Learning-based Inverse Kinematics from Shape as Input for Concentric Tube Continuum Robots

We introduce a methodology to compute the inverse kinematics for concentric tube continuum robots from a desired shape as input. We demonstrate that it is possible to accurately learn joint parameters using neural networks for a discrete point-wise shape representation with different discretization. In comparison to a vanilla numerical method, the learning-based method is preferred in terms of accuracy in joint space and computation. Representing the shape with up to 20 equidistant points, a shape-to-joint inverse kinematics with errors of 2.22 degrees and 1.45 ram is obtained. Further, we extend the shape-to-joint inverse kinematics to image-to-joint inverse kinematics utilizing multi-view images as shape representation. This image-based method achieves errors of 6.02 degrees and 2.76 mm. Roth approaches, i.e., shape-to-joint and image-to-joint, result in higher accuracy compared to the learning-based state-of-the-art approach which only considers the tip pose.