Range Of Curvatures Research Articles

Numerical analysis and flamelet modeling of NO[formula omitted] formation in a thermodiffusively unstable premixed hydrogen flame at elevated-pressure conditions

Fuel-lean premixed hydrogen flames are thermodiffusively unstable and cellular structures over a wide range of length-scales are formed due to strong differential diffusion of hydrogen. Pressure promotes the thermodiffusive instabilities due to the increase in Zeldovich number and the relevant reaction pathways. As the local stoichiometry and temperature correlate with the thermodiffusive instabilities, the NOx formation mechanism is expected to be complicated in fuel-lean hydrogen flames at elevated-pressure conditions. In this work, the characteristics and the NOx formation mechanism of thermodiffusively unstable premixed hydrogen flames at elevated-pressure conditions are investigated through direct numerical simulation (DNS). The designed operating conditions were motivated by findings in experiments investigating NOx emissions in pure hydrogen combustion at elevated-pressure conditions. The flame characteristics are assessed by means of the global burning velocity, flame surface area, stretch factor, and PDFs of curvature and length-scale of cellular structures. The conditioned thermo-chemical quantities are analyzed with respect to the progress variable and curvature to illustrate the key correlations. The contributions of elementary reactions to the NOx formation are quantified and the important reaction pathways are identified in a reaction pathway analysis. The global burning velocity is significantly increased with increasing pressure, which mainly results from the increased reactivity. The positive curvature is more prominent in the elevated-pressure case, which results in a higher probability of smaller cells. Different from the atmospheric case, where the NNH reaction pathway is dominant, the N2O reaction pathway is the most important under elevated-pressure conditions, which suggests the strong correlations of NOx formation with curvature values. To incorporate the wide range of curvatures in a flamelet model, an extended flamelet tabulation method based on the composition space model is proposed. The performance of the composition space model in predicting the important radicals and NOx species is evaluated through an a priori analysis. The composition space model gives better predictions of the radicals and the production and consumption rates of the NOx species compared to conventional flamelet models that do not consider the effects of local flame curvature.

Confinement-induced self-assembly of a diblock copolymer within a non-uniform cylindrical nanopore.

The self-assembly of a diblock copolymer melt confined within a non-uniform cylindrical nanopore is studied using the self-consistent field theory. The non-uniformity manifests in the form of a converging-diverging cylindrical nanopore. The axial variation in pore diameter presents a range of curvatures within the same confinement pore as opposed to a single curvature in a uniform-diameter cylindrical pore. The introduction of multiple curvatures leads to the formation of novel microstructures not accessible in uniform cylindrical confinement. The well-known equilibrium structures like a single helix, double helices, and concentric lamella under cylindrical confinement transition into new morphologies such as hyperboloidal phases, microstructures containing rings with a bead, rings with spheres, and a squeezed helical phase as the pore diameter varies axially. The converging-diverging geometry of the confining pore renders the helical phases seen in the cylindrical pore less favorable. A phase diagram in the parametric space of the block fraction and the ratio of the smallest and largest pore radii has been constructed to depict the order-order transition of various microstructures. The ratio of radii, a measure of the non-uniformity of the pore, along with the pore length brings out some interesting morphologies. The mechanism of these structural transitions is understood as the interplay between the variation in pore curvature attributed to the non-uniformity, the spontaneous curvature of the block copolymer interface, and the enthalpic interaction between the segregated blocks.

High resolution curvature sensor based on enhanced backscattering in side polished optic fiber

A high-resolution curvature sensor based on enhanced backscattering in side polished optic fiber is proposed and experimentally investigated. Directional curvature sensor fabrication procession and operating principle are introduced. A push–pull structure with 2 side polished curvature sensors sticking on opposite sides of an elastic beam is used to enhance sensitivity and responsive linearity. Experiments are carried out by high accuracy relative intensity (RI) measurement system based on modified pulse self-referencing technology. Experimental results show that curvature sensor can achieve a sensitivity of 15.21 dB/m−1 in the curvature range of −0.48–0.48 m−1, and the curvature resolution is as low as 2 × 10−5m−1.

