Leader–follower decentralized optimal control for large population hexarotors with tilted propellers: A Stackelberg game approach |
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| Institution: | 1. School of Electrical and Computer Engineering, Ulsan National Institute of Science and Technology (UNIST), Ulsan, South Korea;2. School of Mechanical, Aerospace and Nuclear Engineering, Ulsan National Institute of Science and Technology (UNIST), Ulsan, South Korea;3. School of Electrical and Computer Engineering, University of Seoul, Seoul, South Korea;1. College of Science, China Jiliang University, Hangzhou 310018, China;2. School of Computer Science and Technology, China University of Mining and Technology, Xuzhou 221116, China;3. College of Information Science and Engineering, Ocean University of China, Qingdao 266100, China |
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| Abstract: | In this paper, we consider leader–follower decentralized optimal control for a hexarotor group with one leader and large population followers. Our hexarotor is modeled based on the quaternion framework to resolve singularity of the rotation matrix represented by Euler angles, and has 6-DoF due to six tilted propellers, which allows to control its translation and attitude simultaneously. In our problem setup, the leader hexarotor is coupled with the follower hexarotors through the followers’ average behavior (mean field), and the followers are coupled with each other through their average behavior and the leader’s arbitrary control. By using the mean field Stackelberg game framework, we obtain a set of decentralized optimal controls for the leader and N follower hexarotors when N is arbitrarily large, where each control is a function of its local information. We show that the corresponding decentralized optimal controls constitute an ?-Stackelberg equilibrium for the leader and N followers, where ? → 0 as N → ∞. Through simulations with two different operating scenarios, we show that the leader–follower hexarotors follow their desired position and attitude references, and the followers are controlled by the leader while effectively tracking their approximated average behavior. Furthermore, we show the nonsingularity and 6-DoF control performance of the leader–follower hexarotor group due to the novel modeling technique of the hexarotor presented in the paper. |
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