Ultrasonic active target positioning method and device

Abstract

The present invention discloses an ultrasonic active target positioning method and device, which includes an ultrasonic sensor array, a control module, and a computer. The present invention uses four ultrasonic sensors to form an array, whose configuration satisfies the condition that an analytical solution for the target position coordinates exists and is unique. The array adopts a one-transmit-multiple-receive signal transmission and reception mode, in which one ultrasonic sensor serves as a reference ultrasonic sensor and operates in a transmit / receive dual mode, and the remaining three ultrasonic sensors operate in a receive mode. The present invention determines an actual ultrasonic sensor array configuration, through which the three-dimensional target coordinates are solved and the distance between the target and the reference ultrasonic sensor is measured. The present invention has a simple sensor array configuration structure, a minimum number of required ultrasonic sensors, the smallest theoretical computational complexity in solving the target coordinates, and the best numerical stability.

Description

Technical Field

[0001] The present invention relates to ultrasonic positioning technology, and in particular to an ultrasonic active target positioning method and device. Background Art

[0002] With the development of computer science, sensor technology, and artificial intelligence, robotics has played a vital role in everything from manufacturing and transportation to space and deep-sea exploration. As one of the key technologies in robotics, target positioning technology is gaining increasing attention.

[0003] Currently, visual sensors, laser sensors, and ultrasonic sensors are the mainstream sensors used in robotic target positioning technology. While visual sensors provide rich information, they struggle to function properly in low-light or dark conditions. Laser sensors offer high accuracy, but they carry safety risks, are expensive, and cannot measure transparent objects. Compared to other sensors, ultrasonic sensors offer advantages such as low cost, low power consumption, small size, and light weight. They also have a wide range of applications, including for transparent objects and low-visibility or dark environments. Consequently, ultrasonic sensors are widely used in robotic target positioning research and applications.

[0004] However, practical applications of ultrasonic positioning technology still require solutions. Currently, most ultrasonic positioning methods employ a large number of ultrasonic sensors to obtain the arrival times or time differences of multiple received ultrasonic echoes. These methods then use the obtained arrival times to determine the target position through relatively complex numerical algorithms. These methods suffer from high computational complexity, a large number of sensors, and, in many cases, require prior knowledge and manual intervention.

[0005] Finding a target positioning method that uses relatively few ultrasonic sensors and has low computational costs has long been a goal of researchers. The present invention aims to achieve target positioning by optimizing the ultrasonic sensor array configuration, using the fewest ultrasonic sensors and the simplest array structure, and using the most stable analytical method with the lowest theoretical computational effort. The present invention proposes an ultrasonic active target positioning method and device. This method involves an ultrasonic sensor array configuration, target position solution, and distance measurement. This method uses a minimum number of ultrasonic sensors, ensures a unique analytical solution for the three-dimensional target position, and has the advantages of a small number of sensors, the lowest theoretical computational effort, the best solution stability, a simple sensor configuration, and high positioning accuracy. Summary of the Invention

[0006] In response to the current state of target positioning technology based on multiple ultrasonic sensors, the present invention provides an ultrasonic active target positioning method and device. The ultrasonic sensor array configuration in the positioning device can achieve target positioning in three-dimensional space. The present invention uses four ultrasonic sensors to form an ultrasonic sensor array. The array adopts a one-transmit-multiple-receive signal transmission and reception mode. One ultrasonic sensor serves as a reference ultrasonic sensor and operates in T / R dual mode, that is, it serves as both an ultrasonic transmitter and an ultrasonic receiver. The remaining three ultrasonic sensors operate in R mode, that is, they only serve as receivers. The time difference is obtained by calculating the time when the reference ultrasonic sensor transmits the ultrasonic wave and the time when the sensor receives the ultrasonic echo, and the target position is obtained. This ultrasonic sensor array configuration and method have the advantages of simple structure, minimal theoretical calculation, optimal solution stability, and high accuracy in target positioning.

