  Knowing the state of a robot is critical for many problems, such as feedback
control. For continuum robots, state estimation is an incredible challenge.
First, the motion of a continuum robot involves many kinematic states,
including poses, strains, and velocities. Second, all these states are
infinite-dimensional due to the robot's flexible property. It has remained
unclear whether these infinite-dimensional states are observable at all using
existing sensing techniques. Recently, we presented a solution to this
challenge. It was a mechanics-based dynamic state estimation algorithm, called
a Cosserat theoretic boundary observer, which could recover all the
infinite-dimensional robot states by only measuring the velocity twist of the
tip. In this work, we generalize the algorithm to incorporate tip pose
measurements for more tuning freedom. We also validate this algorithm offline
using experimental data recorded from a tendon-driven continuum robot. We feed
the recorded tendon force and tip measurements into a numerical solver of the
Cosserat rod model based on our robot. It is observed that, even with purposely
deviated initialization, the state estimates by our algorithm quickly converge
to the recorded ground truth states and closely follow the robot's actual
motion.
