Underwater relative posture perception method based on pressure matrix measurement system

Abstract

This invention discloses an underwater relative pose sensing method based on a pressure lattice measurement system. It primarily involves installing a pressure lattice measurement system on an underwater robot. One or more compression springs within the system are pressed by the target structure, generating pressure. The actual compression of the springs is then determined, allowing for the calculation of the underwater robot's relative distance and attitude information. This results in the output of corresponding underwater relative pose feedback control commands, enabling autonomous and stable pose control of the underwater robot relative to the target structure surface during inspection operations. This invention utilizes pressure lattice feedback data to calculate the distance and attitude of the underwater robot relative to the target structure. For robots requiring close proximity to underwater structures for observation, this method fills the gap in sensing solutions for near-field relative positioning data when laser or visual ranging fails in murky water environments, demonstrating significant application value.

Description

Technical Field

[0001] This invention belongs to the field of underwater robot automation technology, specifically relating to an underwater relative pose perception method based on a pressure dot matrix measurement system. Background Technology

[0002] With the popularization and application of underwater robot technology, more and more underwater structure inspection operations are beginning to use highly automated underwater robots to replace traditional divers, minimizing costs, reducing personnel risks, and improving operational efficiency. When performing underwater structure inspection operations, underwater robots need to overcome adverse underwater environmental influences (such as water pressure, low light, and turbid water) to get as close as possible to the structure surface to obtain sufficiently clear image data. To ensure stable image acquisition during the operation, the robot's position (especially the vertical distance) and attitude relative to the inspected structure surface must be maintained stably. This requires the robot to have the ability to autonomously control its own pose relative to the surface of the object being measured. The prerequisite for achieving this function is to effectively measure the robot's current distance and attitude relative to the surface of the object being measured.

[0003] Existing ranging methods mainly include underwater laser and ultrasonic ranging. Underwater laser ranging offers high accuracy and fast response under ideal water conditions, while acoustic ranging is applicable to a wide range of water conditions, but its measurement accuracy is not high and its timeliness is lower than that of laser ranging. More importantly, these two ranging methods are not well applied to underwater structure inspection tasks. Taking the inspection of inland river bridge piers, which has the most complex environment, as an example, inland river basins generally have high flow velocities, shallow riverbeds, and high sediment content. In this environment, the laser ranging distance is extremely compressed, and the strong reflection of suspended particles can easily cause serious deviations in the measured distance, severely limiting its practical effectiveness. On the other hand, in turbid environments, the robot needs to be very close to the surface of the bridge pier to see the surface condition of the structure. In this case, it is very likely that the minimum range of the ranging sonar will not be reached, and the accuracy will fluctuate significantly. At the same time, there is no technology that can directly measure the posture of the underwater robot relative to the object being measured. Therefore, existing technologies cannot adequately meet the requirements for robot posture perception relative to the surface of the object being measured. Summary of the Invention

[0004] The purpose of this invention is to address the aforementioned shortcomings by providing an underwater relative pose sensing method based on a pressure lattice measurement system. This patent primarily utilizes pressure lattice feedback data to calculate the relative distance and attitude data of the underwater robot, thereby determining the robot's actual spatial position and attitude. This enables the underwater robot to perform subsequent tasks. For robots requiring close-range observation of underwater structures, this method fills the gap in existing sensing solutions lacking relative positioning data under close-range conditions, and has significant application value.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] An underwater relative pose sensing method based on a pressure lattice measurement system includes the following steps:

[0007] Step 1: Install a pressure lattice measurement system on the underwater robot;

[0008] Step two: Navigate the underwater robot to the vicinity of the surface of the target structure to be inspected via remote control or autonomous indexing;

[0009] Step 3: Using the first-person perspective information returned by the onboard camera of the underwater robot, adjust the body posture of the underwater robot so that the pressure dot matrix measurement system is facing the surface of the target structure to be inspected.

