Flexible optical fiber bend sensor and bend estimation model thereof

Abstract

The application discloses a flexible optical fiber bending sensor and a bending estimation model thereof. The bending sensor comprises a sensing unit, and a plurality of sensing units can be connected in a head-to-tail mode for use. The sensing unit comprises a flexible member, a segmented optical fiber and at least one pair of elastic wires are arranged along the length direction of the flexible member, both ends of the flexible member are provided with circuit boards, the circuit boards are connected with the elastic wires, the outer side of the circuit board is provided with a fastener, the end of the segmented optical fiber penetrates through the fastener, the outer side of the fastener is provided with an electric connector, the electric connector is electrically connected with the circuit board through the fastener, the circuit board at the head end is provided with a light emitting member, and the fastener at the head end is provided with a prism. The sensing unit has the combination capability of being connected in a head-to-tail mode. The sensing unit can be flexibly adapted by increasing or reducing the number of sensing units, so that the application cost and development cycle can be reduced, and the expansibility of the sensing unit is improved.

Description

Technical Field

[0001] This application relates to the field of fiber optic sensor technology, and in particular to a flexible fiber optic bending sensor and its bending estimation model. Background Technology

[0002] With the rapid development of wearable electronic devices, smart healthcare, and soft robotics, the demand for high-performance flexible sensors capable of real-time monitoring of human movement and environmental conditions continues to grow. Compared to traditional rigid sensors, flexible sensors offer several advantages, such as excellent mechanical compliance, lightweight structure, and compatibility with curved surfaces. These characteristics make them particularly suitable for non-invasive motion tracking and environmental sensing in various applications. Among various types of flexible sensors, flexible bending sensors have become a core category due to their ability to convert curvature or deformation into measurable signals, enabling quantitative tracking of joint kinematics and soft structure deformation. Their working principle is typically based on changes in resistance or optical response caused by mechanical action, converting geometric strain into readable output. With their lightweight structure, high compliance, and adaptability, these sensors are particularly suitable for wearable health monitoring, soft robot drive systems, and human-machine interface systems.

[0003] In numerous emerging application areas, traditional single-channel flexible bending sensors are increasingly unable to meet the distributed deformation information acquisition requirements of complex dynamic systems. For example, applications such as human joint motion monitoring and proprioceptive sensing in soft robotic platforms essentially require acquiring spatially resolved bending signals from multiple deformation points. These scenarios typically involve wide-ranging, continuous, and heterogeneous mechanical deformations, characteristics that a single sensing node cannot accurately characterize. This trend presents significant challenges to sensing systems, particularly in terms of channel scalability, wiring complexity, modular integration, and signal decoupling. Currently, most mainstream multi-channel flexible sensing systems employ a one-to-one wiring architecture, with each sensing unit equipped with a dedicated driver and readout channel. Electronic multiplexers (MUX) achieve scalable multi-channel readout through time-division multiplexing (TDM) technology, addressing multiple sensing channels sequentially via shared interconnect lines. However, MUX-based architectures require additional switching networks and control circuitry, leading to increased hardware costs and power consumption. Array-based architectures offer another solution to improve channel density, typically using row-column addressing to reduce the wiring count from N×M to N+M. Despite their structural differences, both architectures employ a shared circuit topology. This design inherently introduces parasitic paths, leading to crosstalk, signal attenuation, and reduced measurement accuracy. In conclusion, achieving modular deployment and integration of multi-channel flexible bending sensors while avoiding significant hardware overhead remains a core bottleneck in the development of next-generation soft electronics and intelligent sensing systems.

