Shape and Tip Force Estimation of Concentric Tube Robots Based on Actuation Readings Alone

Recent advances on Concentric Tube Robots (CTRs) enable the construction and analysis of concentric combinations of precurved elastic tubes. These robots are very appropriate for performing Minimally Invasive Surgery (MIS) with a reduction in patient recovery time. In this work, we propose a kinetostatic model for CTRs based on the Geometric Variable-Strain (GVS) approach where the tubes' sliding motion, the distributed external forces along the tubes and concentrated external forces at the tip, are included. Our approach allows us to estimate the shape of CTRs and the tip forces using the displacements of the tubes and the insertion and rotation input forces and torques. Moreover, we propose a modification in the model, which eliminates completely the sliding friction among the tubes. This new approach opens a new way to use CTRs in surgical applications without the need of sensors along the tubes, but only actuation measurements. The simulation results demonstrate the effectiveness of the proposed approach.