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CEAS EuroGNC 2022

A Nonlinear Trigonometric Series Parameterization Approach for Smooth Trajectory Generation
Haichao Hong Postdoctoral Researcher, Technical University of Munich, Institute of Flight System Dynamics, 85748, Garching, Germany.
Patrick Piprek Dr.-Ing., Technical University of Munich, Institute of Flight System Dynamics, 85748, Garching, Germany.
Zhidong Lu PhD Candidate, Technical University of Munich, Institute of Flight System Dynamics, 85748, Garching, Germany.
Florian Holzapfel Professor, Technical University of Munich, Institute of Flight System Dynamics, 85748, Garching, Germany.
Abstract:
This paper introduces a parameterization method for generating trajectories with smooth control commands based on a trigonometric series, where the formulation is nonlinear with respect to the series coefficients. The proposed method aims to achieve a steadier behavior when a path constraint is temporarily active, which is often encountered with e.g., a minimum-time performance index. To this end, first, the control derivatives are parameterized instead of the control variables. Furthermore, the newly developed formulation includes a filtering function depending on the original trigonometric series. This function reduces the series value when it is within a specifiable neighborhood of zero. The performance of the proposed method is tested in two numerical benchmark problems in which a minimum-time and a minimum-effort cost function are considered, respectively.
Keywords: Trajectory Optimization; Trigonometric Series; Control Parameterization; Optimal Control
 View PDF CEAS-GNC-2022-030


Haichao Hong, Patrick Piprek, Zhidong Lu, Florian Holzapfel: A Nonlinear Trigonometric Series Parameterization Approach for Smooth Trajectory Generation. Proceedings of the 2022 CEAS EuroGNC conference. Berlin, Germany. May 2022. CEAS-GNC-2022-030.
BibTeX entry:

@Incollection{CEAS-GNC-2022-030,
    authors = {Hong, Haichao and Piprek, Patrick and Lu, Zhidong and Holzapfel, Florian},
    title = {A Nonlinear Trigonometric Series Parameterization Approach for Smooth Trajectory Generation},
    booktitle = {Proceedings of the 2022 {CEAS EuroGNC} conference},
    address = {Berlin, Germany},
    month = may,
    year = {2022},
    note = {CEAS-GNC-2022-030}
}