Robust Bang-Off-Bang Low-Thrust Guidance Using Model Predictive Static Programming

Model Predictive Static Programming (MPSP) has been always used under the assumption of continuous or impulsive control, but never in low-thrust transfers featuring bang-off-bang control. Following the observation that the sensitivity matrix (SM) is discontinuous across the switching time, this work...

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Bibliographic Details
Published in:Acta astronautica Vol. 176; pp. 357 - 370
Main Authors: Wang, Yang, Topputo, Francesco
Format: Journal Article
Language:English
Published: Elmsford Elsevier Ltd 01.11.2020
Elsevier BV
Subjects:
Asteroids
Bang-off-bang control
Basis functions
Calculus of variations
Cubesat
Equations of motion
Low-thrust transfers
Model predictive static programming
Newton methods
Switching
Thrust
Trajectory optimization
Voyager 1 spacecraft
Bang-off-bang control
Low-thrust transfers
Model predictive static programming
ISSN:0094-5765, 1879-2030
Online Access:Get full text
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Summary:Model Predictive Static Programming (MPSP) has been always used under the assumption of continuous or impulsive control, but never in low-thrust transfers featuring bang-off-bang control. Following the observation that the sensitivity matrix (SM) is discontinuous across the switching time, this work introduces a two-loop MPSP guidance scheme using fuel-optimal trajectories as nominal solutions. In our method, the equations of motion are augmented by the mass costate equation, while the velocity costate is the MPSP control, expressed by a weighted sum of Fourier basis functions. The SM is computed at the switching time by using calculus of variations. Both the MPSP control and the initial mass costate are updated in an inner loop using Newton’s method, and continuation is employed in an outer loop to face large perturbations. A sample interplanetary CubeSat mission to an asteroid is used as study case to illustrate the effectiveness and robustness of the method developed. •A new model predictive static programming method is developed to handle bang-off-bang control.•The sensitivity matrix is shown discontinuous across the switching time for low-thrust transfers with bang-off-bang control.•Effectiveness and robustness are demonstrated through numerical examples.
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ISSN:0094-5765
1879-2030
DOI:10.1016/j.actaastro.2020.06.037