Fully distributed spherical formation tracking control for nonlinear vehicles with spatiotemporal uncertainties and digr
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ORIGINAL PAPER
Fully distributed spherical formation tracking control for nonlinear vehicles with spatiotemporal uncertainties and digraphs Yang-Yang Chen
· Rui Yu · Ya Zhang
Received: 19 April 2020 / Accepted: 6 July 2020 © Springer Nature B.V. 2020
Abstract This paper addresses the spherical formation tracking control problem of nonlinear vehicles under digraphs, where the dynamics of vehicle contains spatiotemporal uncertainties consisted of the mismatched and matched flowfields and model uncertainties. The novel cooperative adaptive flow estimates and adaptive neural networks for the reconstruction of model uncertainties are designed based on the neighbor information. A fully distributed formation tracking protocol is generated by dynamics surface and achieves the three-dimensional sphere landing task with the position restriction, the orbit tracking task and the lateral circular formation task without using any global information of the digraph. The stability of the closed-loop system is analyzed in the Lyapunov sense, and the spherical formation tracking errors converge to a small neighborhood of the origin. Simulation results show the feasibility and effectiveness of the proposed scheme. Keywords Spherical formation tracking · Flowfields · Model uncertainties · Adaptive method · Adaptive neural networks · Dynamics surface Y.-Y. Chen (B) · R. Yu · Y. Zhang School of Automation, Southeast University, Nanjing 210096, People’s Republic of China e-mail: [email protected] Y.-Y. Chen · R. Yu · Y. Zhang Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Southeast University, Nanjing 210096, People’s Republic of China
1 Introduction In the past decades, the control and robotic communities have witnessed a great number of efforts for the Earth monitoring [1,2], the planetary exploration [3,4] and the deep space exploration [5,6]. To achieve the good performance, each vehicle is desired to fly around a center (e.g., the Earth or a master satellite) with a special orbit and simultaneously maintain the desired formation associated with the relative orbits, which is named as the spherical formation tracking control problem. Earlier, a variety of approaches are built upon the flow-free circumstance and the certain dynamics. The details can be found in [7–15]. However, the dynamics of an actual vehicle is inevitably modeled with spatiotemporal uncertainties due to the external flowfields and incomplete system modeling. Therefore, it is well-known challenging to develop a novel theory for spherical formation tracking control with spatiotemporal uncertainties. To fight against the unknown external flowfields, the estimating methods are introduced into the cooperative control. Summers and his colleagues firstly use the adaptive estimate to achieve the circular distribution in the presence of an unknown, mismatched time-invariant flowfield in [16]. In [17], the adaptive method is developed into the uniform rotating flowfield with an unknown parameter. With using the consensu
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