A Dataset and Benchmark for Learning the Kinematics of Concentric Tube Continuum Robots

Establishing a physics-based model capturing the kinetostatic behavior of concentric tube continuum robots is challenging as elastic interactions between the flexible tubes constituting the robot result in a highly non-linear problem. The Goldstandard physics-based model using the Cosserat theory of elastic rods achieves reasonable approximations with 1.5 - 3 % with respect to the robot's length, if well-calibrated. Learning-based models of concentric tube continuum robots have been shown to outperform the Goldstandard model with approximation errors below 1 %. Yet, the merits of learning-based models remain largely unexplored as no common dataset and benchmark exist. In this paper, we present a dataset captured from a three-tube concentric tube continuum robot for use in learning-based kinematics research. The dataset consists of 100 000 joint configurations and the corresponding four 6 dof sensors in SE(3) measured with an electromagnetic tracking system (github.com/ContinuumRoboticsLab/CRL-Dataset-CTCR-Pose). With our dataset, we empower the continuum robotics and machine learning community to advance the field. We share our insights and lessons learned on joint space representation, shape representation in task space, and sampling strategies. Furthermore, we provide benchmark results for learning the forward kinematics using a simple, shallow feedforward neural network. The benchmark results for the tip error are 0.74 mm w.r.t. position (0.4 % of total robot length) and 6.49° w.r.t. orientation.