[0007] The technical solutions of the present invention are as follows:

[0008] The present invention first provides an ultrasonic active target positioning device, which includes an ultrasonic sensor array, a control module and a computer;

[0009] The ultrasonic sensor array includes four ultrasonic sensors that are not in the same plane; one of the ultrasonic sensors serves as a reference ultrasonic sensor, which operates in a transmitting / receiving dual mode, that is, serves as both an ultrasonic transmitter and an ultrasonic receiver;

[0010] The control module controls each ultrasonic sensor to transmit and receive ultrasonic signals. Each sensor transmits a signal containing arrival time information to the control module. After obtaining the arrival time, the control module calculates the corresponding time difference based on the time when the reference ultrasonic sensor transmits the ultrasonic wave and the time when each ultrasonic sensor receives the ultrasonic echo. The control module communicates with the computer via a USB data cable and sends the time difference to the computer. The computer uses this time difference to solve the three-dimensional coordinates of the target object and the distance from the target to the reference ultrasonic sensor, and displays and saves the positioning and ranging results.

[0011] As a preferred solution of the present invention, the location of the reference ultrasonic sensor is taken as the coordinate origin, the other three ultrasonic sensors are respectively on three coordinate axes, and the distances between the other three ultrasonic sensors and the reference ultrasonic sensor are equal.

[0012] As a preferred solution of the present invention, the remaining three ultrasonic sensors operate in a receiving mode, that is, they only serve as ultrasonic receivers.

[0013] The present invention also provides an ultrasonic active target positioning method based on the above device, which comprises the following steps:

[0014] Step 1: Using a reference ultrasonic sensor in the ultrasonic sensor array to actively transmit ultrasonic waves, the ultrasonic waves are transmitted to the target object and reflected, and the four ultrasonic sensors respectively receive the reflected ultrasonic waves, i.e., ultrasonic echoes, and obtain the arrival time;

[0015] Step 2: Calculate the corresponding time difference Δt based on the time t0 when the reference ultrasonic sensor transmits the ultrasonic wave and the arrival time t1, t2, t3 and t4 when the four ultrasonic sensors receive the ultrasonic echo. 10 , Δt 21 , Δt 31 and Δt 41 ;Δt 10 =t1-t0,Δt i1 =t i -t1, i=2, 3, 4;

[0016] Step 3: Calculate the analytical solution of the target coordinates (x, y, z);

[0017] Step 4: Calculate the analytical solution of the distance ρ from the target to the reference ultrasonic sensor.

[0018] Compared with the prior art, the present invention has the following beneficial effects:

[0019] 1) The present invention utilizes an analytical method to solve the target coordinates and adopts a new ultrasonic sensor array configuration that satisfies the condition that the solution to the three-dimensional spatial coordinates of the target position exists and is unique. This overcomes the problems of existing ultrasonic positioning technology, such as high computational cost, large number of sensors, relatively complex sensor arrays, and the need for prior knowledge and manual intervention. Thus, the present invention has the advantages of requiring a small number of ultrasonic sensors, a simple configuration structure, and no need for prior knowledge and manual intervention.

[0020] 2) By arranging the ultrasonic sensors on the coordinate axes and optimizing the sensor coordinates from the perspective of the condition number, the present invention effectively simplifies the analytical solution, reduces the amount of calculation, and improves the stability of the solution, so that the computational complexity of the target coordinate solution is low, the theoretical amount of calculation is minimal, and it has the best numerical stability and high positioning accuracy.

[0021] 3) The device of the present invention is easy to install, small in size, low in power consumption, low in price, and has a wide range of applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a structural diagram of an ultrasonic active target positioning device;

[0023] Figure 2 This is a schematic diagram of four ultrasonic sensors in the same plane;

[0024] Figure 3This is a schematic diagram when the four ultrasonic sensors are not in the same plane;

[0025] Figure 4 yes Figure 3 A further optimized configuration of the ultrasonic sensor array spatial configuration shown;

[0026] Figure 5 yes Figure 4 A further optimized configuration of the ultrasonic sensor array spatial configuration is shown. DETAILED DESCRIPTION

[0027] This paper addresses the problem of target location based on the arrival time of ultrasonic signals and proposes a new ultrasonic sensor array configuration and a target location method based on this configuration. Compared to existing methods, this method utilizes fewer ultrasonic sensors, has a simpler configuration, theoretically minimizes computational effort, offers the best numerical stability, and achieves high positioning accuracy.

