A geometric approach to anguilliform locomotion: modelling of an underwater eel robot

In this paper, we approach the modeling, simulation, and control of snake and eel-like robots from a geometric perspective. We propose basic viscous and fluid drag models to capture the effect of external forces acting on the bodies of land-based snakes and aquatic eels, respectively. Using these models, we show that the dynamics can be decomposed into motions in the position and orientation of the overall system and changes in its internal shape. This allows us to write reduced dynamics for the serpentine and swimming motions that isolate the effect of shape changes on the momentum of the system. We explore in simulation several types of locomotive gaits, and report qualitative experimental results that provide validation for these simulations.