[0010] Step 4: Control the underwater robot to move closer to the target structure to be tested, so that one or more compression springs of the pressure lattice measurement system are squeezed by the target structure. At this time, the compressed springs simultaneously exert pressure on the pressure sensors of the corresponding pressure lattice measurement system. By combining the real-time pressure measurement signal of the pressure sensor with the "force-deformation" model of the compression spring, the actual compression amount of the compression spring can be obtained.

[0011] Step 5: Calculate the relative distance and attitude information of the underwater robot relative to the target structure to be detected by compressing the actual compression of the spring.

[0012] Step 6: Based on the relative distance and attitude information of the underwater robot relative to the target structure to be inspected, formulate and output corresponding underwater relative pose feedback control commands to realize the autonomous and stable pose control of the underwater robot relative to the surface of the target structure to be inspected during the inspection operation.

[0013] The present invention further describes that the pressure dot matrix measurement system includes a mounting base plate and pressure measuring devices; at least four pressure measuring devices are arranged on the mounting base plate; each pressure measuring device consists of a compression spring, a pressure sensor, a spherical caster wheel, and an axially movable positioning optical shaft; the pressure sensor is fixed to a corresponding position on the mounting base plate; one end of the compression spring presses against the pressure sensor, and the other end is connected to the spherical caster wheel; one end of the axially movable positioning optical shaft directly penetrates the inner center of the compression spring and connects to the inner side of the spherical caster wheel to guide the compression spring only along the axial direction, and the other end moves with low resistance along the corresponding through-hole on the mounting base plate.

[0014] The present invention further explains that the compression spring is subjected to a quantitative compression test before installation to obtain matching data between different compression amounts and pressures, and to fit the "force-deformation" model of the compression spring.

[0015] The present invention further explains that the calculation process in step five is as follows:

[0016] Let Q be the point where the spring is compressed in four places. m -x m y m The projection points in the plane are P1, P2, P3, and P4, with coordinates (-a, -b, 0), (a, -b, 0), (a, b, 0), and (-a, b, 0), respectively. Let the contact points between the spherical casters located at the four ends of the compression springs and the object surface be T1, T2, T3, and T4, with coordinates (-a, -b, z1), (a, -b, z2), (a, b, z3), and (-a, b, z4), respectively, where z... i (i = 1, 2, 3, 4) represents the compression amount of the i-th compression spring;

[0017] Let the outward normal unit vector of the reference end face P1P2P3P4 on the underwater robot lie in the reference coordinate system {O}. m The representation of n under} m =[0,0,1] T ;

[0018] By forming a planar triangle using any three of the contact points T1, T2, T3, and T4, four planar combinations are obtained: ΔT4T1T2, ΔT1T2T3, ΔT2T3T4, and ΔT3T4T1. Let their corresponding outward normal unit vectors be n. m1 n m2 n m3 n m4 ;

[0019] Based on the four combinations ΔT4T1T2, ΔT1T2T3, ΔT2T3T4, and ΔT3T4T1, the two sides of each triangle are selected as its orthogonal vectors in the plane according to the right-hand rule as follows:

[0020] For ΔT4T1T2, the vector is chosen as and

[0021] For ΔT1T2T3, the vector is chosen as and

[0022] For ΔT2T3T4, the vector is chosen as and

[0023] For ΔT3T4T1, choose the vector as and

[0024] Based on the cross product operation and the right-hand rule, the outward normal unit vector of the corresponding triangular plane is:

[0025]

[0026] in, It is a vector Euclidean length;

[0027] Similarly, we can conclude that

[0028]

[0029] in,

[0030] Based on the ZYX rotation rule to describe the rotational relationships, each triangular plane ΔT4T1T2, ΔT1T2T3, ΔT2T3T4, and ΔT3T4T1 can be considered as originating from the reference plane P1P2P3P4 on the underwater robot, passing through ① a zero-degree yaw angle, i.e., ψ=0; ② a pitch angle, i.e. ③ Roll angle, i.e. The result is obtained after three rotations; this rotation can be represented by the rotation matrix R∈SO(3);