[0028] like Figure 1 As shown, the present invention provides a device for target positioning based on ultrasonic sensors, comprising an ultrasonic sensor array, a control module, and a computer. Four ultrasonic sensors form an array, and their configuration satisfies the nonsingular coefficient matrix of the linear equations for solving the target position. The configuration of the target positioning ultrasonic sensor array provided by the present invention includes four ultrasonic sensors, each of which is not located in the same plane. Any one of the four ultrasonic sensors is designated as a reference ultrasonic sensor, with its coordinates set to (0, 0, 0). The reference ultrasonic sensor operates in T / R dual mode, i.e., it both transmits and receives ultrasonic waves. The remaining three ultrasonic sensors are capable of operating in at least R mode, i.e., they must be receivers. In a preferred embodiment, the remaining three ultrasonic sensors operate only in R mode, i.e., they only receive ultrasonic waves. The four ultrasonic sensors are connected to the control module via wires to provide power supply, control, and transmission of arrival time information. After obtaining the arrival time, the control module calculates the corresponding time difference based on the time the reference ultrasonic sensor transmits the ultrasonic wave and the time each ultrasonic sensor receives the ultrasonic echo. The control module communicates with the computer via a USB data cable and transmits the time difference to the computer. The computer uses this time difference to solve the three-dimensional coordinates of the target object and the distance from the target to the reference ultrasonic sensor, and displays and saves the positioning and ranging results.

[0029] The process of determining the ultrasonic sensor array configuration of the present invention is as follows:

[0030] The basic model of 3D target positioning is established based on the target and N ultrasonic sensors. The coordinates of the target P are defined as (x, y, z), and the i-th ultrasonic sensor S i The coordinates of (x i,y i ,z i )(i=1,2,…,N). Considering the real-time positioning, the present invention adopts a one-transmit-multiple-receive ultrasonic signal transceiver mode. Let the ultrasonic sensor S1 be the reference ultrasonic sensor (coordinates are (0,0,0)), which can be any one of the N ultrasonic sensors; the reference ultrasonic sensor works in T / R dual mode, that is, it transmits and receives ultrasonic waves; the remaining ultrasonic sensors S i (i=2, 3, ..., N) works in R mode, that is, only receives ultrasonic waves.

[0031] Let t0 be the time when the reference ultrasonic sensor S1 emits ultrasonic waves, t i is the i-th ultrasonic sensor S i The moment when the ultrasonic echo is received (i=1, 2, ..., N) is the arrival time. Because the present invention is an active measurement process, t0 and t i is a known quantity.

[0032] For the reference ultrasonic sensor S1, what it receives is the echo of the ultrasonic wave it transmits, so the relationship between it and the target coordinates (x, y, z) can be expressed as the following equation.

[0033]

[0034] Where c is the speed of sound, Δt 10 =t1-t0.

[0035] For the remaining ultrasonic sensors S that only receive ultrasonic waves i (i=2, 3, ..., N), the ultrasonic wave propagates from S1 to the target object, is reflected by the target object, and the ultrasonic echo is detected by the ultrasonic sensor S i Receive. Therefore, S i The relationship between and the target coordinates can be expressed as the following equation.

[0036]

[0037] Where, Δt i1 =t i -t1, i = 2, 3, ..., N.

[0038] The sound speed in formulas (1) and (2) is calculated as follows.

[0039]

[0040] Where T is the ambient temperature in Celsius, obtained by the temperature sensor, and the obtained sound speed is in m / s.

[0041] Therefore, the target positioning problem can be reduced to the following equation.

[0042]

[0043] The computational cost of directly solving the nonlinear equations described by Equation (4) is relatively high. Therefore, Equation (4) is usually converted into a linear equation system about the position coordinates (x, y, z) of the target P before solving it.

[0044] First, square both sides of formula (4) and expand it to obtain:

[0045]

[0046] Then, the first equation (i.e., the equation determined by the reference ultrasonic sensor) is subtracted from the second to Nth equations in formula (5) in turn, and the following equations are obtained:

[0047]

[0048] Convert formula (6) to the unknown number p = [x, y, z] T The form of the linear equations is:

[0049] Gp=h (7)

[0050] in,

[0051]

[0052]

[0053] The coordinates of the ultrasonic sensor (x i ,y i ,z i ) and the speed of sound c are known. Δt 10 and Δt i1 It can be determined by t0 and t i Therefore, the matrix G and vector h are determined. By solving equation (7), the target positioning can be achieved.

