Intrinsic Optimal Control for Mechanical Systems on Lie Group

Chao Liu, Shengjing Tang*, Jie Guo

*Corresponding author for this work

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Abstract

The intrinsic infinite horizon optimal control problem of mechanical systems on Lie group is investigated. The geometric optimal control problem is built on the intrinsic coordinate-free model, which is provided with Levi-Civita connection. In order to obtain an analytical solution of the optimal problem in the geometric viewpoint, a simplified nominal system on Lie group with an extra feedback loop is presented. With geodesic distance and Riemann metric on Lie group integrated into the cost function, a dynamic programming approach is employed and an analytical solution of the optimal problem on Lie group is obtained via the Hamilton-Jacobi-Bellman equation. For a special case on SO(3), the intrinsic optimal control method is used for a quadrotor rotation control problem and simulation results are provided to show the control performance.

Original languageEnglish
Article number6302430
JournalAdvances in Mathematical Physics
Volume2017
DOIs
Publication statusPublished - 2017

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Liu, C., Tang, S., & Guo, J. (2017). Intrinsic Optimal Control for Mechanical Systems on Lie Group. Advances in Mathematical Physics, 2017, Article 6302430. https://doi.org/10.1155/2017/6302430