Leader–Follower Flocking of Multiple Robotic Fish

In this paper, we study cohesive flocking and formation flocking of multiple robotic fish swimming in the water surface under the guidance of only one leader with zero-value external input. Combining consensus algorithms and attraction/repulsion functions, a distributed flocking algorithm is proposed for the robotic fish system to execute the cohesive flocking task. According to the LaSalle-Krasovskii invariance principle, the proposed algorithm enables followers to asymptotically track the leader´s velocity and approach the equilibrium distances with their neighbors, provided that the initial interaction network of the system is a leader-follower connected graph. Furthermore, by adding the information of a desired formation topology to the potential function term, the proposed algorithm can be extended to solve arbitrarily shaped formation flocking problem of multiple robotic fish. The experimental results demonstrate that the proposed approaches are effective for three robotic fish. Finally, several simulation examples are given to verify the functionality of the proposed approaches for a larger system with ten agents.