  Compared with traditional rigid-body robots, soft robots not only exhibit
unprecedented adaptation and flexibility but also present novel challenges in
their modeling and control because of their infinite degrees of freedom. Most
of the existing approaches have mainly relied on approximated models so that
the well-developed finite-dimensional control theory can be exploited. However,
this may bring in modeling uncertainty and performance degradation. Hence, we
propose to exploit infinite-dimensional analysis for soft robotic systems. Our
control design is based on the increasingly adopted Cosserat rod model, which
describes the kinematics and dynamics of soft robotic arms using nonlinear
partial differential equations (PDE). We design infinite-dimensional state
feedback control laws for the Cosserat PDE model to achieve trajectory tracking
(consisting of position, rotation, linear and angular velocities) and prove
their uniform tracking convergence. We also design an infinite-dimensional
extended Kalman filter on Lie groups for the PDE system to estimate all the
state variables (including position, rotation, strains, curvature, linear and
angular velocities) using only position measurements. The proposed algorithms
are evaluated using simulations.