[0031] Taking a planar triangle ΔT4T1T2 as an example, suppose that it has ψ1 = 0 relative to the reference plane P1P2P3P4. The rotation of the reference coordinate system {O}, which was originally located in the reference plane, will then... m} Rotated to the coordinate system {O} within the triangular plane ΔT4T1T2 m1 The rotation matrix R1 defined by this rotation is:

[0032]

[0033] Wherein, R1 satisfies the following equation:

[0034] R1n m1 =e3(1.6)

[0035] Where, e3 = [0,0,1] T For {O m1} system z m1 The unit vector of the axis in {O m1 Expressions under the} system;

[0036] According to equation (1.6),

[0037]

[0038] (That is: according to equation (1.6), multiply both sides by the inverse matrix of R1 (for the special matrix R1, its inverse matrix is ​​equal to its transpose matrix), and then compare the three components on both sides of the equation to obtain equation (1.7)).

[0039] According to the second equation of equation (1.7), we can obtain that

[0040]

[0041] Furthermore, according to the first and third equations of equation (1.7), we can obtain that...

[0042]

[0043] Similarly, let the rotational relationships between the triangular planes ΔT1T2T3, ΔT2T3T4, and ΔT3T4T1 and the reference plane P1P2P3P4 be represented by rotation matrices R2, R3, and R4, respectively, and satisfy the following conditions.

[0044]

[0045] Then it can be obtained through the corresponding outward normal unit vector n mi Calculate the corresponding attitude angles for (i = 2, 3, 4):

[0046]

[0047] Finally, the average distance between the reference plane P1P2P3P4 and the surface of the target structure being tested, represented by the four pressure contact points T1T2T3T4, is obtained. and average attitude for:

[0048]

[0049] This invention further clarifies that the above calculation method is not limited to an array of four pressure measurement units. Theoretically, as long as there are three sets of non-collinear pressure measurement points T... i (i = 1, 2, ..., k, and k ≥ 3), then the average distance can be calculated. and average attitude The more measurement points there are, the less sensitive the calculated average result is to measurement noise introduced by each measurement unit.

[0050] The measurement system is typically fixed to the underwater robot structure via threaded connections or other connection methods. Generally, the measurement system is installed on the side of the underwater robot that faces the surface to be inspected during inspection operations.

[0051] Advantages of this invention:

[0052] 1. By applying this invention, underwater robots can reliably perceive the distance and attitude of the structure being measured under any aquatic environment conditions (including turbid water), which is an effective method for underwater robots to compensate for the failure of conventional acoustic and optical detection in harsh underwater conditions.

[0053] 2. This invention provides a novel underwater relative pose sensing method based on pressure feedback.

[0054] 3. Based on the acquired relative pose perception information, the underwater robot can achieve stable autonomous control relative to the target structure in terms of distance and angle when facing the structure to be inspected, without requiring the operator to monitor and adjust these degrees of freedom in real time. During the operation, the operator only needs to control the robot to move up and down and left and right towards the surface of the structure being tested, which greatly simplifies the remote control difficulty of the inspection operation, improves the search efficiency for defects on the structural surface, and enhances the clarity of the acquired images. Attached Figure Description

[0055] Figure 1 This is a schematic diagram of the structure of an underwater robot equipped with a pressure dot matrix measurement system in one embodiment of the present invention.

[0056] Figure 2 This is a schematic diagram of the pressure lattice measurement system in one embodiment of the present invention.

[0057] Figure 3 This is a front view of a pressure lattice measurement system and its key geometric relationship diagram in one embodiment of the present invention.

[0058] Figure 4 This is a perspective view of a pressure lattice measurement system and its key geometric relationships in one embodiment of the present invention.