Experimental implementation of quantum-enhanced tapered fiber sensor for simultaneous measurement of curvature and temperature

This work reports a proof-of-principle experimental demonstration of a quantum-enhanced tapered fiber sensor based on intensity-correlated pulse twin beams and a conventional tapered fiber structure, which is prepared by concatenating two tapers along a single-mode fiber. The sensing beam from pulse twin beams is coupled into this structure for simultaneous measurement of curvature and temperature, then it is jointly measured with the other reference beam, this measurement technique can effectively enhance signal-to-noise ratio (SNR) and sensitivity of the tapered fiber sensor, due to the existence of intensity correlation shared by pulse twin beams. If the reference beam is kept unchanged during the measurement process, this measurement is called as unbalanced measurement condition; otherwise it is called as balanced measurement condition. Under balanced measurement condition for curvature sensing (curvature range from 3.266 m−1 to 9.412 m−1), SNR is maximally enhanced by a factor of 1.10 dB with respect to equally classical strategy. Under unbalanced measurement condition for curvature sensing, SNR and sensitivity are maximally enhanced by the factors of 0.98 dB and 1.277 dB/m−1, respectively. Under balanced measurement condition for temperature sensing (temperature range from 35 °C to 60 °C), SNR is maximally enhanced by a factor of 1.14 dB. Under unbalanced measurement condition for temperature sensing, SNR is maximally enhanced by a factor of 0.64 dB. The present research opens a new avenue for quantum-enhanced sensing based on tapered fiber structure.

A simultaneous audio and temperature sensing system based on in-line Mach–Zehnder interferometer

A system integrating audio and temperature sensing capabilities has been developed for simultaneous detection. Within this system, an in-line Mach–Zehnder interferometer (IMZI) sensor has been explored. Manufactured using the electro-discharge method, the sensor comprises a structure connecting single mode fiber (SMF) to polarization-maintaining fiber (PMF) and then back to SMF, with distinctive peanut-shaped junctions. The sensor’s sensitivity to temperature and curvature has been assessed to determine its potential for simultaneous audio and temperature detection. Within the temperature range of 15 °C–48 °C and a curvature range of 0 m−1–0.06654 m−1, the peak sensitivities observed were -0.1072 nm/°C and 63.5569 nm/m−1, respectively. Experimental verification confirmed the system’s audio performance using the proposed IMZI sensor. The system operates over a broad frequency range from 20 Hz to 20,000 Hz. The maximum frequency response and minimum detectable pressures (MDP) are 1804.92 mV/Pa and 11.74 μPa/Hz1/2 at 800 Hz, respectively, indicating notable acoustic sensitivity. Based on both theoretical analyses and empirical methodologies, the system successfully achieves simultaneous audio and temperature detections. This is accomplished by processing the detected data of curvature and temperature variations via high-speed sampling and dual-wavelength demodulation. Notably, this approach addresses and overcomes the sensitivity reduction experienced by acoustic sensors based on interferometers due to temperature-induced Q point drifts.

Arbitrary curvature programming of thermo-active liquid crystal elastomer via topology optimization

Plants can change their morphology upon environmental variations such as temperature. Inspired by plants’ morphological adaptability, we present a computational inverse design framework for systematically creating optimized thermo-active liquid crystal elastomers (LCEs) that spontaneously morph into arbitrary programmed geometries upon temperature changes. The proposed framework is based on multiphysics topology optimization and a statistical mechanics-based LCE model to realize arbitrary curvature programming for LCE composites under large deformations. We propose a curvature-based optimization formulation that enables rotation-invariant and size-insensitive programmability of LCE, accounting for its highly nonlinear deformed shape. We demonstrate that the programmed LCE composites can accurately morph into a wide range of complex target shapes and curvatures, such as those of numbers, letters, flowers, and various objects. The resulting optimized designs exhibit highly irregular material distributions, which surpass intuition-based designs, and precisely produce desired deformed geometries upon temperature increase. The computational inverse design technique holds promise for a wide array of applications requiring function- and performance-driven design of active materials.

