Adaptive Nonparametric Kinematic Modeling of Concentric Tube Robots

Concentric tube robots comprise telescopic precurved elastic tubes. The robot's tip and shape are controlled via relative tube motions, i.e. tube rotations and translations. Non-linear interactions between the tubes, e.g. friction and torsion, as well as uncertainty in the physical properties of the tubes themselves, e.g. the Young's modulus, curvature, or stiffness, hinder accurate kinematic modelling. In this paper, we present a machine-learning-based methodology for kinematic modelling of concentric tube robots and in situ model adaptation. Our approach is based on Locally Weighted Projection Regression (LWPR). The model comprises an ensemble of linear models, each of which locally approximates the original complex kinematic relation. LWPR can accommodate for model deviations by adjusting the respective local models at run-time, resulting in an adaptive kinematics framework. We evaluated our approach on data gathered from a three-tube robot, and report high accuracy across the robot's configuration space.