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CEAS EuroGNC 2024

Flight Trajectory Generation through a Collocation Approach with Successive Linear Programming
Zhidong Lu Ph.D. Candidate, Technical University of Munich, Institute of Flight System Dynamics, 85748, Garching, Germany.
Haichao Hong Associate Professor, Shanghai Jiao Tong University, School of Aeronautics and Astronautics, 200240, Shanghai, People's Republic of China.
Florian Holzapfel Professor, Technical University of Munich, Institute of Flight System Dynamics, 85748, Garching, Germany.
Abstract:
Optimal control methods are widely used to generate flight trajectories for aerial vehicles. These optimal control problems are generally non-convex due to nonlinear flight dynamics and constraints. This study integrates a collocation framework with successive linear programming to address non-convex trajectory generation problems. A linear programming subproblem is constructed by linearizing nonlinear collocation constraints and path constraints. This subproblem aims to find optimal increments of parameters, states, and controls to refine a reference trajectory, which is subsequently re-linearized to formulate subsequent subproblems. An approximate solution to the original optimal control problem is derived through the iterative resolution of these subproblems. To address the potential unboundedness and infeasibility of the subproblem, this paper incorporates linearized constraints into the cost function via exact penalties and enforces trust region on the increments at each collocation node. The maximum allowable trust region size is dynamically adjusted based on the linearization error to assure global convergence. Practical applications in fixed-wing aircraft and quadrotor trajectory generation tasks demonstrate the effectiveness of our approach. Comparative analyses with solutions from state-of-the-art toolboxes indicate that our method achieves near-optimal and dynamically feasible trajectories more efficiently in terms of iterations and computational time. The source code for the algorithm and examples presented in this paper is available at https://github.com/lenleo1/Colloc_SLP.git
Keywords: Trajectory Generation; Optimal Control; Trapezoidal Collocation; Successive Linear Programming
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Zhidong Lu, Haichao Hong, Florian Holzapfel: Flight Trajectory Generation through a Collocation Approach with Successive Linear Programming. Proceedings of the 2024 CEAS EuroGNC conference. Bristol, UK. June 2024. CEAS-GNC-2024-072.
BibTeX entry:

@Incollection{CEAS-GNC-2024-072,
    author = {Lu, Zhidong and Hong, Haichao and Holzapfel, Florian},
    title = {Flight Trajectory Generation through a Collocation Approach with Successive Linear Programming},
    booktitle = {Proceedings of the 2024 {CEAS EuroGNC} conference},
    address = {Bristol, UK},
    month = jun,
    year = {2024},
    note = {CEAS-GNC-2024-072}
}