The Control Design of Ship Formation with the Presence of a Leader

Abstract

Formation control is an important behavior for multi-agents system (swarm). This paper addresses the optimal tracking control problem for swarm whose agents are ships moving together in a specific geometry formation. We study formation control of the swarm model which consists of three agents and one agent has a role as a leader. The agents of swarm are moving to follow the leader path. First, we design the control of the leader with Pontryagin Maximum Principle. The control of the leader is designed for tracking the desired path. We show that the tracking error of the path of the leader tracing a desired path is sufficiently small. After that, geometry approach is used to design the control of the other. We show that the positioning and the orientation of each agent can be controlled dependent on the leader. The simulation results show to illustrate of this method at the last section of this paper.