Parallel Transport Frame for Fiber Shape Sensing

This paper reports a reconstruction method to determine a 3-D space curve from the distributed strain by using the parallel transport frame. Parallel transport frame can efficiently eliminate the singularities and discontinuous point which appear in another existing commonly used reconstruction method Frenet Frame and thus improve the accuracy and stability of the shape sensing. To validate this method, a simulation method based on the rotation minimizing frame is proposed and used. It provides a general procedure to numerically obtain the strain distribution with a certain configuration of the shape sensor and spatial shape. Some typical space curves whose space position is analytically given are reconstructed by two reconstruction methods and the results are compared. The error sources of the reconstruction method are also analyzed.