[0059] Figure 5 This is a diagram showing the coordinate rotation transformation relationship between the contact plane and the robot reference plane of the pressure dot matrix measurement system in one embodiment of the present invention.

[0060] Figure 6 This is a diagram of the architecture of the relative pose stabilization control system based on underwater pressure array relative pose measurement in this invention.

[0061] Reference numerals: 1-Underwater robot body, 2-Horizontal thruster, 3-Vertical thruster, 4-Mounting base plate, 5-Compression spring, 6-Pressure sensor, 7-Spherical caster wheel, 8-Axial movable positioning optical axis. Detailed Implementation

[0062] The present invention will be further described below with reference to the accompanying drawings.

[0063] Example 1:

[0064] An underwater relative pose sensing method based on a pressure lattice measurement system, characterized by the following steps:

[0065] Step 1, as follows Figure 1 As shown, a pressure lattice measurement system is installed on an underwater robot;

[0066] Step two: Navigate the underwater robot to the vicinity of the surface of the target structure to be inspected via remote control or autonomous indexing;

[0067] Step 3: Using the first-person perspective information returned by the onboard camera of the underwater robot, adjust the body posture of the underwater robot so that the pressure dot matrix measurement system is facing the surface of the target structure to be inspected.

[0068] Step 4: Control the underwater robot to move closer to the target structure to be tested, so that one or more compression springs of the pressure lattice measurement system are squeezed by the target structure. At this time, the compressed springs simultaneously exert pressure on the pressure sensors of the corresponding pressure lattice measurement system. By combining the real-time pressure measurement signal of the pressure sensor with the "force-deformation" model of the compression spring, the actual compression amount of the compression spring can be obtained.

[0069] Step 5: Calculate the relative distance and attitude information of the underwater robot relative to the target structure to be detected by compressing the actual compression of the spring.

[0070] Step six: Based on the relative distance and attitude information of the underwater robot relative to the target structure to be detected, a corresponding underwater relative pose feedback control scheme architecture can be designed (e.g., Figure 6 (As shown) and outputs corresponding underwater relative pose feedback control commands to realize the autonomous and stable pose control of the underwater robot relative to the surface of the target structure during the inspection operation.

[0071] Taking the example of keeping the underwater robot always facing the surface of the structure being measured and maintaining a constant distance, the relative pose tracking target is then set as follows: and ψ d =θ d =φ d =0.

[0072] This embodiment further illustrates that the aforementioned pressure matrix measurement system includes a mounting base plate 4 and pressure measuring devices; four pressure measuring devices are arranged on the mounting base plate 4, specifically as follows: Figure 2 , Figure 3 and Figure 4 As shown: with the center of mounting base plate 4 as the origin, the downward direction is marked as X. m The positive direction of the axis, and the right direction are marked as Y. m The positive direction of the axis, determined by the right-hand screw rule, is marked as Z, which is perpendicular to the mounting base 4 and points outward.m The positive axis direction forms an orthogonal coordinate system Q based on the surface of the mounting base plate 4. m -x m y m z m Let {O} be the reference coordinate system. m According to this coordinate system, pressure measuring devices are installed at points (a,b), (a,-b), (-a,b), and (-a,-b) in the four quadrants of the mounting base plate 4.

[0073] The pressure measuring device consists of a compression spring 5, a pressure sensor 6, a spherical caster wheel 7, and an axially movable positioning optical shaft 8. The pressure sensor 6 is fixed to the corresponding position on the mounting base plate 4. One end of the compression spring 5 presses against the pressure sensor 6, and the other end is connected to the spherical caster wheel 7. One end of the axially movable positioning optical shaft 8 directly passes through the inner center of the compression spring 5 and is connected to the inner side of the spherical caster wheel 7 to guide the compression spring 5 only along the axial direction, while the other end moves with low resistance along the corresponding through-hole on the mounting base plate 4.

