Research on optical fiber shape reconstruction algorithm based on Bishop frame and Runge-Kutta method

As intelligent sensing technology advances in areas like smart morphing aircraft, precision medicine, and continuum robots, reconstruction accuracy in optical fiber shape sensing becomes increasingly important. This paper presents a shape reconstruction algorithm combining the Bishop frame with the Runge-Kutta method. The Runge-Kutta method significantly improves complex curve reconstruction accuracy. Experiments show that with a 5 mm sampling interval, the algorithm's error is 11.26 mm (1.13% of the total length). Compared to the Euler method, accuracy improves by 37%. In addition, this paper further validates the general applicability of the algorithm through simulations of cylindrical and conical helical curves. The algorithm effectively reduces error accumulation, especially with sparse sampling. This research supports the advancement of optical fiber shape sensing and highlights broad application potential.