The International Journal of Robotics Research, 41(13-14):1099-1120, 2022
Abstract
Continuum robots have the potential to enable new applications in medicine, inspection, and countless other areas due to
their unique shape, compliance, and size. Excellent progess has been made in the mechanical design and dynamic modelling
of continuum robots, to the point that there are some canonical designs, although new concepts continue to be explored.
In this paper, we turn to the problem of state estimation for continuum robots that can been modelled with the common
Cosserat rod model. Sensing for continuum robots might comprise external camera observations, embedded tracking coils or
strain gauges. We repurpose a Gaussian process (GP) regression approach to state estimation, initially developed for
continuous-time trajectory estimation in SE(3). In our case, the continuous variable is not time but arclength and we
show how to estimate the continuous shape (and strain) of the robot (along with associated uncertainties) given
discrete, noisy measurements of both pose and strain along the length. We demonstrate our approach quantitatively
through simulations as well as through experiments. Our evaluations show that accurate and continuous estimates of a
continuum robot's shape can be achieved, resulting in average end-effector errors between the estimated and ground truth
shape as low as 3.5 mm and 0.016 deg in simulation or 3.3 mm and 0.035 deg for unloaded configurations and 6.2 mm and 0.041 deg
for loaded ones during experiments, when using discrete pose measurements.