Analytic Calculation and Application of the Q-Law Guidance Algorithm Partial Derivatives

The closed-loop Q-Law guidance algorithm has been shown to be a very capable and efficient method for producing low-thrust trajectories. This paper poses a Q-Law optimization problem for computing locally optimal gain values and for enforcing nonlinear constraints on the initial state using nonlinea...

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Bibliographic Details
Published in:The Journal of the astronautical sciences Vol. 70; no. 3; p. 14
Main Authors: Shannon, Jackson L., Ellison, Donald H., Hartzell, Christine M.
Format: Journal Article
Language:English
Published: New York Springer US 17.05.2023
Springer Nature B.V
Subjects:
Aerospace Technology and Astronautics
Algorithms
Closed loops
Engineering
Genetic algorithms
Mathematical Applications in the Physical Sciences
Nonlinear programming
Optimization
Original Article
Production methods
Propagation
Space Exploration and Astronautics
Space Sciences (including Extraterrestrial Physics
Spacecraft
Thrust
Trajectory optimization
Low-thrust
Optimization
Trajectory design
ISSN:2195-0571, 0021-9142, 2195-0571
Online Access:Get full text
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Summary:The closed-loop Q-Law guidance algorithm has been shown to be a very capable and efficient method for producing low-thrust trajectories. This paper poses a Q-Law optimization problem for computing locally optimal gain values and for enforcing nonlinear constraints on the initial state using nonlinear programming (NLP). Gradient-based optimization methods have been shown to benefit greatly when analytical partial derivatives are supplied to the optimizer. Therefore, we present derivations of the Q-Law thrust vector partial derivatives with respect to the Q-law gains as well as with respect to the spacecraft’s state. These partials are leveraged to produce a state transition matrix, which contains exact partial derivatives of the terminal state with respect to the NLP problem decision vector. The Q-Law NLP problem can be coupled with the Sims–Flanagan interplanetary model in the same optimization problem. In this approach, the NLP solver uses a Q-Law model to design the planetocentric capture/escape spirals and a Sims–Flanagan model to design the interplanetary legs, resulting in end-to-end trajectory optimization.
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content type line 14
ISSN:2195-0571
0021-9142
2195-0571
DOI:10.1007/s40295-023-00371-1