[0074] This embodiment further illustrates that the compression spring 5 undergoes a quantitative compression test before installation to obtain matching data between different compression amounts and pressures, and a "force-deformation" model of the compression spring 5 is fitted. This provides fundamental knowledge for subsequent relative pose calculation algorithms in real time.

[0075] In further explanation of this embodiment, the calculation process of step five above is as follows:

[0076] like Figure 2 , Figure 3 , Figure 4 , Figure 5 As shown, taking the arrangement of four pressure measuring devices on the mounting base plate as an example, let Q be the pressure of the four compression springs. m -x m y m The projection points in the plane are P1, P2, P3, and P4, with coordinates (-a, -b, 0), (a, -b, 0), (a, b, 0), and (-a, b, 0), respectively. Let the contact points between the spherical casters located at the four ends of the compression springs and the object surface be T1, T2, T3, and T4, with coordinates (-a, -b, z1), (a, -b, z2), (a, b, z3), and (-a, b, z4), respectively, where z... i (i = 1, 2, 3, 4) represents the compression amount of the i-th compression spring; the following calculations can obtain the distance and attitude of the virtual plane (which is also the structural surface that the underwater robot is in contact with) formed by the four points T1, T2, T3, and T4 relative to the end face P1P2P3P4 of the underwater robot, and finally realize the robot's self-perception of the relative pose information of the current position of the structural surface to be detected directly in front of it.

[0077] Let the unit vector of the outward normal (pointing to the target structure to be detected) of the reference end face P1P2P3P4 on the underwater robot be represented as n in the reference coordinate system {Om}. m =[0,0,1] T ;

[0078] By forming a planar triangle using any three of the contact points T1, T2, T3, and T4, four planar combinations are obtained: ΔT4T1T2, ΔT1T2T3, ΔT2T3T4, and ΔT3T4T1. Let their corresponding outward normal unit vectors be n. m1 n m2 n m3 n m4 ;

[0079] Based on the four combinations ΔT4T1T2, ΔT1T2T3, ΔT2T3T4, and ΔT3T4T1, the two sides of each triangle are selected as its orthogonal vectors in the plane according to the right-hand rule as follows:

[0080] For ΔT4T1T2, the vector is chosen as and

[0081] For ΔT1T2T3, the vector is chosen as and

[0082] For ΔT2T3T4, the vector is chosen as and

[0083] For ΔT3T4T1, choose the vector as and

[0084] Based on the cross product operation and the right-hand rule, the outward normal unit vector of the corresponding triangular plane is:

[0085]

[0086] in, It is a vector Euclidean length;

[0087] Similarly, we can conclude that

[0088]

[0089] in,

[0090] Based on the ZYX rotation rule to describe the rotational relationships, each triangular plane ΔT4T1T2, ΔT1T2T3, ΔT2T3T4, and ΔT3T4T1 can be considered as originating from the reference plane P1P2P3P4 on the underwater robot, passing through ① a zero-degree yaw angle, i.e., ψ=0; ② a pitch angle, i.e. ③ Roll angle, i.e. The result is obtained after three rotations; this rotation can be represented by the rotation matrix R∈SO(3);

[0091] Taking a planar triangle ΔT4T1T2 as an example, suppose that it has ψ1 = 0 relative to the reference plane P1P2P3P4. The rotation of the reference coordinate system {O}, which was originally located in the reference plane, will then... m} Rotated to the coordinate system {O} within the triangular plane ΔT4T1T2 m1}(like Figure 5 The rotation matrix R1 defined by this rotation is:

[0092]

[0093] Wherein, R1 satisfies the following equation:

[0094] R1n m1 =e3(1.6)

[0095] Where, e3 = [0,0,1] T For {O m1} system z m1 The unit vector of the axis in {O m1 Expressions under the} system;

[0096] According to equation (1.6),

[0097]

[0098] According to the second equation of equation (1.7), we can obtain that

[0099]

[0100] Furthermore, according to the first and third equations of equation (1.7), we can obtain that...