[0054] According to linear algebra, if Equation (7) has a unique solution, then the matrix G should be a 3×3 square matrix and non-singular. This means that for the single-transmitter, multiple-receiver ultrasonic sensor array of the present invention, four ultrasonic sensors are required, that is, N = 4. Then Equation (7) can be simplified to:

[0055]

[0056] When G in the equation is non-singular, the analytical expression of the coordinates (x, y, z) of the target P can be obtained, that is, the analytical solution of the target coordinates is:

[0057]

[0058] Accordingly, the distance ρ from the target to the reference ultrasonic sensor can be calculated by the following formula.

[0059]

[0060] According to the above, the condition for the three-dimensional target coordinates (x, y, z) in formula (10) to have a unique analytical solution is that the matrix G is non-singular. The four ultrasonic sensor coordinates in the configuration of the target positioning ultrasonic sensor array are configured to meet this condition, where the expression of the matrix G is:

[0061]

[0062] The necessary and sufficient condition for the matrix G to be non-singular is that the four ultrasonic sensors in the ultrasonic sensor array are not in the same plane. The specific proof is as follows:

[0063] The position vectors of ultrasonic sensors S2, S3, and S4 are defined as s2 = [x2, y2, z2], s3 = [x3, y3, z3], and s4 = [x4, y4, z4], respectively. According to formula (13), it can be seen that vectors s2, s3, and s4 are the three row vectors of matrix G.

[0064] The positional relationship of the four ultrasonic sensors S1 , S2 , S3 and S4 in space can be divided into two types: one is that the four ultrasonic sensors are in the same plane, and the other is that the four ultrasonic sensors are not in the same plane.

[0065] First consider the case where the four ultrasonic sensors are in the same plane. Without loss of generality, Figure 2 As shown, assume that they are all in the xOy plane, that is, z2=z3=z4=0. At this time, the matrix G can be expressed as

[0066]

[0067] The determinant of G is det(G)=0, that is, G is singular.

[0068] Consider the case where the four ultrasonic sensors are not in the same plane. Without loss of generality, if Figure 3 As shown, assume that S1, S2 and S3 are in the xOy plane and S4 is outside the plane, that is, z2=z3=0 and z4≠0. In this case, G can be expressed as

[0069]

[0070] The determinant of G is

[0071] det(G)=z4(x2y3-x3y2) (16)

[0072] Since z4 ≠ 0, the necessary and sufficient condition for det(G) = 0 is x2y3 - x3y2 = 0. However, x2y3 - x3y2 = 0 implies that S1, S2, and S3 are collinear, and S1, S2, S3, and S4 are in the same plane. However, this contradicts the premise that the four ultrasonic sensors are not in the same plane. Therefore, det(G) ≠ 0, meaning that G is nonsingular.

[0073] Therefore, the necessary and sufficient condition for the matrix G to be non-singular is that the four ultrasonic sensors in the ultrasonic sensor array are not in the same plane. The proof is complete.

[0074] In fact, from a vector perspective, we can also reach the same conclusion based on linear algebra. If the four ultrasonic sensors are in the same plane, vectors s2, s3, and s4 are linearly correlated, meaning the three row vectors of matrix G are linearly correlated. Therefore, det(G) = 0, meaning G is singular. If the four ultrasonic sensors are not in the same plane, vectors s2, s3, and s4 are linearly independent, meaning the three row vectors of matrix G are linearly independent. Therefore, det(G) ≠ 0, meaning G is nonsingular. Therefore, G is nonsingular if and only if the four ultrasonic sensors are not in the same plane.

[0075] Based on the above discussion, the target coordinates (x, y, z) can be uniquely solved by formula (11) if and only if the four ultrasonic sensors are not in the same plane.

