A Novel Dual-Permanent-Magnet Mechanical Antenna for Pipeline Robot Localization and Communication

The demand for pipeline inspection has promoted the development of pipeline robots and associated localization and communication technologies. Among these technologies, ultra-low-frequency (30–300 Hz) electromagnetic waves have a significant advantage because of their strong penetration, which can penetrate metal pipe walls. Traditional low-frequency transmitting systems are limited by the size and power consumption of the antennas. In this work, a new type of mechanical antenna based on dual permanent magnets was designed to solve the above problems. An innovative amplitude modulation scheme that involves changing the magnetization angle of dual permanent magnets is proposed. The ultra-low-frequency electromagnetic wave emitted by the mechanical antenna inside the pipeline can be easily received by the antenna outside to localize and communicate with the robots inside. The experimental results showed that when two N38M-type Nd–Fe–B permanent magnets with a volume of 3.93 cm3 each were used, the magnetic flux density reached 2.35 nT at 10 m in the air and the amplitude modulation performance was satisfactory. Additionally, the electromagnetic wave was effectively received at 3 m from the 20# steel pipeline, which preliminarily verified the feasibility of using the dual-permanent-magnet mechanical antenna to achieve localization of and communication with pipeline robots.


Introduction
Oil and gas pipelines underground and underwater need to be tested to ensure their safety, which necessitates the development of pipeline detection robot systems [1][2][3]. Achieving localization of and communication with cable-free pipeline robots is one of the key problems to be solved [4]. There are several localization methods, including the wheel odometer method, ray method, acoustic method, and electromagnetic wave method. The wheel odometer method can only provide off-line position information, and skidding between the wheels and pipe wall and wheel-locked situations result in accumulated position errors [5]. To improve its accuracy, some signal-processing methods including the prior-backtracking, data fusion, and point cloud registration methods have been proposed and achieved good results [6,7]. The ray method uses rays released by radioactive elements to achieve localization of robots. Although these rays can easily penetrate metal pipe walls, they are harmful to biological systems and the environment [8]. The acoustic method uses acoustic sensors to monitor the robot's position, but it is susceptible to environmental noise and requires high sensitivity of the acoustic sensors. Moreover, when a robot stops running due to unexpected factors, it cannot be located [9,10]. The electromagnetic wave method uses magnetic sensors to receive electromagnetic wave signals emitted by the pipeline robots for localization with little external interference [11][12][13]. However, metal pipelines shield high-frequency electromagnetic waves. In contrast, ultra-low-frequency electromagnetic waves have low attenuation and can penetrate metal pipelines, making this the preferred frequency band for localization of and communication with pipeline robots.  [23,24] Needs a modulator Normal in structure Sensitive to noise This work Needs a modulator Normal in structure Lower sensitivity to noise The rest of this paper is organized as follows. Section 2 describes the structure and working principles of the new mechanical antenna. Section 3 presents its prototype and Sensors 2023, 23, 3228 3 of 12 describes the experimental verification of its effectiveness in both air and pipelines. Finally, Section 4 provides the conclusions and discussion.

Theoretical Fundamentals
As shown in Figure 1, a cylinder-shaped permanent magnet with uniform magnetization along the radial direction is placed in infinite space. Its diameter and height are D and h, respectively, and its magnetic moment m 0 = M 0 V where M 0 is the magnetization intensity and V is the volume. A single stationary magnet can be equivalent to a magnetic dipole with the moment m 0 when r >> max(D,h). If it rotates counterclockwise at a uniform angular velocity ω, the magnet can be equivalent to two time-varying dipoles orthogonal in both time and space, and this moment m 0 (t) = m x (t)e x + m y (t)e y and . m x = j . m y . The rest of this paper is organized as follows. Section 2 describes the structure and working principles of the new mechanical antenna. Section 3 presents its prototype and describes the experimental verification of its effectiveness in both air and pipelines. Finally, Section 4 provides the conclusions and discussion.

