The Mechanics and Control of Robotic Locomotion with Applications to Aquatic Vehicles
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.
Thesis
(PDF, 924K, 123 pages)
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