[0004] Using light as a sensing medium offers several inherent advantages over traditional electrical sensing. First, optical signals are virtually unaffected by electromagnetic interference, achieving high signal-to-noise ratios and stable operation even in complex or electromagnetically harsh environments. Furthermore, optical fibers combine low transmission loss with high bandwidth, enabling highly sensitive and high-resolution measurements of mechanical deformation. Optical sensing is inherently a passive technology—no current flows through the sensing element, thus enhancing operational safety. Moreover, the lightweight and flexible nature of optical fibers allows for seamless integration into flexible electronic devices, soft robotic systems, and wearable platforms. Overall, optical sensing, with its superior anti-interference capabilities, excellent transmission characteristics, high sensitivity, and system-level scalability, has become an ideal medium for realizing multi-point, distributed, and flexible sensing. Among existing optical sensing technologies, methods based on fiber Bragg gratings (FBGs) have become one of the most widely adopted solutions for distributed deformation sensing. Despite these inherent advantages of optical media, key limitations remain in related systems: Specifically, FBG sensing achieves wavelength division multiplexing (WDM) sensing through wavelength-selective Bragg reflection, enabling scalable multi-point measurements over a single fiber. However, FBG-based systems require high-precision wavelength demodulation units and expensive optical components, which not only increases the complexity of fiber optic cabling but also limits the scalability of fiber optic sensing systems. Summary of the Invention

[0005] The main technical problem addressed by this application is to provide a flexible optical fiber bending sensor, which solves the problems of complex optical fiber cabling and poor scalability.

[0006] To address the aforementioned technical problems, this application provides a flexible optical fiber bending sensor, comprising sensing units, multiple of which can be connected end-to-end for combined use. Each sensing unit includes a flexible component, with segmented optical fibers and at least one pair of elastic conductors passing through it along its length. The segmented optical fibers are located on the axis of the flexible component and comprise multiple fiber segments. If the sensing unit bends, an air cavity exists between adjacent fiber segments. Circuit boards are provided at both ends of the flexible component, connected to the elastic conductors. Fasteners are provided on the outer side of the circuit boards, with the ends of the segmented optical fibers passing through the fasteners. Electrical connectors are provided outside the fasteners, passing through them and electrically connecting to the circuit boards. A light-emitting element is provided on the circuit board at the first end, and a prism is located within the fastener at the first end. The prism refracts the light emitted by the light-emitting element onto the segmented optical fibers.

[0007] The beneficial effects of this application are as follows: The sensing unit of this application has a modular capability that can be connected end-to-end. Each sensing unit, as an independent functional module, has electrical connectors and matching fasteners at both ends. For short-distance, small radius of curvature measurement scenarios, a single sensing unit can be used; for long-distance or large-scale deformation monitoring, multiple sensing units can be connected to extend the measurement length. During use, there is no need to customize dedicated sensors for different ranges; simply increasing or decreasing the number of sensing units allows for flexible adaptation, thereby reducing application costs, shortening the development cycle, and improving the scalability of the sensing unit. Simultaneously, the segmented structure facilitates fault location and maintenance; only damaged sensing units need to be replaced, avoiding complete scrapping. Each sensing unit completes signal and power transmission between the two circuit boards through only a pair of elastic wires. Furthermore, the segmented optical fiber itself requires no additional leads; the optical signal is transmitted along the segmented optical fiber, and the circuit signal is transmitted along the elastic wires, both integrated within the same flexible component. This allows the sensor unit to be connected to the outside world through only one electrical connector, thereby reducing the complex multi-point wiring into a simple serial link and significantly reducing the number of external wiring harnesses. Attached Figure Description

[0008] Figure 1 This is a schematic diagram of the structure of a sensing unit according to an embodiment of this application;

[0009] Figure 2 This is a schematic diagram of the manufacturing process of a sensing unit according to an embodiment of this application;

[0010] Figure 3 This is a schematic diagram of a driving circuit according to an embodiment of this application;

[0011] Figure 4 This is a schematic diagram of the impedance-frequency curves of a series LC network with different resonant frequencies according to an embodiment of this application;

[0012] Figure 5 This is a schematic diagram of the light attenuation sensing principle according to an embodiment of this application;

[0013] Figure 6 This is a schematic diagram of the three stages of a bending sensor according to an embodiment of this application;

[0014] Figure 7 This is a schematic diagram illustrating the selective activation of a sensor at different stages according to an embodiment of this application;

[0015] Figure 8 This is a schematic diagram of a sensing system according to an embodiment of this application;