Theoretical Fundamentals
As shown in Figure 1, a cylinder-shaped permanent magnet with uniform magnetization along the radial direction is placed in infinite space. Its diameter and height are D and h, respectively, and its magnetic moment m0 = M0V where M0 is the magnetization intensity and V is the volume. A single stationary magnet can be equivalent to a magnetic dipole with the moment m0 when r >> max(D,h). If it rotates counterclockwise at a uniform angular velocity ω, the magnet can be equivalent to two time-varying dipoles orthogonal in both time and space, and this moment m0(t) = mx(t)ex + my(t)ey and ̇x = j̇y. In a spherical coordinate system, the magnetic flux density generated by the dipole my can be expressed as follows: where k is the propagation constant and k = ω� 0 0 in which μ0 and ε0 are the permeability and dielectric constant of the vacuum, respectively. The magnetic flux density generated by the dipole mx can be expressed as follows: In a spherical coordinate system, the magnetic flux density generated by the dipole m y can be expressed as follows: where k is the propagation constant and k = ω √ ε 0 µ 0 in which µ 0 and ε 0 are the permeability and dielectric constant of the vacuum, respectively. The magnetic flux density generated by the dipole m x can be expressed as follows: Therefore, the magnetic flux density generated by a single rotating permanent magnet is as follows: Based on the magnetic field distribution of a single rotating permanent magnet, the dual-permanent-magnet mechanical antenna model is presented, as shown in Figure 2. In this model, the permanent magnets A and B rotate uniformly around the z axis with the same angular velocity ω, and their centers are both at a distance d from the coordinate origin O. The dimensions of the permanent magnets are same as those in Figure 1, and the angle between the magnetic moments is α. Assume that the magnetic flux densities generated by A and B are expressed by . B A and . B B , and then the magnetic flux density generated by the model shown in Figure 2 is as follows according to Equation (3): net is as follows: Based on the magnetic field distribution of a single rotating permanent magnet, the dual-permanent-magnet mechanical antenna model is presented, as shown in Figure 2. In this model, the permanent magnets A and B rotate uniformly around the z axis with the same angular velocity ω, and their centers are both at a distance d from the coordinate origin O. The dimensions of the permanent magnets are same as those in Figure 1, and the angle between the magnetic moments is α. Assume that the magnetic flux densities gen-    In particular, when r >> max(D,h,d), the impact of d is ignored and d ≈ 0; thus, From Equation (5), the amplitude of . B d changes when α changes and amplitude modulation is achieved. Suppose that a message comprising code elements 0 and 1 must be sent. When element 0 is sent, let α = 0 and B 0 = 2 . B s . When element 1 is sent, let α = α 1 , and B 1 = (1 + e jα 1 ) . B s (x, y, z) . Figure 3 shows the waveforms of the ideal amplitude Sensors 2023, 23, 3228 5 of 12 modulation signal in the time domain. If the difference between B 0 and B 1 is not significant and the ambient background magnetic field noise is large at the receiver, the quality of the amplitude modulation signal will become poor, which increases the bit error rate during demodulation. Here the modulation depth T m is defined as in Equation (6). According to Equation (5), T m = 1 − cos(α 1 /2). T m can reach the value of 1 when α = 180 • . The larger the α 1 , the larger the T m , and the stronger the antinoise performance of the system and the more reliable the communication.
From Equation (5), the amplitude of d & B changes when α changes and amplitude modulation is achieved. Suppose that a message comprising code elements 0 and 1 must be sent. When element 0 is sent, let α = 0 and When element 1 is sent, let α=α1, . Figure 3 shows the waveforms of the ideal amplitude modulation signal in the time domain. If the difference between B0 and B1 is not significant and the ambient background magnetic field noise is large at the receiver, the quality of the amplitude modulation signal will become poor, which increases the bit error rate during demodulation. Here the modulation depth Tm is defined as in Equation (6). According to . Tm can reach the value of 1 when α = 180°. The larger the α1, the larger the Tm, and the stronger the antinoise performance of the system and the more reliable the communication. Figure 3. Waveforms of the amplitude modulation signal in an ideal case.

