Collective Motion of Robotic Fish Synchronized with Antiphases

The study of design principles for individual robotic fish can be traced back to at least the early 1990’s. More recently, different central pattern generator (CPG) models have been utilized to control the locomotions of robotic fish and some results have been reported to use proper sensing and planning to control multiple robotic fish. However, less effort has been made to study how robotic fish can bene- fit from collective hydrodynamics they generate while they are swimming together cooperatively. It was first pointed out by Weihs [2] that diamond-shape formations with antiphase body waves are hydrodynamically advantageous for fish to improve propulsion efficiency while cruising (Fig.1). In this paper, we design distributed control laws for teams of robotic fish to lock the phases of their sinusoidal body waves in an antiphase fashion. We model the phase dynamics of the body waves of the robotic fish by coupled Kuramoto oscillators. We prove that when such phase dynamics are coupled through real-time communications with a diamond-shape topology, they can be synchronized with the desired relative phase differences of zero or π to mimic the fish swimming patterns predicted in the corresponding biological studies.