[0016] Figure 9 This is a schematic diagram illustrating the performance characteristics of a sensing unit according to an embodiment of this application;

[0017] Figure 10This is a schematic diagram of the performance of a sensing unit according to an embodiment of this application;

[0018] Figure 11 This is a schematic diagram of an attitude monitoring experiment according to an embodiment of this application;

[0019] Figure 12 This is a schematic diagram illustrating the verification results of a bending sensor and optical motion capture system according to an embodiment of this application. Detailed Implementation

[0020] To enable those skilled in the art to better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0021] It should be noted that when a component is referred to as being "fixed to" or "set on" another component, it can be directly on or indirectly set on the other component; when a component is referred to as being "connected to" another component, it can be directly connected to or indirectly connected to the other component.

[0022] It should be understood that the terms "length", "width", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "vertical", "top", "bottom", "inner", and "outer" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or component referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application.

[0023] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "multiple" or "several" means two or more, unless otherwise explicitly specified.

[0024] It should be noted that the structures, proportions, sizes, etc., shown in the accompanying drawings of this specification are only used to complement the content disclosed in the specification for those skilled in the art to understand and read, and are not intended to limit the conditions under which this application can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and purposes that this application can produce, should still fall within the scope of the technical content disclosed in this application.

[0025] Figure 1 - Figure 12 An embodiment of the flexible fiber optic bending sensor of this application is shown, including a sensing unit, multiple sensing units can be connected end to end for combined use; the sensing unit includes a flexible member 1, with segmented optical fibers 2 and at least one pair of elastic wires 3 passing through it along the length of the flexible member 1. The segmented optical fibers 2 are located on the axis of the flexible member 1, and the segmented optical fibers 2 include multiple optical fiber segments 21. If the sensing unit bends, there is an air cavity 22 between adjacent optical fiber segments 21; both ends of the flexible member 1 are provided with circuit boards 4, the circuit boards 4 are connected to the elastic wires 3, the outer side of the circuit boards 4 is provided with fasteners 5, the ends of the segmented optical fibers 2 pass through the fasteners 5, the outer side of the fasteners 5 is provided with electrical connectors 6, the electrical connectors 6 pass through the fasteners 5 and are electrically connected to the circuit boards 4, the circuit board 4 at the first end is provided with a light-emitting element 9, and the fastener 5 at the first end is provided with a prism 7, the prism 7 is used to refract the light emitted by the light-emitting element 9 onto the segmented optical fibers 2.

[0026] The sensing units in this application have the capability of being connected end-to-end. Each sensing unit can function as an independent functional module, with electrical connectors 6 and matching fasteners 5 at both ends. For short-distance, small radius of curvature measurement scenarios, a single sensing unit can be used; for long-distance or large-scale deformation monitoring, multiple sensing units can be connected to extend the measurement length. During use, there is no need to customize dedicated sensors for different ranges; simply increasing or decreasing the number of sensing units allows for flexible adaptation, thereby reducing application costs and development cycles, and improving the scalability of the sensing units. Simultaneously, the independent structure of the sensing units facilitates fault location and repair; only damaged sensing units need to be replaced, avoiding complete scrapping. Each sensing unit completes signal and power transmission between the two circuit boards 4 via only a pair of elastic wires 3. Furthermore, the segmented optical fiber 2 itself requires no additional leads; the optical signal is transmitted along the segmented optical fiber 2, and the circuit signal is transmitted along the elastic wires 3, both integrated within the same flexible component 1. This allows the sensor unit to be connected to the outside world through only one electrical connector 6, thereby reducing the complex multi-point wiring into a simple serial link and significantly reducing the number of external wiring harnesses.

[0027] Segmented optical fibers 2 are threaded along the axis inside the sensing unit. When the flexible component 1 bends, the optical fiber segments 21 at the axis will undergo relative displacement due to the bend. Compared with traditional continuous optical fiber sensors, the optical coupling efficiency between the optical fiber segments 21 is more sensitive to bending deformation. Even a slight bend can lead to a significant change in the distance between the end faces or the centering deviation, thereby causing a significant modulation of the transmitted light intensity. This can improve the bending sensitivity of the sensor and detect more subtle curvature changes. The elastic conductor 3 has good flexibility and tensile strength, and can adapt to repeated bending of the flexible component 1 without breakage or poor contact. Compared with rigid conductors, the elastic conductor 3 can maintain stable conductivity under dynamic bending scenarios.