Scaling analysis for azimuthal spreading and contact time of droplet impacting on superhydrophobic cylindrical surfaces

Drop impact on superhydrophobic surfaces has gained great attention because of its physics and application in water repellency, drag reduction, and anti-icing. Spreading lengths and the contact time are the crucial parameters determining the extend of drop–surface interaction and effective heat transfer between the two and are, hence, trivial to many engineering applications. Post-collisional dynamics over cylindrical geometries are quite different from that of the flat surfaces due to the asymmetry in spreading and retraction dynamics. The dynamics are mainly governed by the impact Weber number and curvature ratio of impacting surface to drop. The spreading dynamics in axial direction is found to be fairly predicted by the governing laws coined for flat surfaces. However, the spreading dynamics in the azimuthal direction is quite complex. Herein, we propose a simple scaling analysis for the spreading dynamics in the azimuthal direction as well as for the contact time of the impacting drop with the surface. A modified capillary length is proposed accounting the curvature effect of the substrate by incorporating a centrifugal component of acceleration for the expanding lamella over the curved surface. With the proposed modified capillary length, a universal scaling relationship for azimuthal spreading length and contact time is developed. The proposed scaling laws are found to be in good agreement with the experimental results from the present study as well as with the existing literature for a wide range of Weber numbers and surface curvature.

A Novel Quasilinear Viscoelastic Model of the Bending of a Steerable Catheter

Abstract The present study proposes a novel model that establishes the relationship between the bending moment and the curvature of a steerable catheter. The catheters exhibit a nonlinear viscoelastic tendency, so the moment-curvature relationship is modeled as a bending of a quasi-linear viscoelastic (QLV) cantilever beam. Stress relaxation tests with multiple magnitudes are performed on a catheter, and the parameter tuning is carried out with the test results to find out the coefficients of the model. The form of the instantaneous moment response, which is an important term within the QLV equation, is selected as a logarithmic form by analyzing the test results. This differentiates the accuracy of the model from using the commonly used exponential form. The performance of the logarithmic QLV model is compared to the conventional models by checking the curvature range each model can cover with a certain accuracy. The covering range for elastic, linear viscoelastic, and exponential QLV models are 22.1%, 64.4%, and 55.5%, respectively, whereas the covering range of the logarithmic QLV model is 100%.

Multiple equilibrium states of a curved-sided hexagram: Part II—Transitions between states

Curved-sided hexagrams with multiple equilibrium states have great potential in engineering applications such as foldable architectures, deployable aerospace structures, and shape-morphing soft robots. In Part I, the classical stability criterion based on energy variation was used to study the elastic stability of the curved-sided hexagram and identify the natural curvature range for the stability of each state with circular and rectangular rod cross-sections. Here, we combine a multi-segment Kirchhoff rod model, finite element simulations, and experiments to investigate the transitions between four basic equilibrium states of the curved-sided hexagram. The four equilibrium states, namely the star hexagram, the daisy hexagram, the 3-loop line, and the 3-loop "8", carry uniform bending moments in their initial states, and the magnitudes of these moments depend on the natural curvatures and their initial curvatures. Transitions between these equilibrium states are triggered by applying bending loads at their corners or edges. It is found that transitions between the stable equilibrium states of the curved-sided hexagram are influenced by both the natural curvature and the loading position. Within a specific natural curvature range, the star hexagram, the daisy hexagram, and the 3-loop "8" can transform among one another by bending at different positions. Based on these findings, we identify the natural curvature range and loading conditions to achieve transition among these three equilibrium states plus a folded 3-loop line state for one specific ring having a rectangular cross-section with a height to thickness ratio of 4. The results obtained in this part also validate the elastic stability range of the four equilibrium states of the curved-sided hexagram in Part I. We envision that the present work could provide a new perspective for the design of multi-functional deployable and foldable structures.

Pass-through and tax incidence in differentiated product markets

The role of demand curvature in determining firm behavior in symmetric oligopolistic product markets is well-understood. We consider the empirically relevant discrete choice differentiated product demand and point to two forces that drive curvature in logit demand: the impact of outside-good spending on the consumer’s indirect utility and the heterogeneity in this response across consumers. We use the canonical example of the ready-to-eat cereal market (Nevo, 2000) to contrast elasticity and curvature estimates across several workhorse models. We illustrate that the log-concave Multinomial Logit and Nested Logit demands yield significantly biased curvature estimates. In contrast, a Mixed Logit specification generates a wider range of curvatures, including curvatures larger than one. These results are of immediate relevance to the robust assessment of tax incidence and the pass-through of cost savings, such as from a horizontal merger, in differentiated product markets.

