Fixed-time adaptive distributed cooperative formation control for multiple unmanned surface vessels

Abstract

Compared with a single unmanned surface vessel (USV), multiple USVs have the advantages of strong maneuverability, high reliability, and low cost. Multiple USVs have potential oceanic transportation, resource exploration, and maritime rescue applications. However, cooperative formation control of multiple USVs is a significant yet challenging problem. The main difficulties arise from the limited communication and the existence of model uncertainties and external perturbations. Therefore, this paper proposes a fixed-time adaptive distributed control strategy consisting of a fixed-time distributed observer and local controller for cooperative formation control of multiple USVs under local communication in complex marine environment. First, a fixed-time distributed observer is constructed for each follower USV to estimate the virtual leader’s position and velocity in fixed time by considering that only a portion of follower USVs can directly access the state information from the virtual leader. Based on the estimated information, a fixed-time local controller is designed for each follower USV to track the desired trajectory generated by the virtual leader in a fixed time using the backstepping method. In particular, in the local controller design process, a parameter adaptive mechanism is introduced to estimate the square of the upper bound of the lumped disturbance term, including model uncertainty and external disturbance to compensate for them. Thus, the proposed controller is smooth to guarantee the control accuracy, and the chattering phenomenon can be avoided simultaneously. Stability analysis of the proposed fixed-time observer and local controller is also presented. Mathematical proofs show that the proposed observer and controller can ensure that each USV can complete the position estimation and virtual leader velocity in a fixed time, thereby making the tracking error converge to the zero neighborhood in a fixed time. Finally, USVs with the proposed control strategy can follow the virtual leader and maintain the formation as shown in the simulation. Additionally, a comparative simulation is designed, where the control performance of the proposed strategy is compared with that of the commonly used PD controller under the same condition. The simulation results show that the proposed controller has superior control accuracy and convergence rate in controlling the USVs to track the desired position and velocity of the demanded formation. Moreover, the chattering phenomenon of the control inputs is significantly suppressed.

Keywords

• multiple unmanned surface vessels
• cooperative formation control
• distributed control
• fixed-time control
• adaptive control