| This work illuminates the utility of a theory of locomotion rooted in geometric mechanics and nonlinear control. We regard the internal configuration of a deformable body, together with its position and orientation in ambient space, as a point in a trivial principal fiber bundle over the manifold of body deformations. We obtain connections on such bundles which describe the nonholonomic constraints, conservation laws, and force balances to which certain propulsors are subject, and construct and analyze control-affine normal forms for different classes of systems. We examine the applicability of results involving geometric phases to the practical computation of trajectories for systems described by single connections. We propose a model for planar carangiform swimming based on reduced Euler-Lagrange equations for the interaction of a rigid body and an incompressible fluid, accounting for the generation of thrust due to vortex shedding through controlled coupling terms. We investigate the correct form of this coupling experimentally with a robotic propulsor, comparing its observed behavior with that predicted numerically. |