Directional Bending Sensor and Multiparameter Sensor Based on D-Core Multimode Fiber

For the sensor with interference between fiber core mode and cladding mode, the directional bending sensor can be realized by processing asymmetric structure on the cladding or using eccentric fiber, but the temperature and strain crosstalk of the sensor with interference between fiber core mode and cladding mode is large. In this article, a kind of fiber intermode interference sensor with asymmetric structure is proposed, which can realize vector bending sensing and reduce temperature and strain crosstalk. The designed D-core multimode fiber has cladding and air on both sides of the fiber core. When 0° and 180° bending are applied to it, the interference spectrum moves in different directions, thus realizing the recognition of bending direction. For curvature detection, in the curvature range of 0–0.62 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{m}^{-{1}}$ </tex-math></inline-formula> , the sensitivity of 0° bending is 11.00 nm/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{m}^{-{1}}$ </tex-math></inline-formula> , and that of 180° bending is −11.40 nm/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{m}^{-{1}}$ </tex-math></inline-formula> . For liquid level detection, the sensing sensitivity is 234 pm/mm with the range of 0–4 cm, and the linearity is 0.993. In addition, the temperature sensitivity is as low as 10 pm/°C, and the strain sensitivity is as low as −1.28 pm/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \varepsilon $ </tex-math></inline-formula> . The proposed sensor realized the directional bending sensing and liquid level sensing of intermodal interference. Its low sensitivity to temperature and strain can be used to avoid the cross-sensitivity problems. In the field of water flow detection, the simultaneous detection of water level and water flow direction can be realized by the proposed sensor.

Shape sensing of optical fiber Bragg gratings based on deep learning

Continuum robots in robot-assisted minimally invasive surgeries provide adequate access to target anatomies that are not directly reachable through small incisions. Achieving precise and reliable shape estimation of such snake-like manipulators necessitates an accurate navigation system, that requires no line-of-sight and is immune to electromagnetic noise. Fiber Bragg grating (FBG) shape sensing, particularly eccentric FBG (eFBG), is a promising and cost-effective solution for this task. However, in eFBG sensors, the spectral intensity of the Bragg wavelengths that carries the strain information can be affected by undesired bending-induced phenomena, making standard characterization techniques less suitable for these sensors. We showed in our previous work that a deep learning model has the potential to extract the strain information from the eFBG sensor’s spectrum and accurately predict its shape. In this paper, we conducted a more thorough investigation to find a suitable architectural design of the deep learning model to further increase shape prediction accuracy. We used the Hyperband algorithm to search for optimal hyperparameters in two steps. First, we limited the search space to layer settings of the network, from which, the best-performing configuration was selected. Then, we modified the search space for tuning the training and loss calculation hyperparameters. We also analyzed various data transformations on the network’s input and output variables, as data rescaling can directly influence the model’s performance. Additionally, we performed discriminative training using the Siamese network architecture that employs two convolutional neural networks (CNN) with identical parameters to learn similarity metrics between the spectra of similar target values. The best-performing network architecture among all evaluated configurations can predict the shape of a 30 cm long sensor with a median tip error of 3.11 mm in a curvature range of 1.4 m−1 to 35.3 m−1.

Acoustic feature based geometric defect identification in wire arc additive manufacturing

ABSTRACT In additive manufacturing of metals, numerous techniques have been employed to sense print defects. Among these, acoustic-based sensing has the advantage of low cost and shows the most potential to identify both external and internal defects as an in-situ monitoring system. Using acoustic signals, researchers have broadly investigated non-machine learning and machine learning-based approaches to identify defects like balling, micro defects, lack of fusion pores, keyhole pores, cracks, and porosity. While most of these works have shown promising results for laser-based AM systems, few have explored how acoustic signals can be used effectively for Wire Arc Additive Manufacturing (WAAM) defect detection. This paper proposes a methodology to construct machine learning (ML)-based models on identifying geometrically defective bead segments using acoustic signals during the WAAM process. Geometrically defective bead segment or geometric defect is a defect that causes voids in the final printed part due to incomplete fusion between two non-uniform overlapping bead segments. Such a defect is currently not explored in the literature. The proposed methodology uses a novel dataset labeling approach to identify good and bad bead segments based on an optimal threshold of the range of mean curvature. Furthermore, the methodology targets defective bead segments based on acoustic feature inputs like Principal Components (PC) or Mel Frequency Cepstral Coefficients (MFCC). To understand the resulting performance of the defect identification models constructed based on the proposed methodology, experiments are performed and tested on a variety of ML models (KNN, SVM, RF, NN, and CNN) based on the Inconel 718 material. The results show that the combinatorics of two acoustic input features and five ML models can be able to identify geometrically defective segments accurately with F1 score that ranges from 80% to 85%.

