Formation Control of Leader-Following Multi-UUVs With Uncertain Factors and Time-Varying Delays

Abstract

This paper is concerned with the multi-UUVs formation control problem and proposes the control protocol with an additional function when considering environmental disturbances. Firstly, the leaderfollowing configuration is adopted to discuss the consensus problem for multi-UUVs system, the leader's behavior directs the follower's motion trajectory and the follower UUVs could, in turn, communicate with each other, respectively. Secondly, three types of coordination control protocols are proposed: the control protocol is designed without additional function and time delay; the control protocol with additional function and without time delay; the control protocol with additional function and time-varying delay. Sufficient consensus conditions are analyzed and derived by using the Lyapunov-Krasovskii functional theory, algebraic graph theory and matrix theory. Finally, two simulation experiments are given to illustrate the effectiveness of the proposed formation control methods. INDEX TERMS Multiple unmanned underwater vehicles, leader-following consensus, uncertain factors, time-varying delays. I. INTRODUCTION In the past decades, with the development of artificial intelligence and new engineering techniques, the cooperation and coordination problems of multi-Unmanned Underwater Vehicles (multi-UUVs) system have been rapidly developed and widely studied due to its broad applications in military and commercial fields, especially in ocean-graphic observation, ocean exploration, plane crash searches, trajectory tracking, etc. Compared with a single UUV, multi-UUVs formation equipped with more sensors can accomplish more complex and larger-scale deep-sea missions with efficient and stable communications. It is worth mentioning that the researches on motion control of a single UUV are getting deeper in recent years, there are several control methods such as robust control [1], adaptive control [2] and fuzzy control approaches [3] in ocean engineering applications, but the above algorithms cannot well applied to the formation problem of multi-UUVs system. The basic problem of formation The associate editor coordinating the review of this article and approving it for publication was Nagarajan Raghavan.

Distributed Event-Based Control of Hierarchical Leader-Follower Networks with Time-Varying Layer-To-Layer Delays

“…In recent years, coordination problems of multi-agent systems (MAS) have attracted research interests, which cover a wide area such as flocking [1,2], formation control [3][4][5], consensus tracking of a robot [6], and rendezvous in distributed robotics [7][8][9]. On these issues, many remarkable and significant results have emerged one after another.…”

Energy-Limited Time-Varying Formation Control for Second-Order Multiagent Systems

“…Jia et al [28] investigated the three-dimensional leaderless flocking problem and proposed a simplified distributed control algorithm, which was verified by the LaSalle-Krasovskii invariance principle. Furthermore, the leader-following formation aroused much attention in [29][30][31][32][33], where followers tracked the leader and maintained a specified formation with it. Considering the condition of uncertain factors and time delay, the leader-follower collaborative formation was achieved for the multi-unmanned underwater vehicle formation in [32].…”

“…Furthermore, the leader-following formation aroused much attention in [29][30][31][32][33], where followers tracked the leader and maintained a specified formation with it. Considering the condition of uncertain factors and time delay, the leader-follower collaborative formation was achieved for the multi-unmanned underwater vehicle formation in [32]. e time-varying protocol of second-order leader-following MAS was obtained in [33] through solving an algebraic Riccati equation.…”

“…In this case, the desired formation structure not only must be formed but also the practical energy consumption of the time-varying formation is less than the given energy, where the practical energy is a performance index function composed of the quadratic form of the control protocol. However, the formation control problem in [32][33][34] did not consider energy limitation. Secondly, in the process of solving the control gain, the numerical solution solved by Matlab's LMI Toolbox is replaced by a feasible analytical solution, so it is not needed to verify the feasibility of the solution.…”

“…Secondly, in the process of solving the control gain, the numerical solution solved by Matlab's LMI Toolbox is replaced by a feasible analytical solution, so it is not needed to verify the feasibility of the solution. In [32][33][34], the control gains were obtained by the LMI Toolbox instead of the analytical solution. irdly, the critical contribution is that a two-step transformation method is presented so as to transform the whole Laplacian matrix into the dimensionlowering diagonal matrix; in this case, the leaderless and leader-following communication topologies are unified into the identical multiagent system framework.…”