[0028] In some embodiments, the end with the prism 7 is designated as the head end of the sensing unit, and the opposite end as the tail end. Light emitted by the light-emitting element 9 can enter the segmented optical fiber 2 through the prism 7. The bending sensor can have a groove or protrusion on the fastener 5 at the head end and a corresponding protrusion or groove on the fastener 5 at the tail end. The tail end of one sensing unit is connected to the head end of another sensing unit through the interference fit between the protrusion and the groove.

[0029] In some embodiments, a connector 8 is provided on the outer side of the fastener 5. The connector 8 is used to connect the tail end of one sensing unit to the head end of another sensing unit. The connector 8 can be an interference fit of a protrusion and a groove.

[0030] In some embodiments, the connector 8 is a magnetic component, which is sleeved around the fastener 5. A magnetic component refers to any magnet or metal that can attract ferrite magnets, AlNiCo magnets, rare earth magnets, or similar magnets.

[0031] In some embodiments, the connector 8 is a ring magnet. This reduces the size of the sensing unit and facilitates quick connection between sensing units.

[0032] In some embodiments, the electrical connector 6 includes a male connector and a female connector, the male connector being insertable into the female connector and electrically connected to the female connector. The male connector is disposed on the fastener 5 at the beginning, and the female connector is disposed on the fastener 5 at the end, the female connector at the end being electrically connected to the male connector of another sensing unit.

[0033] In some embodiments, the electrical connector 6 can be a spring probe, which includes a male and a female. A spring is provided inside the male, which can press the end of the male into the female, thereby improving the stability of the electrical connection between the sensing units.

[0034] Figure 1Image (a) shows the structure of one of the sensing units. The sensing unit uses a colored silicone shell as a flexible component, providing both mechanical protection and structural flexibility. Two elastic wires are embedded within the silicone shell as an electrical interface bus, and segmented optical fibers are used to transmit optical signals. Each sensing unit is also equipped with two ring magnets, two fasteners, and two pairs of spring probes. The circuit boards (PCBs) at both ends of the sensing unit not only provide reliable connections for the spring probes and elastic wires but also provide structural support. The PCB on the left also integrates electronic components. Furthermore, a prism is embedded within the sensor channel to guide the direction of the light path. Figure 1 As shown in (b), rapid and repeatable mechanical coupling is achieved during assembly via a ring magnet, which can provide a contact force of up to 10 Newtons; two pairs of spring probes ensure a reliable electrical connection between adjacent sensing units. Figure 1 (c) shows the sensing units connected end-to-end. Each unit is electrically controllable, and its light-emitting diodes (LEDs) are driven via a shared bus, while the optical signals are transmitted through a unified optical transmission path. This architecture offers extremely high scalability.

[0035] In some embodiments, the segmented fiber optic bending sensor comprises multiple sensing units magnetically connected. The manufacturing process of the sensing units is as follows: Figure 2 As shown: First, three steel rods 20 are placed into mold 10 and their ends are fixed. Then, liquid silicone is injected into mold 10 and cured by heating. After curing, the mold is removed, and the steel rods 20 are taken out of the mold to form a flexible part. Segmented optical fibers and elastic wires are then inserted into it. Finally, circuit boards, spring probes, prisms, magnets, and fasteners are installed at both ends of the silicone body. Ultimately, the two end components are integrated with the silicone body, thus completing the assembly of the sensing unit.

[0036] This application uses a driving circuit to drive the sensing units. The driving circuit utilizes the frequency-dependent impedance characteristics of inductors and capacitors to achieve selective activation of the proposed bending sensor. A driving scheme is employed where each sensing unit can be driven independently, thus requiring only one photodetector 30 to detect multiple bends. The specific working principle of this driving scheme will be described in detail in a later section.

