Viscous phenomena can be used to aid in the locomotion and control of robotic systems. With the aid of Lagrangian reduction techniques, it is shown that dissipation can be used to model nonholonomic, holonomic, and kinematically constrained systems. This is shown theoretically, analytically, and numerically for a class of robotic systems. Using techniques from geometric mechanics, control problems for novel planar robots that incorporate nonholonomic constraints, dissipation, and geometric phase are explored. A robotic fish is introduced, and experiments demonstrate it can harvest energy from fluid vortices to assist in propulsion, consistent with geometric models in the literature. Experimental fluid vortices are also generated and characterized with the aid of particle image velocimetry.