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arXiv · 2403.06167

Direct Shooting Method for Numerical Optimal Control: A Modified Transcription Approach

Jiawei Tang·Yuxing Zhong·Pengyu Wang·Xingzhou Chen·Shuang Wu·Ling Shi
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Abstract

Direct shooting is an efficient method to solve numerical optimal control. It utilizes the Runge-Kutta scheme to discretize a continuous-time optimal control problem making the problem solvable by nonlinear programming solvers. However, conventional direct shooting raises a contradictory dynamics issue when using an augmented state to handle {high-order} systems. This paper fills the research gap by considering the direct shooting method for {high-order} systems. We derive the modified Euler and Runge-Kutta-4 methods to transcribe the system dynamics constraint directly. Additionally, we provide the global error upper bounds of our proposed methods. A set of benchmark optimal control problems shows that our methods provide more accurate solutions than existing approaches.

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Jiawei Tang, Yuxing Zhong, Pengyu Wang, Xingzhou Chen, Shuang Wu, Ling Shi. 2024-03-10. Direct Shooting Method for Numerical Optimal Control: A Modified Transcription Approach. https://arxiv.org/abs/2403.06167

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