[0037] The driving circuit can employ a series inductor-capacitor (LC) resonant circuit, which can be used to selectively drive the sensing unit. The light-emitting elements include a first light-emitting diode (LED1) and a second light-emitting diode (LED2). A schematic diagram of the driving circuit is shown below. Figure 3As shown, the driving circuit includes an inductor L and a capacitor C connected in series. One lead of the inductor is connected to the negative terminal of the power supply, and the other lead of the inductor is connected to one lead of the capacitor. The other lead of the capacitor is connected to the cathode of the first LED, and the other lead of the capacitor is also connected to the anode of the second LED. The first and second LEDs are connected in anti-parallel, and the anode of the first LED and the cathode of the second LED are connected to the positive terminal of the power supply. During the positive half-cycle of the AC voltage, the driving circuit uses the inductor, capacitor, and the first LED; during the negative half-cycle of the AC voltage, the driving circuit uses the inductor, capacitor, and the second LED. The first and second LEDs are connected in anti-parallel, utilizing the positive and negative half-cycles of the AC voltage to achieve alternating conduction.

[0038] For a resonant circuit, the input impedance reaches its minimum value at the resonant frequency. In the resonant state, the reactances of the inductor and capacitor have equal amplitudes but opposite signs, thus completely canceling each other out. Therefore, the small-signal AC input impedance of the sensing unit can be expressed as:

[0039]

[0040] in, This represents the input impedance, and j represents the imaginary unit. L represents angular frequency, C represents inductance, and C represents capacitance. This represents the dynamic junction resistance of a light-emitting diode (LED) (typically on the order of a few ohms). This indicates its parasitic series resistance (typically a few ohms to tens of ohms). and Together, they constitute the small-signal resistance of the LED. Each parallel branch corresponds to a sensing unit, containing a pair of anti-parallel LEDs, a capacitor, and an inductor. As shown in the above equation, the branch impedance is mainly composed of C, L, and... The impedance of the sensing unit can be adjusted accordingly by regulating the values ​​of C or L, or by adjusting the AC drive frequency. An ideal series LC network has a series resonant frequency f. _s The input impedance is zero at this point. Assume f _s1 >f _s2 >…>f _sn The corresponding impedance and frequency response are as follows: Figure 4 As shown.

[0041] The sensing unit was analyzed using an estimation model: Light intensity modulation is a signal conversion mechanism widely used in segmented fiber optic sensors for bending and strain detection. This mechanism relies on the total internal reflection effect at the core-cladding interface to guide light propagation. Bending interferes with the total internal reflection process, increasing radiation and scattering losses, thereby causing a measurable attenuation of transmitted optical power.

[0042] This application employs segmented optical fibers. Upon bending, air cavities 22 are formed between the segments. Multiple air cavities 22 can be formed within a flexible structure, thereby further enhancing the modulation effect. These air cavities 22 locally weaken the total internal reflection effect, creating additional optical loss paths. Therefore, the overall attenuation becomes more sensitive to deformation caused by bending, significantly improving measurement sensitivity. Compared to other attenuation mechanisms, the inherent transmission loss of the segmented optical fiber is negligible, ensuring that changes in the measurement signal primarily originate from optical attenuation caused by bending. Figure 5 As shown, when light propagates from the segmented fiber core to the cladding and the incident angle exceeds the critical angle... At this time, total internal reflection occurs at the core-cladding interface, thus confining the light within the core and allowing it to propagate along the waveguide axis. The value can be calculated using the following formula:

[0043]

[0044] Where n1 and n2 represent the refractive indices of the fiber core and cladding, respectively. In this application, the numerical aperture (NA) of the segmented fiber is 0.65, corresponding to a maximum external incident angle θ. max The angle ≈40.5° indicates its strong light-gathering capability. When light exits from the segmented fiber, Fresnel reflection occurs at the fiber-air interface, and the corresponding power reflectivity R (perpendicular incidence) is given by the following formula:

[0045]

[0046] Where, n air Let θ be the refractive index of air. After passing through the core-air interface, light rays will pass through an air cavity of length d and diverge linearly according to the angle of incidence. Only those rays that remain within the core of the next fiber segment (radius a) and have an angle of incidence less than θ will diverge. max Only light rays that are properly reflected can be recaptured through total internal reflection. Assuming the power is isotropically distributed within the solid angle, the coupling efficiency of the nth cavity in the kth sensing unit can be obtained by integrating the angular power distribution, as shown in the following expression:

[0047]

[0048] in, This represents the integral angle variable. This represents the coupling efficiency of the nth cavity of the kth sensing unit.

