Control of an underwater biomimetic vehicle using Floquet theory

Aqua is an underwater biomimetic vehicle designed and built at McGill University that uses six paddles to produce control and propulsion forces. It has the particularity of having time-periodic thrust due to its oscillating paddles. Using an existing model of the vehicle, two types of controller were developed: a PD controller and a Floquet controller. The Floquet controller has the advantage of explicitly addressing the time-periodicity of the system. The performance of the controllers was assessed through simulation and experimentally in the Caribbean Sea. We find that the vehicle was able to follow the prescribed trajectories with relative accuracy using both controllers, though, the Floquet controller slightly outperforms the PD controller. Furthermore, a key advantage of the Floquet controller is that it requires no tuning while the PD controller had to be tuned by trial and error.