[0076] The present invention realizes positioning by solving formula (10). Since the computational complexity and stability of the analytical solution are important, the present invention ensures that the analytical solution of the target coordinates is simple in form, has a small computational complexity, and has good stability by reasonably selecting the coordinates of the four ultrasonic sensors. In order to simplify the expression of the analytical solution and reduce the computational complexity, the matrix G is designed as a diagonal matrix by setting S2, S3, and S4 on the three coordinate axes respectively. Figure 4 As shown, let the coordinates of ultrasonic sensor S2 be (x2, 0, 0), the coordinates of ultrasonic sensor S3 be (0, y3, 0), and the coordinates of ultrasonic sensor S4 be (0, 0, z4). The matrix G under this configuration is non-singular and has the form:

[0077]

[0078] Furthermore, in order to improve the numerical stability of solving the target coordinates (x, y, z), the coordinates of the four ultrasonic sensors can be optimized from the perspective of the condition number cond(G) of the matrix G.

[0079] This method achieves positioning by solving a system of linear equations with G as the coefficient matrix. According to linear algebra, cond(G) is an important indicator of solution stability. A large cond(G) means that measurement errors may have a significant impact on the solution, and the solution may fluctuate greatly. A small cond(G) means that the measurement errors have a small impact on the solution, and the solution is stable. According to linear algebra, regardless of the norm, the minimum value of the condition number cond(G) of the matrix G is 1. When cond(G) = 1, the solution is most stable.

[0080] Based on the above two considerations, the present invention proposes a practical four-element ultrasonic sensor array configuration, which requires that S2, S3, and S4 are on three coordinate axes respectively, and the distances between these three ultrasonic sensors and the reference ultrasonic sensor (origin) are equal. Let x2 = y3 = z4 = a, that is, the coordinates of ultrasonic sensor S2 are (a, 0, 0), the coordinates of ultrasonic sensor S3 are (0, a, 0), and the coordinates of ultrasonic sensor S4 are (0, 0, a), and a is the distance between S2, S3, and S4 and the reference ultrasonic sensor. The coordinates of the proposed array configuration are as follows: Figure 5 shown.

[0081] The corresponding matrix G can be expressed as:

[0082]

[0083] At this time, the diagonal elements of G are equal, and the condition number of the matrix G is 1 regardless of the norm, cond(G) = 1, the condition number of the matrix G reaches the minimum value, and the stability of the solution is the best.

[0084] The corresponding inverse matrix G -1 for:

[0085]

[0086] The corresponding vector h is:

[0087]

[0088] The analytical expression of the target coordinates (x, y, z) corresponding to the actual four-element ultrasonic sensor array configuration, that is, the analytical solution of the target coordinates is:

[0089]

[0090] Correspondingly, the analytical expression of the distance ρ from the target to the reference ultrasonic sensor is:

[0091]

[0092] During the implementation of the method of the present invention, the control module first controls the reference ultrasonic sensor to emit an ultrasonic pulse. The ultrasonic pulse is transmitted outward and reflected after encountering a target. The reflected ultrasonic echo is received by four ultrasonic sensors. The four sensors then transmit a signal containing arrival time information to the control module. After obtaining the arrival time, the control module uses the time t0 when the reference ultrasonic sensor emits the ultrasonic wave and the arrival times t1, t2, t3, and t4 when the four ultrasonic sensors receive the ultrasonic echo to calculate the corresponding time difference Δt. 10 , Δt 21 , Δt 31 and Δt 41 ; The control module communicates with the computer via the USB data cable and 10 , Δt 21 , Δt 31 and Δt 41 The data is sent to the computer, which solves the coordinates of the target object according to formula (21) and the distance from the target to the reference ultrasonic sensor according to formula (22), and displays and saves the positioning and ranging results.

[0093] Specifically, you can follow the steps below:

[0094] Step 1: Using a reference ultrasonic sensor in the ultrasonic sensor array to actively transmit ultrasonic waves, the ultrasonic waves are transmitted to the target object and reflected, and the four ultrasonic sensors respectively receive the reflected ultrasonic waves, i.e., ultrasonic echoes, and obtain the arrival time;

[0095] Step 2: Calculate the corresponding time difference Δt based on the time t0 when the reference ultrasonic sensor transmits the ultrasonic wave and the arrival time t1, t2, t3 and t4 when the four ultrasonic sensors receive the ultrasonic echo. 10 , Δt 21 , Δt 31 and Δt 41 ;Δt 10 =t1-t0,Δt i1 =t i -t1, i=2, 3, 4;

[0096] Step 3: Calculate the analytical solution of the target coordinates (x, y, z) according to formula (21);

[0097] Step 4: Calculate the analytical solution of the distance ρ from the target to the reference ultrasonic sensor according to formula (22).