[0049] This analytical expression is derived under the geometrical optics approximation, with assumptions including: isotropic angular power distribution, ideal coaxial alignment, angle-independent Fresnel reflection, and negligible diffraction or mode interference. Therefore, the relationship between the input optical power and output optical power of the k-th sensing unit can be expressed as:

[0050]

[0051]

[0052] in, and Let these represent the incident optical power and the output optical power of the k-th sensing unit, respectively. For optical coupling efficiency. The coupling efficiency decreases as the distance *d* from the air cavity increases. When bending occurs in a single direction, the coupling efficiency exhibits a strictly monotonic and bijective relationship with the bending angle; there is a one-to-one correspondence between the coupling efficiency and the bending angle, and the direction of change is fixed. Therefore, the bending angle of the sensing unit can be accurately quantified as follows:

[0053]

[0054] Taking three sensing units as an example, the frequency-selective impedance characteristics of the LC resonant circuit can be used to selectively activate different sensing units, thereby significantly simplifying the system's wiring and control architecture. Each sensing unit is assigned a unique resonant frequency, enabling parallel operation without the need for an independent drive circuit. Figure 6 The demonstration shows three stages (stage 1, stage 2, and stage 3): in each stage, the LED is activated individually, and the light intensity detected by the photodetector in each stage is used to calculate the corresponding bending angle. Assume the light intensity emitted by the LED is I1. K The received light intensity measured by the photodetector is I. K The optical coupling efficiency of the three sensing units (sensing unit 1, sensing unit 2, and sensing unit 3) is calculated as follows:

[0055]

[0056] The above formula contains three expressions, each corresponding to a stage. In each stage, the optical coupling efficiency of the corresponding sensing unit is first determined, and then the bending angle of the sensing unit is estimated according to the following formula:

[0057]

[0058] To verify the feasibility and effectiveness of the sensor driving circuit, a simulation circuit model corresponding to the driving scheme was built on the MATLAB / Simulink platform (e.g., Figure 3Verification was performed as shown in the figure. See Table 1 for detailed drive circuit parameter settings. Figure 7 As shown, Figure 7 (a) represents stage 1, (b) represents stage 2, and (c) represents stage 3. In each stage, only the corresponding sensing unit has sufficient current to drive the LED, thereby enabling selective activation of the bending sensor.

[0059] Table 1 Drive Circuit Parameters

[0060]

[0061] To comprehensively evaluate the performance of the proposed modular flexible bending sensor, a series of systematic experiments were conducted, covering key indicators such as sensitivity, linearity, repeatability, and resolution, to verify its applicability and reliability in practical applications. The overall architecture diagram of the sensing system and the prototype of the modular flexible fiber optic bending sensor are shown below. Figure 8 As shown in (a), the system consists of a digital processing module, a signal generation module, a drive module, and multiple sensing units. The digital processing module sends a control signal, which the signal generation module converts into an adjustable AC signal. This adjustable AC signal is amplified by the drive module to generate a drive signal, which drives the light-emitting element in the corresponding sensing unit to emit light, outputting modulated light. Finally, the photodetector converts the light signal (modulated light) output by the sensing unit into a digital signal. This digital signal is then re-input into the digital processing module as data. The digital processing module analyzes the data based on an estimation model to determine the bending angle of the sensor. A physical prototype of the modular flexible fiber optic bending sensor is shown below. Figure 8 As shown in (b) of the diagram.

