Shape Estimation of Concentric Tube Robots Using Single Point Position Measurement

Accurate shape estimation of concentric tube robots (CTRs) using mathematical models remains a challenge, reinforcing the need to develop techniques for accurate and real-time shape sensing of CTRs. In this paper, we develop a fusion algorithm that predicts the robot's shape by combining a mathematical model of the CTR with a measurement of the Cartesian coordinates of the robot's tip using an electro-magnetic sensor. We experimentally validated our method in static and dynamic scenarios with and without external loading. Results demonstrated that the fusion algorithm improves the error of model-based shape prediction by an average of 44.3%, corresponding to 2.43% of the robot's arc length. Furthermore, we demonstrate that our method can be used in real-time to simultaneously track the robot's tip position and predict its shape.