Underwater positioning and posture monitoring device of desilting robot for pool and use method of underwater positioning and posture monitoring device

Abstract

The invention relates to an underwater positioning and posture monitoring device of a desilting robot for a pool and a use method of the underwater positioning and posture monitoring device, which belong to the technical field of underwater positioning of robots and comprise a desilting pool, a desilting robot, a desilting robot platform deck, a pressure sensor, a pressure signal processing and converting system, a high-pressure jet pump, a high-pressure nozzle, a binocular camera, an image processing system and a base mark, according to the method, the underwater high-pressure jet technology and the visual identification technology are adopted, high-precision monitoring of the position and the posture of the underwater robot is achieved through the reasonable device and the implementation method, and the problem of high-precision positioning of the underwater robot in a semi-closed space and a turbid water body can be effectively solved.

Description

Technical Field

[0001] The present invention relates to a positioning device and its usage method in the technical field of robot underwater positioning, in particular to an underwater positioning and attitude monitoring device and its usage method for a dredging robot in a semi-closed space and a turbid water pool. Background Art

[0002] Underwater positioning and attitude monitoring of a dredging robot are the basis for its efficient and stable operation. During the dredging process, the water body is relatively turbid and the visibility is low, making it difficult for the human eye to directly identify its position and attitude. For special application scenarios, such as a semi-closed space like a pool, the application of some relatively mature underwater positioning technologies is severely restricted. The ultra-short baseline technology is widely used in robot underwater positioning, but when it is applied to underwater positioning of a robot in a pool, due to the existence of the multi-path reflection effect, its measurement accuracy is severely affected. Three-dimensional sonar can also be applied to underwater positioning, but it has the disadvantages of poor real-time performance and high cost. In view of the relatively special semi-closed environment of a pool and the blocked line of sight caused by the turbid water body due to dredging operations, it is very necessary to propose an underwater positioning and attitude monitoring method with good real-time performance, low cost, and easy implementation. Summary of the Invention

[0003] In view of the deficiencies of the prior art, the present invention provides a device and its usage method for underwater positioning and attitude monitoring of a dredging robot, thereby effectively solving the problem of high-precision positioning of an underwater robot in a semi-closed space and turbid water body. The main method adopted is the underwater high-pressure jet technology plus the visual recognition technology, and high-precision monitoring of the position and attitude of the underwater robot is achieved through a reasonable device and implementation method.

[0004] The present invention is realized through the following technical solutions:

[0005] The present invention includes an underwater positioning and attitude monitoring device for a dredging robot, which comprises a dredging pool and a deck platform of the dredging robot. The dredging robot is arranged on the deck platform of the dredging robot. The special feature lies in that it further includes a first high-pressure nozzle, a second high-pressure nozzle, a third high-pressure nozzle, a fourth high-pressure nozzle, a first pressure sensor, a second pressure sensor, a third pressure sensor, a first high-pressure water pipe, a second high-pressure water pipe, a third high-pressure water pipe, a fourth high-pressure water pipe, a first signal transmission line, a second signal transmission line, a third signal transmission line, a pressure signal processing and conversion system, a high-pressure jet pump, a data transmission line, a reference mark, and a binocular camera; the deck of the dredging robot platform is horizontally structured, and when the dredging robot lands on the horizontal plane, the distances from each point on the platform deck to the horizontal plane are equal; the first high-pressure nozzle, the second high-pressure nozzle, the third high-pressure nozzle, and the fourth high-pressure nozzle are arranged vertically at equal intervals on the deck platform of the dredging robot, and the nozzles face upward; the first pressure sensor, the second pressure sensor, and the third pressure sensor are respectively arranged at the central positions of the two side edges and the central position of the rear of the robot platform deck; the pressure signal processing and conversion system and the high-pressure jet pump are also arranged on the deck platform of the dredging robot. The high-pressure jet pump is connected to the first high-pressure nozzle, the second high-pressure nozzle, the third high-pressure nozzle, and the fourth high-pressure nozzle respectively through the first high-pressure water pipe, the second high-pressure water pipe, the third high-pressure water pipe, and the fourth high-pressure water pipe; the pressure signal processing and conversion system and the high-pressure jet pump are connected through the data transmission line, and the pressure signal processing and conversion system is connected to the first pressure sensor, the second pressure sensor, and the third pressure sensor respectively through the first signal transmission line, the second signal transmission line, and the third signal transmission line; the reference mark is arranged above the dredging pool; the binocular camera is arranged on the shore of the dredging pool, and its visual range can cover the entire dredging pool and the reference mark.

[0006] Further, in the present invention, the pressure signal processing and conversion system receives the pressure sensor signal, processes the signal, and outputs a control signal to the high-pressure jet pump according to the magnitude of the pressure signal measurement value to control the rotation speed of the high-pressure jet pump. The rotation speed of the high-pressure jet pump is directly proportional to the magnitude of the pressure value measured by the pressure sensor.