[0062] like Figure 9 As shown in (a), a bending test device was designed to test sensor performance. The test device includes a platform 70, in which a stepper motor 40 is installed. The output shaft of the stepper motor 40 is wound with three sets of pull wires 60, which are threaded through a flexible limiting seat 50 and evenly distributed circumferentially around the edge of the flexible limiting seat 50. A sensing unit is installed inside the flexible limiting seat 50. The stepper motor 40 can tighten the pull wires 60 to bend the flexible limiting seat 50, and the sensing unit inside the flexible limiting seat 50 will also bend accordingly. After the stepper motor 40 releases the pull wires 60, the flexible limiting seat 50 and the sensing unit inside it can be reset. This process can be repeated to test the performance of the sensing unit.

[0063] The bending angle of the sensing unit is precisely controlled by a stepper motor, with a maximum angle of 120°, which is sufficient to cover the typical range of motion of human joints. Figure 9Figure (b) shows the relationship between light intensity and bending angle, which exhibits a highly linear correlation (R² = 0.9952). To further evaluate repeatability and durability, the sensing unit underwent 1000 bending cycles at a 120° bending angle, as shown in Figure (b). Figure 10 As shown in (a), Figure 10 (a) in the figure is a stability analysis diagram of the sensing unit, which is derived from... Figure 10 As shown in (a), the sensor's hysteresis error is only 2.88%, indicating that the sensor maintains stable response characteristics and high mechanical reliability. The resolution of the modular sensing unit was tested by sequentially applying deformations of 1°, 10°, 20°, 50°, 80°, and 110°. Figure 10 As shown in (b) of the diagram. Figure 10 (b) in the diagram is a schematic diagram of resolution analysis. Figure 10 Results (b) show that a bending angle of 1° was successfully captured, demonstrating that the sensor can effectively detect most human joint movements. In conclusion, through a comprehensive evaluation of sensitivity, linearity, repeatability, and resolution using bending experiments, the proposed modular sensing unit demonstrates great potential for wearable motion monitoring applications.

[0064] The wrist joint is crucial for maintaining hand dexterity and enabling fine motor skills, thus playing a key role in human movement and daily activities. To verify the applicability of the proposed modular flexible fiber optic bend sensor in wearable scenarios, it was applied to wrist posture monitoring, a technology also showing significant potential in rehabilitation assessment and training. Three sensing units were installed at the wrist, metacarpophalangeal, and phalangeal joints, respectively, enabling continuous tracking of hand movements. During the experiment, each sensing unit was independently controlled using a time-division multiplexing scheme to ensure that the measurement data from each joint did not interfere with each other. The system has a sampling frequency of 400 Hz, sufficient to capture the full range of hand movements in daily activities. Flexion and extension movements were performed at the three joints, and the corresponding output data of the proposed sensor were recorded, such as... Figure 11 As shown in the figure. These results were then compared with reference data obtained by the optical motion capture (MoCap) system.

[0065] A comparative analysis was conducted between the proposed flexible fiber optic bending sensor and the MoCap system. For example... Figure 12 As shown in (a), the measured bending angles exhibit a clear linear relationship, with a regression slope of 1.032, indicating a high degree of consistency between the results of the two measurement methods. Meanwhile, Figure 12 (b) shows the Bland-Altman analysis results, revealing an average deviation of only -0.4509°. Taken together, these results demonstrate that the proposed sensor, with its frequency-selective addressing and actuation scheme, possesses extremely high accuracy and reliability.

[0066] This application proposes a modular multi-segment sensing framework based on a low-complexity, frequency-selective addressing and driving scheme. This application achieves multi-segment bending detection with minimal circuit components, effectively reducing wiring complexity and control overhead, while improving scalability and integration. Frequency domain modeling and circuit-level simulations verify the feasibility of the proposed method; the prototype developed for human wrist posture sensing exhibits high accuracy, good repeatability, and excellent angular resolution.

[0067] The above are merely embodiments of this application and do not limit the scope of this patent application. Any equivalent structural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of this application.

