At plant construction and maintenance sites, the dimensional measurement and positioning of various equipment, piping, and parts are extremely important technologies for ensuring construction quality and safety. These tasks are essential for maintaining consistency with design drawings, ensuring the accuracy of piping connections, and directly relate to post-construction maintenance and inspection work.
Conventionally, high-precision 3D scanning devices such as laser trackers have been used for spatial dimension measurement. However, these require specialized knowledge and skills, necessitating dedicated measurement personnel with advanced expertise. Furthermore, optical motion capture, which is widely used as a real-time position measurement technology, utilizes light and thus requires many measurement components. Signal processing also requires high-speed peripheral circuits, which tends to complicate the system configuration and increase implementation costs.
Therefore, for the purpose of streamlining measurement and positioning at plant construction and maintenance sites, we have developed "Orientator," an airborne ultrasonic spatial dimension measurement technology capable of measuring the spatial relative positional relationship (position, orientation, and angle) of two objects. This technology consists of ultrasonic transmitters, receivers, and a temperature compensation mechanism. Compared to optical systems, the system components are simpler, allowing site workers without specialized knowledge to handle it easily, which is expected to rationalize measurement tasks.
In this paper, we describe the measurement principle of the Orientator, evaluate the performance of the trial-manufactured prototype, and discuss future challenges and prospects.
The measurement principle of this device is a method that implements the principle of radio-wave GPS [1, 2] using ultrasonic waves [3]. It is based on the Time-of-Flight (ToF) method using ultrasonic waves that propagate and diffuse radially (hemispherically) and an extension of the 3-side measurement technique. As a basic theorem of rigid body physics, knowing the orientation information of an object with six degrees of freedom only requires knowing the spatial coordinates of three points included in that object [4]. This measurement method utilizes that property.
The system is configured to perform three sets of 3-side measurements in real-time using three ultrasonic transmitters and three ultrasonic receivers (see Fig. 1(a)). It is assumed that the spatial coordinates where the transmitters are installed are known. Additionally, it is necessary to identify which transmitter emitted the ultrasonic wave received by the receiver. For instance, the Time Division Multiple Access (TDMA) method, where transmitters are switched temporally to emit waves one by one, is an effective method.
When defining the symbols as above, the distance between each transducer and each microphone is described by coordinate parameters as follows:
On the other hand, describing the distance between each transducer and each microphone using the speed of sound, constant, ambient temperature, and arrival time of the transmitted wave results in:
Here, from equations (1) and (2), the following is established:
Equation (3) consists of three sets of nonlinear simultaneous equations in three variables. To derive the solution ((xi, yi, zi), i = 1,2,3), it is common to perform numerical calculations using an iterative method (Newton's method) [5, 6]. With the performance of modern PCs, this iterative calculation converges almost instantly (in real-time) to calculate the solution.
The plane equation (4) containing the three transmitter points is assumed to be known, and the plane equation (5) containing the three receiver points obtained in section 2.1 is derived (see Fig. 1(b)).
The normal vector for each plane equation is easily obtained, and from the cosine theorem for vectors in 3D space and the dot product formula [7], the angle formed by the normal vectors is calculated (see Fig. 1(b)):
The position, orientation, and angle of an object containing plane equation (5) relative to an object containing plane equation (4) can be quantitatively calculated in real-time.
The processing from equations (3) to (6) is repeated. Note that in equation (6), if the n1 vector is set to the normal vector (0,0,1) of the x-y plane, the angle between plane equation (5) and the x-y plane can be calculated.
At this time, if the transmitter is installed on a reference plane and the receiver on the other measurement target surface, and the measurement target surface is held stationary, a spatial dimension measurement device can be configured. If the measurement target surface is moved, a motion capture system can be configured.
