A fast torsionally compliant kinematic model of concentric-tube robots

Concentric-tube robots have the potential to become an important surgical tool for robot-assisted percutaneous interventions. They can provide dexterous operation in a small constrained environment. The kinematic model of a concentric-tube robot has been well developed in terms of accuracy, but the computational cost places limitations on real-time implementation. In this paper, we propose a new technique that will substantially improve the computational efficiency of evaluating the kinematics of a concentric-tube robot in the context of developing a control strategy without sacrificing the accuracy of the results. In this paper we develop a torsionally compliant kinematic model using global variables. The model is validated by comparing the results obtained by computing the kinematic model corresponding to an experimental setup of a concentric-tube robot to which a force/torque sensor has been mounted at its base with those obtained directly from the experimental setup. The results indicate that it is feasible to compute the kinematics of the concentric-tube robot fast enough to allow the position/force control loop to be implemented at a rate of 1 kHz.