Abstract
Abstract This paper presents a method for the cooperative formation control of a group of underactuated USVs. The problem of formation control is first converted to one of stabilisation control of the tracking errors of the follower USVs using system state transformation design. The followers must keep a fixed distance from the leader USV and a specific heading angle in order to maintain a certain type of formation. A global differential homeomorphism transformation is then designed to create a tracking error system for the follower USVs, in order to simplify the description of the control system. This makes the complex formation control system easy to analyse, and allows it to be decomposed into a cascaded system. In addition, several intermediate state variables and virtual control laws are designed based on nonlinear backstepping, and actual control algorithms for the follower USVs to control the surge force and yaw moment are presented. A global system that can ensure uniform asymptotic stability of the USVs’ cooperative formation control is achieved by combining Lyapunov stability theory and cascade system theory. Finally, several simulation experiments are carried out to verify the validity, stability and reliability of our cooperative formation control method.
Highlights
An unmanned surface vehicle (USV) is an intelligent autonomous surface vessel, of a type that has played an indispensable role in several fields such as science, economics and the military [1,2,3]
A method of cooperative formation control is proposed in this paper for a group of underactuated USVs based on nonlinear backstepping and cascade system theory
A novel description of the problem of cooperative formation control of a group of USVs is presented, and the desired positions and attitude angles of the follower USVs are transformed into intermediate variables that facilitate the design of the controller
Summary
An unmanned surface vehicle (USV) is an intelligent autonomous surface vessel, of a type that has played an indispensable role in several fields such as science, economics and the military [1,2,3]. The problem of cooperative formation tracking control of multiple USVs has attracted increasing amounts attention from researchers from all over the world over recent years, since a team of USVs working together is often more effective than a single vehicle for challenging missions such as surveillance, hydrographic surveys, autonomous exploration of ocean resources, reconnaissance, rescue operations and perimeter security [4,5,6] It is well-known that the control system of an USV is generally underactuated, since the number of control inputs is less than the degrees of freedom and there is an unintegrable acceleration constraint on the system. A new robust model predictive control (MPC) algorithm for trajectory tracking of an autonomous surface vehicle (ASV) in the presence of time-varying external disturbances was proposed in [5], and a high-performance super-twisting sliding mode control method for a maritime autonomous surface ship (MASS) using approximate dynamic programming (ADP)-based adaptive gains and time delay estimation was presented in [26]. The main contributions of this paper can be summarised as follows: (i) we present a novel description of the cooperative formation control problem for a group of USVs, in which the desired positions and attitude angles of the follower USVs are transformed into intermediate variables that can help in the design of the controller; (ii) we design a new kind of global differential homeomorphism transformation for the tracking error system of the follower USVs, which simplifies the description of the control system, making the complex formation control system easy to analyse and allowing it to be decomposed into a cascaded system; (iii) we propose an improved controller for the cooperative formation control of a group of underactuated USVs by combining a backstepping technique with Lyapunov’s direct method and cascade system theory, and devise some intermediate state variables and virtual control laws for the design process of the control algorithm
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