[0098] In order to verify the effectiveness and positioning effect of this method and device, a target positioning experiment was carried out.

[0099] according to Figure 5The coordinates shown here represent a practical ultrasonic sensor array, where a = 8 cm. The target to be measured is a 20 × 20 cm plastic plate. The center coordinates of the plastic plate serve as the location coordinates of the object under test. The ambient temperature for the experiment was 25°C.

[0100] Experiments show that this method and device can locate and measure the distance to a target object with good accuracy within a 3.0m test range. The absolute errors of the positioning coordinates x, y, and z, as well as the distance ρ from the measured object to the reference ultrasonic sensor, are all within 3.0cm.

[0101] The present invention comprises a sensor array composed of four ultrasonic sensors, whose configuration satisfies the requirement for a unique analytical solution to the target's position coordinates. This ultrasonic sensor array configuration and the target position determination method based on ultrasonic signal arrival times enable the positioning and ranging of target objects in three-dimensional space. Compared to existing methods, this method requires fewer ultrasonic sensors, has a simpler configuration, theoretically minimizes computational effort, offers the best numerical stability, and achieves high positioning accuracy.

Claims

1. An ultrasonic active target positioning device, characterized in that including an ultrasonic sensor array, a control module, and a computer; The ultrasonic sensor array includes four ultrasonic sensors that are not in the same plane; one of the ultrasonic sensors serves as a reference ultrasonic sensor and operates in a transmit / receive dual mode, that is, as both an ultrasonic transmitter and an ultrasonic receiver; the location of the reference ultrasonic sensor is used as the coordinate origin, and the other three ultrasonic sensors are respectively on three coordinate axes, and the distances between the other three ultrasonic sensors and the reference ultrasonic sensor are equal; The control module controls each ultrasonic sensor to transmit and receive ultrasonic signals. Each sensor transmits a signal containing arrival time information to the control module. After obtaining the arrival time, the control module calculates the corresponding time difference based on the time when the reference ultrasonic sensor transmits the ultrasonic wave and the time when each ultrasonic sensor receives the ultrasonic echo. The control module communicates with the computer via a USB data cable and sends the time difference to the computer. The computer uses this time difference to solve the three-dimensional coordinates of the target object and the distance from the target to the reference ultrasonic sensor, and displays and saves the positioning and ranging results. The four ultrasonic sensors are respectively denoted as 、 、 and , so that the ultrasonic sensor is the reference ultrasonic sensor, and its coordinates are , 、 and The coordinates of ,in for 、 and The distance to the reference ultrasonic sensor; the time when the reference ultrasonic sensor transmits ultrasonic waves And the arrival time of the ultrasonic echo received by the four ultrasonic sensors 、 、 and , calculate the corresponding time difference 、 、 and ; , , ; Object under test Coordinates It is expressed as follows analytically: ； ； ； in is the speed of sound.

2. The ultrasonic active target positioning device according to claim 1, characterized in that: The other three ultrasonic sensors work in receiving mode, that is, they only serve as ultrasonic receivers.

3. An ultrasonic active target positioning method for the device according to claim 2, characterized in that: The steps include: Step 1: Using a reference ultrasonic sensor in the ultrasonic sensor array to actively transmit ultrasonic waves, the ultrasonic waves are transmitted to the target object and reflected, and the four ultrasonic sensors respectively receive the reflected ultrasonic waves, i.e., ultrasonic echoes, and obtain the arrival time; Step 2: The time when the ultrasonic sensor emits ultrasonic waves And the arrival time of the ultrasonic echo received by the four ultrasonic sensors 、 、 and , calculate the corresponding time difference 、 、 and ; , , ; Step 3: Calculate the target coordinates The analytical solution of Step 4: Calculate the distance from the target to the reference ultrasonic sensor Analytical solution of .

4. The ultrasonic active target positioning method according to claim 3, characterized in that: Step 4: The distance from the object to the reference ultrasonic sensor Specifically: 。

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