Continuum robot state estimation using Gaussian process regression on SE(3)

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