3D vessel extraction using a scale-adaptive hybrid parametric tracker.

3D vessel extraction has great significance in the diagnosis of vascular diseases. However, accurate extraction of vessels from computed tomography angiography (CTA) data is challenging. For one thing, vessels in different body parts have a wide range of scales and large curvatures; for another, the intensity distributions of vessels in different CTA data vary considerably. Besides, surrounding interfering tissue, like bones or veins with similar intensity, also seriously affects vessel extraction. Considering all the above imaging and structural features of vessels, we propose a new scale-adaptive hybrid parametric tracker (SAHPT) to extract arbitrary vessels of different body parts. First, a geometry-intensity parametric model is constructed to calculate the geometry-intensity response. While geometry parameters are calculated to adapt to the variation in scale, intensity parameters can also be estimated to meet non-uniform intensity distributions. Then, a gradient parametric model is proposed to calculate the gradient response based on a multiscale symmetric normalized gradient filter which can effectively separate the target vessel from surrounding interfering tissue. Last, a hybrid parametric model that combines the geometry-intensity and gradient parametric models is constructed to evaluate how well it fits a local image patch. In the extraction process, a multipath spherical sampling strategy is used to solve the problem of anatomical complexity. We have conducted many quantitative experiments using the synthetic and clinical CTA data, asserting its superior performance compared to traditional or deep learning-based baselines.

Effects of Curvature on Flexible Bragg Grating in Off-Axis Core: Theory and Experiment

A high curvature flexible Bragg grating, in planar technology, is designed, fabricated and experimentally characterized by employing silica glass. The curvature sensing mechanism for slightly off-axis core is theoretically explained and experimentally demonstrated. The electromagnetic behavior of the proposed sensor is investigated through conformal mapping, modal analysis, and coupled-mode theory. The experimental measurement reveals different sensitivities to positive and negative curvatures. The reflection spectrum of the planar Bragg grating sensor and the relationship between its resonant wavelengths and the curvature is measured for a large curvature range up to 1/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> = ± 33 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> . The interest toward off-axis core on planar flexible platform for curvature monitoring is due to the lateral stiffness and low Young's modulus of the substrate.

Biomechanical evaluation of the thoracolumbar spine comparing healthy and irregular thoracic and lumbar curvatures

BackgroundThe geometric alignment of the spine plays an integral role in stability, biomechanical loading, and consequently, pain, and a range of healthy sagittal curvatures has been identified. Spinal biomechanics when sagittal curvature is outside the optimal range remains a debate and may provide insight into the load distribution throughout the spinal column. MethodA thoracolumbar spine model (Healthy) was developed. Thoracic and lumbar curvatures were adjusted by 50% to create models with varying sagittal profiles: hypolordotic (HypoL), hyperlordotic (HyperL), hypokyphotic (HypoK), and hyperkyphotic (HyperK). In addition, lumbar spine models were constructed for the former three profiles. The models were subjected to loading conditions simulating flexion and extension. Following validation, intervertebral disc stresses, vertebral body stresses, disc heights, and intersegmental rotations were compared across all models. ResultsOverall trends demonstrated that HyperL and HyperK models had a noticeable reduction in disc height and greater vertebral body stresses compared to the Healthy model. In comparison, the HypoL and HypoK models displayed opposite trends. Considering the lumbar models, the HypoL model had reduced disc stresses and flexibility, while the contrary was observed in the HyperL model. Results indicate that the models with excessive curvature may be subjected to greater stress magnitudes, while the straighter spine models may reduce these stresses. ConclusionsFinite element modeling of spine biomechanics demonstrated that variations in sagittal profiles influence the load distribution and range of motion of the spine. Considering patient-specific sagittal profiles in finite element modeling may provide valuable insight for biomechanical analyses and targeted treatments.

Fidelity of hyperbolic space for Bayesian phylogenetic inference.