Fig. 2(a) shows a diagram of the apparatus. Ultrasonic waves are emitted from three transducers one by one alternately (TDMA method), and these waves are received by three receivers. A thermocouple is used for sound speed correction according to the ambient temperature. Based on the data obtained, calculations are performed on a PC, and the relative positional relationship of objects is projected on the PC screen (see Fig. 2(b)).
An important implementation point is utilizing the property that ultrasonic waves propagate and diffuse radially (hemispherically) when passed through a hole with a diameter sufficiently smaller than the wavelength [8]. By using 40kHz band ultrasonic waves and passing them through a φ1mm hole on the transmitter side and a φ0.5mm hole on the receiver side, we confirmed that waves can be projected hemispherically and received from any direction on the hemisphere.
Additionally, to measure the flight time when receiving the transmitted wave, it is necessary to perform cross-correlation as a wave identification method. This was made possible by generating and using a characteristic transmission ultrasonic waveform [9].
Fig. 3(a) shows a photograph of the apparatus, and Fig. 3(b) shows the 3D display program screen running on a PC. By acquiring the position, orientation, and angle (orientation) information of object B relative to object A in real-time and displaying it continuously on the PC screen, the system can be used as a spatial dimension measurement device or motion capture.
The software screen display in Fig. 3(b) is a demonstration showing that when piping objects with flanges are created in advance and the device is properly deployed on the flange surfaces, the positional, orientation, and angular relationships between the pipes can be instantly measured. In plant construction, minute errors when installing equipment like tanks and pumps are absorbed during piping connection. Since the position, orientation, and angle between pipes are displayed on the PC simply by aligning the transmitter and receiver with the objects, specialized measurement knowledge is unnecessary. As the movement of the connected pipes is displayed in real-time, we confirmed that alignment tasks can be rationalized according to drawing requirements.
Table 1 shows the performance test results of the apparatus prototype. Objects A and B in Fig. 3(a) were fixed, and the distance displayed on the PC program was compared with the physically managed distance. Fluctuations in digital values (fluctuation from the true value over time) were checked. The mismeasurement rate was measured by fixing object A and moving object B freely.
| Performance Item | Value |
|---|---|
| Spatial dimension measurement range | About 1000 mm |
| Motion capture operating range | About 700 mm |
| Spatial dimensional accuracy | About ±1 mm |
| Measurement angle accuracy | About ±1 ° |
| Frame per Second (FPS) | About 13 FPS |
| Mismeasurement rate (MAX.) | 5 FPS* |
* Depends on the device's speed, position, direction, and orientation.
In Table 1, the measurable range is approximately 1000mm, but over 2000mm is desired for plant sites. To extend the range while maintaining accuracy, it is necessary to improve the S/N ratio by increasing transmitter output, enhancing receiver sensitivity, and optimizing cross-correlation methods for the transmitted and received waveforms. Optimization of the number of integrations for reception data is also required.
As shown in Table 1, motion capture performance features a range of 700mm at 13 FPS, with errors in convergence calculations at a maximum of 5 FPS. To enhance work safety by monitoring during pipe movement, increasing the frame rate and decreasing convergence errors are necessary. This includes investigating transmission waveforms that are easier to identify [9] and improving the numerical calculation routines for Newton's method to ensure more reliable convergence.
Compared to optical motion capture, this ultrasonic device has fewer parts and lower computational loads for 3D drawing and iterative calculations. To supply it more cheaply, we plan to replace general-purpose FPGA boards with dedicated circuits, minimize part counts, and implement MEMS technology for transmitters, as receivers already use MEMS microphones.
We demonstrated that spatial dimension measurement and motion capture can be configured with ultrasonic waves, allowing positional relationship measurement by constructing piping objects within a PC. In the future, we aim to improve measurable range and frame rate performance based on hardware S/N ratio improvements. We also intend to expand applications by combining with sensors like gyros and gravity sensors, and explore fields where only sound waves can measure, such as inside opaque liquids or dark environments. We expect this to be a highly compatible device for the CPS era.