[0101]

[0102] Similarly, let the rotational relationships between the triangular planes ΔT1T2T3, ΔT2T3T4, and ΔT3T4T1 and the reference plane P1P2P3P4 be represented by rotation matrices R2, R3, and R4, respectively, and satisfy the following conditions.

[0103]

[0104] Then it can be obtained through the corresponding outward normal unit vector n mi Calculate the corresponding attitude angles for (i = 2, 3, 4):

[0105]

[0106] Finally, the average distance between the reference plane P1P2P3P4 and the surface of the target structure being tested, represented by the four pressure contact points T1T2T3T4, is obtained. and average attitude for:

[0107]

[0108] It is worth noting that the present invention is not limited to the array configuration of the four pressure measuring units in the above embodiments. Theoretically, as long as there are three sets of non-collinear pressure measuring points T, the invention can be implemented. i (i = 1, 2, ..., k, and k ≥ 3), then the average distance can be calculated. and average attitude The more measurement points there are, the less sensitive the calculated average result is to measurement noise introduced by each measurement unit.

[0109] Obviously, the above embodiments are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description; it is neither necessary nor possible to exhaustively list all possible implementations; however, obvious variations or modifications derived therefrom are still within the scope of protection of the present invention.

Claims

1. An underwater relative pose sensing method based on a pressure lattice measurement system, characterized in that... Includes the following steps: Step 1: Install a pressure lattice measurement system on the underwater robot; Step two: Navigate the underwater robot to the vicinity of the surface of the target structure to be inspected via remote control or autonomous indexing; Step 3: Using the first-person perspective information returned by the onboard camera of the underwater robot, adjust the body posture of the underwater robot so that the pressure dot matrix measurement system is facing the surface of the target structure to be inspected. Step 4: Control the underwater robot to move closer to the target structure to be tested, so that one or more compression springs of the pressure lattice measurement system are squeezed by the target structure. At this time, the compressed springs simultaneously exert pressure on the pressure sensors of the corresponding pressure lattice measurement system. By combining the real-time pressure measurement signal of the pressure sensor with the "force-deformation" model of the compression spring, the true compression amount of the compression spring can be obtained. Step 5: Calculate the relative distance and attitude information of the underwater robot relative to the target structure to be detected by compressing the actual compression of the spring. Step 6: Based on the relative distance and attitude information of the underwater robot relative to the target structure to be inspected, formulate and output the corresponding underwater relative pose feedback control commands to realize the autonomous and stable pose control of the underwater robot relative to the surface of the target structure to be inspected during the inspection operation. The pressure dot matrix measurement system includes a mounting base plate (4) and pressure measuring devices; at least four pressure measuring devices are arranged on the mounting base plate (4); the pressure measuring devices consist of a compression spring (5), a pressure sensor (6), a spherical caster wheel (7), and an axially movable positioning optical shaft (8); the pressure sensor (6) is fixed to the corresponding position on the mounting base plate (4); one end of the compression spring (5) presses on the pressure sensor (6), and the other end is connected to the spherical caster wheel (7); one end of the axially movable positioning optical shaft (8) directly penetrates the inner center of the compression spring (5) and connects to the inner side of the spherical caster wheel (7) to guide the compression spring (5) only along the axial direction, and the other end moves with low resistance along the corresponding through-hole on the mounting base plate (4); Before installation, the compression spring (5) undergoes a quantitative compression test to obtain matching data between different compression amounts and pressures, and a "force-deformation" model of the compression spring (5) is fitted.

