Fourier Pseudospectral Method for Trajectory Optimization with Stability Requirements

Periodic trajectories that satisfy stability-based requirements are useful in many engineering applications. In this work, a time-domain approach using Fourier collocation for solving the Floquet eigenvector boundary value problem, and consequently estimating Floquet exponents and eigenvectors, is i...

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Bibliographic Details
Published in:Journal of guidance, control, and dynamics control, and dynamics, 2020-11, Vol.43 (11), p.2073-2090
Main Authors: Laad, Dhruv, Elango, Purnanand, Mohan, Ranjith
Format: Article
Language:English
Subjects:
Aerospace engineering
Aircraft models
Boundary value problems
Damping
Eigenvalues
Eigenvectors
Estimates
Optimization
Orbits
Spectral methods
Stability
Time domain analysis
Trajectory optimization
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Summary:Periodic trajectories that satisfy stability-based requirements are useful in many engineering applications. In this work, a time-domain approach using Fourier collocation for solving the Floquet eigenvector boundary value problem, and consequently estimating Floquet exponents and eigenvectors, is introduced. This method is incorporated into a Fourier pseudospectral trajectory optimization framework for generating open-loop stable solution, and for improving the damping of a specific mode identified using the information from Floquet eigenvectors. These applications are illustrated on the dynamic soaring solutions of three- and six-degree-of-freedom aircraft models, and numerical results highlighting the effectiveness of the pseudospectral Floquet computation over the traditional time-march approach are also presented.
ISSN:0731-5090
1533-3884
DOI:10.2514/1.G005038