Effectiveness of the Analytical Formula
The derivation of Equation (4) requires that a single rotating permanent magnet be equivalent to two time-varying magnetic dipoles. The effectiveness of this equivalence is verified by maintaining the volume V of the cylindrical permanent magnet as a constant and changing the outer dimension, i.e., the ratio of cross-sectional diameter to height D/h. The magnetic field distribution obtained using Equation (4) is compared with that obtained using finite-element calculations. Assume a radially magnetized permanent magnet is N38M-type and its volume V = 3.93 cm 3 , and the rotation frequency f = 30 Hz. For different values of (D/h), the magnetic field distribution along the y axis direction is shown in Figure 4, in which the errors are considerable when the spatial position r is close to the permanent magnets. However, when r/max(D,h) ≥ 4, the errors between two methods are approximately less than 5%, in which case the magnetic field calculated using Equation (4) is more accurate and the influence of the magnets' dimensions can be ignored.

Effectiveness of the Analytical Formula
The derivation of Equation (4) requires that a single rotating permanent magnet be equivalent to two time-varying magnetic dipoles. The effectiveness of this equivalence is verified by maintaining the volume V of the cylindrical permanent magnet as a constant and changing the outer dimension, i.e., the ratio of cross-sectional diameter to height D/h. The magnetic field distribution obtained using Equation (4) is compared with that obtained using finite-element calculations. Assume a radially magnetized permanent magnet is N38M-type and its volume V = 3.93 cm 3 , and the rotation frequency f = 30 Hz. For different values of (D/h), the magnetic field distribution along the y axis direction is shown in Figure 4, in which the errors are considerable when the spatial position r is close to the permanent magnets. However, when r/max(D,h) ≥ 4, the errors between two methods are approximately less than 5%, in which case the magnetic field calculated using Equation (4) is more accurate and the influence of the magnets' dimensions can be ignored.

Dual-Permanent-Magnet Mechanical Antenna
The structure of the dual-permanent-magnet mechanical antenna is shown in Figure  5a and the physical prototype of the antenna is shown in Figure 5b. It consists of a carrier module, a modulation module, and a control and monitoring module. The carrier module comprises a carrier motor, a rotating shaft, and permanent magnets A and B, in which the carrier motor drives A and B through the rotating shaft to rotate at a constant speed so that the magnetic field is radiated outward steadily. In Figure 5b, the carrier motor is a 12 V RK-370CA permanent magnet DC motor with a maximum speed of 5400 rpm, and both A and B are N38M-type radially magnetized permanent magnets with a remanence of 1.25 T, D = 25 mm, h = 8 mm, and d = 32.5 mm. The modulation module comprises a modulation motor, limiters, and brushes. The modulation motor is a 6 V geared motor rated at 300 rpm which is used to adjust the angle α of magnetic moments between A and B, and the limiters can limit the value of α. The modulation motor rotates along with the rotating shaft of the carrier motor, and the brushes are installed to prevent the wires at the outlet of the modulation motor from becoming entangled during the rotation process. The control and monitoring module comprises an Arduino UNO microcontroller, an AQMH2407ND DC motor driver, and a photoelectric sensor, which are used to control the rotation of the carrier and modulation motors and collect their status information through the photoelectric sensor. The power grid working frequency of 50 Hz should be avoided as the operating frequency of the antenna. The smaller the operating frequency, the deeper the wave will penetrate underground and underwater.

