Planar Formation Control of a School of Robotic Fish

This paper presents a nonlinear control design for the stabilization of parallel and circular motion in a model school of robotic fish. The closed-loop swimming dynamics of the fish robots are represented by the canonical Chaplygin sleigh-a nonholonomic mechanical system driven by an internal rotor. The fish robots exchange relative state information according to a connected, undirected communication graph and form a system of coupled, nonlinear, second-order oscillators. Prior work on collective motion of constant-speed, self-propelled particles serves as the foundation of our approach. However, unlike the self-propelled particle, the fish robots follow limit-cycle dynamics to sustain periodic flapping for forward motion with a varying speed. Parallel and circular motions are achieved in an average sense. The proposed control laws do not include feedback linearization of the agents' dynamics. Numerical simulations illustrate the approach.