SCIENCE CHINA Information Sciences, Volume 60, Issue 7: 070203(2017) https://doi.org/10.1007/s11432-016-9091-8

## Saturated coordinated control of multiple underactuated unmanned surface vehicles over a closed curve

• AcceptedApr 23, 2017
• PublishedJun 9, 2017
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### Abstract

This paper presents a design method for saturated coordinated control of multiple underactuated unmanned surface vehicles (USVs) on a closed curve,holding a symmetric formation pattern. Each vehicle is subject tounknown sideslip, uncertain vehicle kinetics, and limited control torques.First, the course angle and surge velocity are considered as immediate signals to stabilize the along-track and cross-track path following errors. In the vehicle kinematics, a reduced-order extended state observer is utilized to compensate for the effect of the unknown sideslip. Next, a bounded neural network control law is constructed at the kinetic level with the aid of the a saturated function, a projection operator, and a dynamic surface design method. Finally, a parameter cyclic pursuit approach is presented to guarantee that the vehicles are evenly spaced over the closed curve for achieving a symmetric formation pattern. The input-to-state stability of the closed-loop system is analyzedvia cascade theory. Comparative studies are given to show the effectiveness of the proposed method.

### Acknowledgment

This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61673081, 51579023), China Postdoctoral Science Foundation (Grant No. 2015M570247), Fundamental Research Funds for the Central Universities (Grant No. 3132016313), National Key Research and Development Program of China (Grant No. 2016YFC0301500), and High Level Talent Innovation and Entrepreneurship Program of Dalian (Grant No. 2016RQ036).

• Figure 1

(Color online) A geometrical illustration of LOS guidance.

• Figure 2

(Color online) Communication topology.

• Figure 3

Communication topology.

• Figure 4

(Color online) Path following performance.

• Figure 5

(Color online) Tracking errors. (a) Along-track errors; (b) cross-track errors.

• Figure 6

(Color online) The estimation performance of neural networks. (a) The estimation of $\bar{f}_{1u}$ ($\text{bar}f_{1u}=\bar{f}_{1u}$); protectłinebreak (b) the estimation of $\bar{f}_{1r}$ ($\text{bar}f_{1r}=\bar{f}_{1r}$).

• Figure 7

(Color online) Comparisons of control inputs using different methods. (a) Control inputs of the control method in [41]; (b) control inputs of the proposed method.

• Figure 8

(Color online) Comparisons of tracking errors.

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