Bayesian inference for phylogenetics is a gold standard for computing distributions of phylogenies. However, Bayesian phylogenetics faces the challenging computational problem of moving throughout the high-dimensional space of trees. Fortunately, hyperbolic space offers a low dimensional representation of tree-like data. In this paper, we embed genomic sequences as points in hyperbolic space and perform hyperbolic Markov Chain Monte Carlo for Bayesian inference in this space. The posterior probability of an embedding is computed by decoding a neighbour-joining tree from the embedding locations of the sequences. We empirically demonstrate the fidelity of this method on eight data sets. We systematically investigated the effect of embedding dimension and hyperbolic curvature on the performance in these data sets. The sampled posterior distribution recovers the splits and branch lengths to a high degree over a range of curvatures and dimensions. We systematically investigated the effects of the embedding space's curvature and dimension on the Markov Chain's performance, demonstrating the suitability of hyperbolic space for phylogenetic inference.

Automated measurement of penile curvature using deep learning-based novel quantification method.

Develop a reliable, automated deep learning-based method for accurate measurement of penile curvature (PC) using 2-dimensional images. A set of nine 3D-printed models was used to generate a batch of 913 images of penile curvature (PC) with varying configurations (curvature range 18° to 86°). The penile region was initially localized and cropped using a YOLOv5 model, after which the shaft area was extracted using a UNet-based segmentation model. The penile shaft was then divided into three distinct predefined regions: the distal zone, curvature zone, and proximal zone. To measure PC, we identified four distinct locations on the shaft that reflected the mid-axes of proximal and distal segments, then trained an HRNet model to predict these landmarks and calculate curvature angle in both the 3D-printed models and masked segmented images derived from these. Finally, the optimized HRNet model was applied to quantify PC in medical images of real human patients and the accuracy of this novel method was determined. We obtained a mean absolute error (MAE) of angle measurement <5° for both penile model images and their derivative masks. For real patient images, AI prediction varied between 1.7° (for cases of ∼30° PC) and approximately 6° (for cases of 70° PC) compared with assessment by a clinical expert. This study demonstrates a novel approach to the automated, accurate measurement of PC that could significantly improve patient assessment by surgeons and hypospadiology researchers. This method may overcome current limitations encountered when applying conventional methods of measuring arc-type PC.

Dual-parameter measurements of curvature and strain using cladding-etched two-mode fiber Bragg grating

Even though single-mode fibers are commonly used for optical fiber sensing, few-mode fibers, as potential alternatives, have also been investigated for multiple-parameter measurements, mainly because such fibers support only a few transverse modes with their own propagation constants. These modes respond in varied situations to different parameters and, therefore, can be retrieved and recognized. In this study, a two-mode fiber Bragg grating (TM-FBG) structure was fabricated, with its cladding layer surrounding the grating area partially etched away for enhanced sensitivity for curvature and strain variations. The experimental results show that within a curvature range of 0–19 m−1, the difference in reflection peaks between the linear polarized LP01 and LP11 modes decreases at a rate of 0.46 dB/m−1. The TM-FBG sensor is insensitive to fluctuations induced by the source and also independent of the grating’s central wavelength. Within the specific range of 0–100 mN for strain measurement, the reflections of the two modes have similar responses of 27 nm/N.

Shape Reconstruction for Continuum Robot Based on Pythagorean Hodograph–Bézier Curve With IMU and Vision Sensors

The shape information is the key to realize real-time, accurate, and effective control of continuum robots. Traditional image processing method and start-to-end-point fitting method are combined. Inertial measurement unit (IMU) and camera are used to capture the end position and attitude information of continuum robot and do not rely on the acquisition of the global image to solve the problem of limited vision in a traditional image processing method. In addition, a new start-to-end-point fitting method is proposed, which is the Pythagorean hodograph—Bézier (PH-B) fitting method. The new method simplifies the solving steps of control points of fitting curve. The control points can be obtained only through the geometric relationship and do not need to rely on an optimization algorithm for iterative solution. This method has good shape fitting accuracy and applicability in the curvature range from 0° to 90° through the simulation analysis. A variety of experiments are designed to verify the results. The experimental results show that the maximum shape reconstruction error by the proposed method is about 2 mm. This proves the applicability of the PH-B method in the shape reconstruction of continuum robots.