The Mechanics and Control of Robotic Locomotion with Applications to Aquatic Vehicles

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Scott D. Kelly
PhD Dissertation, Caltech, June 1998

This work illuminates 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.