  This paper discusses modelling, controllability and gait design for a
spherical flexible swimmer. We first present a kinematic model of a low
Reynolds number spherical flexible swimming mechanism with periodic surface
deformations in the radial and azimuthal directions. The model is then
converted to a finite dimensional driftless, affine-in-control principal
kinematic form by representing the surface deformations as a linear combination
of finitely many Legendre polynomials. A controllability analysis is then done
for this swimmer to conclude that the swimmer is locally controllable on
$\mathbb{R}^3$ for certain combinations of the Legendre polynomials. The rates
of the coefficients of the polynomials are considered as the control inputs for
surface deformation. Finally, the Abelian nature of the structure group of the
swimmer's configuration space is exploited to synthesize a curvature based gait
for the spherical flexile swimmer and a rigid-link swimmer.