Dual-Permanent-Magnet Mechanical Antenna
The structure of the dual-permanent-magnet mechanical antenna is shown in Figure 5a and the physical prototype of the antenna is shown in Figure 5b. It consists of a carrier module, a modulation module, and a control and monitoring module. The carrier module comprises a carrier motor, a rotating shaft, and permanent magnets A and B, in which the carrier motor drives A and B through the rotating shaft to rotate at a constant speed so that the magnetic field is radiated outward steadily. In Figure 5b, the carrier motor is a 12 V RK-370CA permanent magnet DC motor with a maximum speed of 5400 rpm, and both A and B are N38M-type radially magnetized permanent magnets with a remanence of 1.25 T, D = 25 mm, h = 8 mm, and d = 32.5 mm. The modulation module comprises a modulation motor, limiters, and brushes. The modulation motor is a 6 V geared motor rated at 300 rpm which is used to adjust the angle α of magnetic moments between A and B, and the limiters can limit the value of α. The modulation motor rotates along with the rotating shaft of the carrier motor, and the brushes are installed to prevent the wires at the outlet of the modulation motor from becoming entangled during the rotation process. The control and monitoring module comprises an Arduino UNO microcontroller, an AQMH2407ND DC motor driver, and a photoelectric sensor, which are used to control the rotation of the carrier and modulation motors and collect their status information through the photoelectric sensor. The power grid working frequency of 50 Hz should be avoided as the operating frequency of the antenna. The smaller the operating frequency, the deeper the wave will penetrate underground and underwater.

Experiment in Air
The operating frequency of the antenna was maintained at 30 Hz. By switching α between 0° and 120°, the antenna transmitted codes 0 and 1 at a rate of 1 bit/s. Figure 6a shows the waveforms of the magnetic flux densities Bx, By, and Bz measured at y = 5 m along the positive y axis using a three-dimensional symmetrical induction coil [28]. In addition to the spectral component at 30 Hz, the components at 50 Hz and its harmonic frequencies were also measured. The waveforms after filtering these components are shown in Figure 6b. The distribution of magnetic flux density B and the modulation depth Tm along the positive y axis are shown in Figure 7 when α = 0 and α = 120°. It can be seen the magnetic field reached 2.35 nT at y = 10 m when α = 0 and the values of Tm ranged from 50% to 60%.

Experiment in Air
The operating frequency of the antenna was maintained at 30 Hz. By switching α between 0 • and 120 • , the antenna transmitted codes 0 and 1 at a rate of 1 bit/s. Figure 6a shows the waveforms of the magnetic flux densities B x , B y , and B z measured at y = 5 m along the positive y axis using a three-dimensional symmetrical induction coil [28]. In addition to the spectral component at 30 Hz, the components at 50 Hz and its harmonic frequencies were also measured. The waveforms after filtering these components are shown in Figure 6b. The distribution of magnetic flux density B and the modulation depth T m along the positive y axis are shown in Figure 7 when α = 0 and α = 120 • . It can be seen the magnetic field reached 2.35 nT at y = 10 m when α = 0 and the values of T m ranged from 50% to 60%.

