Synthesis of autonomous periodic motion of a small blimp system using the van der Pol equation

In this paper, we develop a method to realize an autonomous periodic motion of a small blimp system in a horizontal plane. The idea behind the method is to make the dynamics of a small blimp system approach asymptotically to that of the van der Pol equation that has a limit cycle. The method consists of the following two steps: First, we introduce two constraints. One has a role to connect the motion equation of a small blimp system with the van der Pol equation, and the other has a role to divide the coupled system into two independent systems. Second, we design an output stabilizing controller for each of two independent systems, so that the two constraints are fulfilled.