint embedding
Metadata
Show full item recordPublisher
SPRINGER HEIDELBERGCitation
Johnston, H., Schiassi, E., Furfaro, R. et al. Fuel-Efficient Powered Descent Guidance on Large Planetary Bodies via Theory of Functional Connections. J Astronaut Sci (2020). https://doi.org/10.1007/s40295-020-00228-xRights
Copyright © American Astronautical Society 2020.Collection Information
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.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.Note
12 month embargo; published 25 September 2020ISSN
0021-9142EISSN
2195-0571Version
Final accepted manuscriptSponsors
Johnson Space Centerae974a485f413a2113503eed53cd6c53
10.1007/s40295-020-00228-x