Simulation and Experiments in Pipelines
Due to the shielding effect of the metal pipe wall, when the antenna is placed inside a pipeline, the magnetic field signal will be weakened. To verify the effectiveness of the antenna in a pipeline, finite-element simulations were conducted. The simulation model is shown in Figure 8, wherein the mechanical antenna was placed at the center of the pipeline. The pipeline's outer radius r p = 0.07 m, length l p = 1 m, and thickness h p = 0.005 m. The material of the pipeline was set to be air (no pipeline), aluminum, or iron. The aluminum's conductivity σ Al = 3.77 × 10 7 S/m. The iron's relative permeability µ Fe = 4000 and conductivity σ Fe = 1.12 × 10 7 S/m. The magnets had a diameter D = 0.025 m, height h = 0.008 m, distance 2d = 0.065 m, and rotation frequency f = 30 Hz. Due to the shielding effect of the metal pipe wall, when the antenna is placed inside a pipeline, the magnetic field signal will be weakened. To verify the effectiveness of the antenna in a pipeline, finite-element simulations were conducted. The simulation model is shown in Figure 8, wherein the mechanical antenna was placed at the center of the pipeline. The pipeline's outer radius rp = 0.07 m, length lp = 1 m, and thickness hp = 0.005 m. The material of the pipeline was set to be air (no pipeline), aluminum, or iron. The aluminum's conductivity σAl = 3.77 × 10 7 S/m. The iron's relative permeability μFe = 4000 and conductivity σFe = 1.12 × 10 7 S/m. The magnets had a diameter D = 0.025 m, height h = 0.008 m, distance 2d = 0.065 m, and rotation frequency f = 30 Hz.  Figure 9 when y = 0.2 m. It can be seen that when the antenna was placed in the pipeline, B was about 10 −5 T and it was attenuated due to the shielding effect of the pipe wall. The shielding effect of the iron pipeline with high permeability was more obvious than that of the aluminum pipeline. Pipelines made of 20# steel are mainly used for boilers and heat exchangers to transport fluids, which are widely used in petrochemical, power stations, and large-scale equipment. In the experiment, the antenna was placed in a practical 20# steel pipeline with an outer radius of 180 mm, length of 1200 mm, thickness of 8 mm, and conductivity of about 4.22 MS/m, as shown in Figure 10. The measured results are shown in Table 2. It can be seen that when a 20# steel pipeline was used, the magnetic flux density was effectively received at 3 m from the carbon steel pipeline with a receiving antenna able to measure a magnetic flux density of as low as 0.15 pT. Bx, By, and Bz all had high attenuation The distribution of magnetic flux density B is shown in Figure 9 when y = 0.2 m. It can be seen that when the antenna was placed in the pipeline, B was about 10 −5 T and it was attenuated due to the shielding effect of the pipe wall. The shielding effect of the iron pipeline with high permeability was more obvious than that of the aluminum pipeline. Due to the shielding effect of the metal pipe wall, when the antenna is placed inside a pipeline, the magnetic field signal will be weakened. To verify the effectiveness of the antenna in a pipeline, finite-element simulations were conducted. The simulation model is shown in Figure 8, wherein the mechanical antenna was placed at the center of the pipeline. The pipeline's outer radius rp = 0.07 m, length lp = 1 m, and thickness hp = 0.005 m. The material of the pipeline was set to be air (no pipeline), aluminum, or iron. The aluminum's conductivity σAl = 3.77 × 10 7 S/m. The iron's relative permeability μFe = 4000 and conductivity σFe = 1.12 × 10 7 S/m. The magnets had a diameter D = 0.025 m, height h = 0.008 m, distance 2d = 0.065 m, and rotation frequency f = 30 Hz.  Figure 9 when y = 0.2 m. It can be seen that when the antenna was placed in the pipeline, B was about 10 −5 T and it was attenuated due to the shielding effect of the pipe wall. The shielding effect of the iron pipeline with high permeability was more obvious than that of the aluminum pipeline. Pipelines made of 20# steel are mainly used for boilers and heat exchangers to transport fluids, which are widely used in petrochemical, power stations, and large-scale equipment. In the experiment, the antenna was placed in a practical 20# steel pipeline with an outer radius of 180 mm, length of 1200 mm, thickness of 8 mm, and conductivity of about 4.22 MS/m, as shown in Figure 10. The measured results are shown in Table 2. It can be seen that when a 20# steel pipeline was used, the magnetic flux density was effectively received at 3 m from the carbon steel pipeline with a receiving antenna able to measure a magnetic flux density of as low as 0.15 pT. Bx, By, and Bz all had high attenuation  Table 2. It can be seen that when a 20# steel pipeline was used, the magnetic flux density was effectively received at 3 m from the carbon steel pipeline with a receiving antenna able to measure a magnetic flux density of as low as 0.15 pT. B x , B y , and B z all had high attenuation which was consistent with the simulation results. When α was changed, the amplitudes of B x , B y , and B z changed significantly, indicating a good modulation. which was consistent with the simulation results. When α was changed, the amplitudes of Bx, By, and Bz changed significantly, indicating a good modulation.

