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.