2. The underwater relative pose sensing method based on a pressure lattice measurement system according to claim 1, characterized in that: The calculation process in step five is as follows: Taking the arrangement of four pressure measuring devices on the mounting base plate (4) as an example, that is: taking the center of the mounting base plate (4) as the origin, and the downward direction is marked as X. m The positive direction of the axis, and the right direction are marked as Y. m The positive direction of the axis, determined by the right-hand screw rule, is marked as Z, which is perpendicular to the mounting base (4) and points outward. m The positive axis direction forms an orthogonal coordinate system Q based on the surface of the mounting base plate (4). m -x m y m z m Let {O} be the reference coordinate system. m According to the coordinate system, pressure measuring devices are installed at the (a,b), (a,-b), (-a,b), and (-a,-b) points in the four quadrants of the mounting base plate (4); Let Q be the point where the spring is compressed in four places. m -x m y m The projection points in the plane are P1, P2, P3, and P4, with coordinates (-a, -b, 0), (a, -b, 0), (a, b, 0), and (-a, b, 0), respectively. Let the contact points between the spherical casters located at the four ends of the compression springs and the object surface be T1, T2, T3, and T4, with coordinates (-a, -b, z1), (a, -b, z2), (a, b, z3), and (-a, b, z4), respectively, where z... i (i = 1, 2, 3, 4) represents the compression amount of the i-th compression spring; Let the outward normal unit vector of the reference end face P1P2P3P4 on the underwater robot lie in the reference coordinate system {O}. m The representation of n under} m =[0,0,1] T ; By forming a planar triangle using any three of the contact points T1, T2, T3, and T4, four planar combinations are obtained: ΔT4T1T2, ΔT1T2T3, ΔT2T3T4, and ΔT3T4T1. Let their corresponding outward normal unit vectors be n. m1 n m2 n m3 n m4 ; Based on the four combinations ΔT4T1T2, ΔT1T2T3, ΔT2T3T4, and ΔT3T4T1, the two sides of each triangle are selected as its orthogonal vectors in the plane according to the right-hand rule as follows: For ΔT4T1T2, the vector is chosen as and For ΔT1T2T3, the vector is chosen as and For ΔT2T3T4, the vector is chosen as and For ΔT3T4T1, choose the vector as and Based on the cross product operation and the right-hand rule, the outward normal unit vector of the corresponding triangular plane is: in, It is a vector Euclidean length; Similarly, we can conclude that in, Based on the ZYX rotation rule to describe the rotational relationships, each triangular plane ΔT4T1T2, ΔT1T2T3, ΔT2T3T4, and ΔT3T4T1 is considered to originate from the reference plane P1P2P3P4 on the underwater robot through ① a zero-degree yaw angle, i.e., ψ=0; ② a pitch angle, i.e. ③ Roll angle, i.e. The result is obtained after three rotations; this rotation is represented by the rotation matrix R∈SO(3); Taking a planar triangle ΔT4T1T2 as an example, suppose that it has ψ1 = 0 relative to the reference plane P1P2P3P4. The rotation of the reference coordinate system {O}, which was originally located in the reference plane, will then... m } Rotated to the coordinate system {O} within the triangular plane ΔT4T1T2 m1 The rotation matrix R1 defined by this rotation is: Wherein, R1 satisfies the following equation: R1n m1 =e3(1.6) Where, e3 = [0,0,1] T For {O m1 } system z m1 The unit vector of the axis in {O m1 Expressions under the} system; According to equation (1.6), According to the second equation of equation (1.7), we can obtain that Furthermore, according to the first and third equations of equation (1.7), we can obtain that... Similarly, let the rotational relationships between the triangular planes ΔT1T2T3, ΔT2T3T4, and ΔT3T4T1 and the reference plane P1P2P3P4 be represented by rotation matrices R2, R3, and R4, respectively, and satisfy the following conditions. Then through the corresponding outward normal unit vector n mi Calculate the corresponding attitude angles for (i = 2, 3, 4): Finally, the average distance between the reference plane P1P2P3P4 and the surface of the target structure being tested, represented by the four pressure contact points T1T2T3T4, is obtained. and average attitude for:

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