Conclusions and Discussion
For pipeline robot positioning, compared with the wheel odometer, ray, and acoustic wave methods, the proposed method utilizes ultra-low-frequency electromagnetic waves with low attenuation, long transmission distance, and strong penetrability generated by the new small mechanical antenna made of permanent magnets. In this method, the amplitude modulation of the magnetic flux density is realized by changing the angle of the magnetic moments between the two permanent magnets. The effects of the mechanical antenna size on the magnetic field signal were studied using analytical theory and finiteelement simulations. When r/max(D,h) ≥ 4, the influence of the magnets' outer dimensions can be ignored. The experimental results showed that using the developed antenna, the quality of magnetic signal was satisfactory for communication at 10 m in the air and 3 m from a 20# steel pipeline, which preliminarily verified the feasibility of the antenna for localizing and communicating with pipeline robots.
The main factors affecting the communication quality of the proposed antenna can be summarized as follows: a. The magnetization M0 and volume V of the permanent magnet. According to (3) and (4), the amplitude of the magnetic flux density increases linearly with M0 and V. Thus, M0 and V affect only the strength of the magnetic field and do not affect the modulation performance. Increasing M0 and V can improve the signal propagation distance. However, if V is substantially large, the overall volume and rotational inertia of the antenna will increase. Therefore, for a fixed propagation distance, a permanent magnetic material with a larger M0 can be selected without increasing the antenna volume. b. The spacing d between the permanent magnets affects the near-field distribution and modulation performance of the antenna. When r >> max(D,h), the effect of d is negligible.

Conclusions and Discussion
For pipeline robot positioning, compared with the wheel odometer, ray, and acoustic wave methods, the proposed method utilizes ultra-low-frequency electromagnetic waves with low attenuation, long transmission distance, and strong penetrability generated by the new small mechanical antenna made of permanent magnets. In this method, the amplitude modulation of the magnetic flux density is realized by changing the angle of the magnetic moments between the two permanent magnets. The effects of the mechanical antenna size on the magnetic field signal were studied using analytical theory and finite-element simulations. When r/max(D,h) ≥ 4, the influence of the magnets' outer dimensions can be ignored. The experimental results showed that using the developed antenna, the quality of magnetic signal was satisfactory for communication at 10 m in the air and 3 m from a 20# steel pipeline, which preliminarily verified the feasibility of the antenna for localizing and communicating with pipeline robots.
The main factors affecting the communication quality of the proposed antenna can be summarized as follows: a.
The magnetization M 0 and volume V of the permanent magnet. According to (3) and (4), the amplitude of the magnetic flux density increases linearly with M 0 and V. Thus, M 0 and V affect only the strength of the magnetic field and do not affect the modulation performance. Increasing M 0 and V can improve the signal propagation distance. However, if V is substantially large, the overall volume and rotational inertia of the antenna will increase. Therefore, for a fixed propagation distance, a permanent magnetic material with a larger M 0 can be selected without increasing the antenna volume. b.
The spacing d between the permanent magnets affects the near-field distribution and modulation performance of the antenna. When r >> max(D,h), the effect of d is negligible.
c. The rotational speeds ω of the carrier motor and ω 1 of the modulation motor. Due to the limits of power consumption and long communication distance in conductive media such as underground or underwater, ω cannot be too large. However, the symbol transmission rate v (bit/s) depends on both ω and ω 1 . Assume the time required for the change of α: α = 0 → α 1 or α = α 1 → 0 is t 1 , which is the switch time of the modulation motor from start to stop, and, to improve the demodulation accuracy at the receiver, the conditions v << 1/t 1 and v ≤ ω/π should be satisfied.
The new dual-permanent-magnet mechanical antenna has many application prospects in the field of communication through conductive media and finite space, such as in pipelines, underwater, undersea, and underground. However, there is still much work to be done before it can be applied. For the positioning of and communication with pipeline robots, its size needs to be further reduced, which can be implemented by using permanent magnets of higher magnetic energy density and optimizing the antenna structure. In addition, the current amount of data for validation is not very large. The antenna should be placed in industrial pipelines with different electromagnetic characteristics to test its ability to function despite electromagnetic interference from low-frequency atmospheric noise and noise from human sources, or the low-frequency magnetic field transmitted by the robot itself. Moreover, we also need to study the high-efficiency receiving antenna and the high-accuracy positioning algorithm based on the received signals. In the future, this method will become more practical.