Unbound Multi-Core Fiber Shape Sensing via Frenet-Serret Curve Fitting
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Solution Overview
Problem
Conventional fiber optic shape sensing methods are error-prone due to the dependency on accurate strain measurements, which are prone to errors when calculating bending parameters, especially when the fiber optic cable twists, leading to less than optimal shape determination of objects.
Innovation Solution
A method and apparatus that utilize the natural torsion of an unbound multi-core optical fiber, applying Frenet-Serret formulas and curve fitting to strain data from sensors like Fiber Bragg Gratings, to accurately determine the 3D shape and end position by minimizing strain measurement errors and accounting for torsion, allowing the fiber to act as an elastic tube.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional fiber optic shape sensing methods using successive strain measurements are used, then shape determination can be achieved, but measurement errors accumulate leading to reduced accuracy
Solution Approach 1:
The patent extracts and eliminates the source of error accumulation by removing the successive/iterative calculation approach. Instead of calculating bending parameters sequentially from one segment to the next (which accumulates errors), the invention directly fits a continuous curve to all strain measurements simultaneously, extracting the true shape without propagating errors through multiple calculation steps.
Solution Approach 2:
The patent implements feedback by using the complete set of strain measurements from all cores to continuously refine and verify the fitted curve. The system constantly compares the fitted curve predictions against actual measurements across the entire fiber length, adjusting parameters to minimize overall error rather than accepting cumulative errors from sequential calculations.
2Strength
If the fiber optic cable is bound or bonded to a protective jacket, then mechanical protection is provided, but natural torsion is constrained leading to increased measurement errors
Solution Approach 1:
The patent segments the protective system by introducing an unbound section of the fiber optic cable where the fiber is separated from the protective jacket. This unbound segment allows natural torsion and bending without constraint from the jacket, providing accurate shape sensing in this region while the bound sections at the ends continue to provide mechanical protection and anchoring.
Solution Approach 2:
The patent applies different qualities to different sections of the fiber cable: the end sections remain bound to the protective jacket for mechanical strength and protection, while the middle sensing section is unbound to allow natural torsion. This local differentiation optimizes both protection and measurement accuracy in their respective zones.
3Adaptability or versatility
If multi-core fiber is used to improve shape sensing capability, then additional utility is gained, but complexity of the system increases
Solution Approach 1:
The patent makes the multi-core fiber system universal by using all cores for the same primary function of shape sensing through a unified curve fitting approach. Rather than assigning different specialized functions to different cores, the invention uses all cores simultaneously to measure bending in different orientations, providing comprehensive 3D shape sensing capability through a single integrated mathematical model.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach significantly reduces measurement errors and provides a more accurate determination of the 3D shape and end position of the fiber optic cable and connected objects by leveraging the fiber's natural torsion and elastic behavior, improving upon the limitations of conventional methods.
Implementation Method 1
sensors known as Fiber Bragg Gratings can be formed by laser-inscribing, writing, or otherwise embedding a periodic variation of refractive index into the cores of the optical fiber, thus effectively creating an in-line optical filter designed to block particular wavelengths of light transmitted through or along the core
Implementation Method 2
Rayleigh scatter detectors can be used to detect elastic light scatter occurring within a core at specific axial locations of the optical fiber
Implementation Method 3
a single-core optical fiber has a single light-guiding core contained within the reflective cladding of the cable
Data Source
AI summary
A method of determining the shape of an unbound optical fiber includes collecting strain data along a length of the fiber, calculating curvature and bending direction data of the fiber using the strain data, curve-fitting the curvature and bending direction data to derive curvature and bending direction functions, calculating a torsion function using the bending direction function, and determining the 3D shape from the curvature, bending direction, and torsion functions. An apparatus for determining the 3D shape of the fiber includes a fiber optic cable unbound with respect to a protective sleeve, strain sensors positioned along the cable, and a controller in communication with the sensors. The controller has an algorithm for determining a 3D shape and end position of the fiber by calculating a set of curvature and bending direction data, deriving curvature, bending, and torsion functions, and solving Frenet-Serret equations using these functions.