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Formation control is an important behavior for multy agents system (swarm). This paper addresses the optimal tracking control problem for swarm whose agents are Dubin's airplane moving together in a specific geometry formation.

We study formation control of the swarm model which consist 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 Tracking error dynamics. The control of the leader is designed for tracking the desired path. We show that the tracking error of the path of the leader tracking a desired path is sufficiently small. The desired path is obtained using calculus variational method. After that, geometry approach is used to design the control of the leader. We show that the positioning and the orientation of each agent can be controlled dependent on the leader.

We also compute the tracking error of the path of the leader tracking a desired path is sufficiently small and the distance between the leader path and the desired path is preserved.

 

 

 

Figure 1. Three Dubin’s Airplane

 

Figure 1 shows the position of the three airplane. Where  and  are the distance of the follower airplane to the leader airplane.  and  are the orientation of the follower airplane to position of the leader airplane. In this paper, and  are assumed to be constant.

 

Calculus Variational, Dubin's Airplane, Model of Swarm, Numerical Simulation, Tracking Error.