Claims

1. A bending estimation model for a flexible optical fiber bending sensor, characterized in that, The bending sensor includes a sensing unit, and multiple sensing units can be connected end-to-end for combined use. Each sensing unit includes a flexible component, with segmented optical fibers and at least one pair of elastic wires passing through it along its length. The segmented optical fibers are located on the axis of the flexible component and include multiple fiber segments. If the sensing unit bends, an air cavity exists between adjacent fiber segments. Circuit boards are provided at both ends of the flexible component, and driving circuits are provided on the circuit boards to drive the sensing units. The circuit boards are connected to the elastic wires. Fasteners are provided on the outer side of the circuit boards, and the ends of the segmented optical fibers pass through the fasteners. Electrical connectors are provided outside the fasteners, passing through the fasteners and electrically connecting to the circuit boards. A light-emitting element is provided on the circuit board at the first end, and a prism is located within the fastener at the first end. The prism refracts the light emitted by the light-emitting element onto the segmented optical fibers. A bending estimation model is used to estimate the bending angle of the sensing unit. Represented as: in, For optical coupling efficiency; It decreases as the distance d between the air chambers increases; when the bending occurs in a single direction, the coupling efficiency exhibits a monotonic and bijective relationship with the bending angle. in, and These represent the incident light power and the output light power of the k-th sensing unit, respectively. Where N represents the number of air cavities, n∈N; This represents the coupling efficiency of the nth cavity of the kth sensing unit.

2. The bending estimation model for the flexible fiber optic bending sensor according to claim 1, characterized in that, The fastener has a connector on its outer side, which is used to connect the tail end of one sensing unit to the head end of another sensing unit.

3. The bending estimation model for the flexible fiber optic bending sensor according to claim 2, characterized in that, The connector is a magnetic component, which is sleeved around the fastener.

4. The bending estimation model for the flexible fiber optic bending sensor according to claim 1, characterized in that, The electrical connector includes a male connector and a female connector. The male connector can be inserted into the female connector and is electrically connected to the female connector. The male connector is disposed on the fastener at the first end, and the female connector is disposed on the fastener at the last end. The female connector at the last end is electrically connected to the male connector of another sensing unit.

5. The bending estimation model for the flexible fiber optic bending sensor according to claim 1, characterized in that, The light-emitting element includes a first light-emitting diode and a second light-emitting diode. The driving circuit includes an inductor and a capacitor connected in series. One pin of the inductor is connected to the negative terminal of the power supply, and the other pin of the inductor is connected to one pin of the capacitor. The other pin of the capacitor is connected to the cathode of the first light-emitting diode, and the other pin of the capacitor is also connected to the anode of the second light-emitting diode. The first light-emitting diode and the second light-emitting diode are connected in anti-parallel. The anode of the first light-emitting diode and the cathode of the second light-emitting diode are connected to the positive terminal of the power supply. During the positive half-cycle of the AC voltage, the driving circuit uses the inductor, capacitor, and first light-emitting diode. During the negative half-cycle of the AC voltage, the driving circuit uses the inductor, capacitor, and second light-emitting diode.

6. The bending estimation model for the flexible fiber optic bending sensor according to claim 5, characterized in that, The small-signal AC input impedance of the sensing unit is expressed as: in, This represents the input impedance, and j represents the imaginary unit. L represents the angular frequency, C represents the inductance, and C represents the capacitance. This represents the dynamic junction resistance of the light-emitting diode. This represents the parasitic series resistance of the light-emitting diode.

7. The bending estimation model for the flexible fiber optic bending sensor according to claim 1, characterized in that, When light is emitted from the segmented optical fiber, Fresnel reflection occurs at the interface between the segmented optical fiber and air, and the corresponding power reflectivity R is given by the following formula: Where n1 represents the refractive index of the fiber core in the segmented optical fiber, n air Let be the refractive index of air. After light passes through the interface between the fiber core and the air, it will pass through an air cavity of length d and diverge linearly according to the angle of incidence.

8. The bending estimation model for the flexible fiber optic bending sensor according to claim 7, characterized in that, The kth sensing unit The coupling efficiency of the nth air cavity is obtained by integrating the angular power distribution, and the expression is as follows: in, Indicates the critical angle. This represents the radius of the fiber core in the segmented optical fiber. This represents the integral angle variable.

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