[0007] The present invention also includes a method for using an underwater positioning and attitude monitoring device for a dredging robot in a pool, which comprises the following steps:

[0008] Step 1: On the premise that the plane position information (x0, y0) of the reference mark is known, control the reference mark to emit laser light towards the water surface and form a characteristic light ring on the water surface;

[0009] Step 2: Control the high-pressure jet pump to start, so that the four high-pressure nozzles spray water columns upward to form four vortices with prominent centers on the water surface;

[0010] Step 3: Calculate the attitude of the robot according to the following formula:

[0011]

[0012] Among them, θ 左右 is the inclination angle of the dredging robot in the lateral direction (the traveling direction of the robot is the longitudinal direction); the unit is radian; θ 前后 is the inclination angle of the dredging robot in the longitudinal direction (the traveling direction of the robot is the longitudinal direction), the unit is radian; h1, h2, and h3 are the water depths measured by the first pressure sensor, the second pressure sensor, and the third pressure sensor respectively, the unit is m; d 12 is the distance between the first pressure sensor and the second pressure sensor, d 123 is the distance between the midpoint of the line connecting the first pressure sensor and the second pressure sensor and the third pressure sensor, the unit is m;

[0013] Step 4: Obtain an image containing the water surface vortex and the fiducial mark through the binocular camera, and transmit the image information to the image processing system through the data cable; the image processing system extracts the image feature information to obtain the position information of the four vortex points relative to the fiducial mark:

[0014]

[0015] Among them, x0, y0 are the coordinate values in the X-axis direction and the Y-axis direction of the reference point, the unit is m; x1, x2, x3, x4 are the coordinate values in the X direction of the 4 vortex points respectively, the unit is m; y1, y2, y3, y4 are the coordinate values in the Y direction of the 4 vortex points respectively; Δx1, Δx2, Δx3, Δx4 are the coordinate differences between the 4 vortex points in the X direction and the reference point respectively, the unit is m; Δy1, Δy2, Δy3, Δy4 are the coordinate differences between the 4 vortex points in the Y direction and the reference point respectively, the unit is m;

[0016] Step 5: According to the relative position relationship between the three pressure sensors and the four high-pressure nozzles and the characteristics of the rigid body, the water depths at the four high-pressure nozzles can be obtained as follows:

[0017]

[0018] Among them, H1, H2, H3, and H4 are the water depths at the four high-pressure nozzles respectively, the unit is m; h1, h2, and h3 are the water depths measured by the first pressure sensor, the second pressure sensor, and the third pressure sensor respectively, the unit is m;

[0019] Step 6: After obtaining the inclination angles calculated according to formula (1) and formula (2), the vortex point coordinates calculated according to formula (3), and the water depths at the four high-pressure nozzles calculated according to formula (4), the planar coordinates of the four high-pressure nozzles are calculated according to the following formula:

[0020]

[0021] Among them, x′1, x'2, x'3, x'4 are the coordinate values in the X direction of 4 high-pressure nozzles respectively, with the unit of m; y′1, y'2, y'3, y'4 are the coordinate values in the Y direction of 4 high-pressure nozzles respectively, with the unit of m; x1, x2, x3, x4 are the coordinate values in the X direction of 4 vortex points respectively, with the unit of m; y1, y2, y3, y4 are the coordinate values in the Y direction of 4 vortex points respectively, with the unit of m; θ 左右 is the inclination angle of the dredging robot in the transverse direction (the traveling direction of the robot is the longitudinal direction), with the unit of radian; θ 前后 is the inclination angle of the dredging robot in the longitudinal direction (the traveling direction of the robot is the longitudinal direction), with the unit of radian;

[0022] Step 7: Further obtain the coordinates of the center point of the robot deck platform to realize the positioning of the robot.

[0023] Furthermore, in the above Step 3, the postures of the robot are divided into left inclination, right inclination, forward inclination and backward inclination. The left and right inclination angles are calculated as shown in formula (1). When the calculated value is positive, it indicates left inclination; when the calculated value is negative, it indicates right inclination. The forward and backward inclination angles are calculated as shown in formula (2). When the calculated value is positive, it indicates forward inclination; when the calculated value is negative, it indicates right inclination.

[0024] Compared with the prior art, the beneficial effects of the present invention are as follows: The method adopted by the present invention is the underwater high-pressure jet technology plus the visual recognition technology. Through reasonable devices and implementation methods, high-precision monitoring of the position and posture of the underwater robot is realized. It not only has good real-time performance, low cost and is easy to implement, but also can effectively solve the problem of high-precision positioning of underwater robots in semi-closed spaces and turbid water bodies. Description of the Drawings

[0025] Figure 1 is a schematic structural diagram of an embodiment of the present invention;

[0026] Among them, 1 is a dredging pool, 2 is a dredging robot deck platform, 3 is a No. 1 high-pressure nozzle, 4 is a No. 2 high-pressure nozzle, 5 is a No. 3 high-pressure nozzle, 6 is a No. 4 high-pressure nozzle, 7 is a No. 1 pressure sensor, 8 is a No. 2 pressure sensor, 9 is a No. 3 pressure sensor, 10 is a No. 1 high-pressure water pipe, 11 is a No. 2 high-pressure water pipe, 12 is a No. 3 high-pressure water pipe, 13 is a No. 4 high-pressure water pipe, 14 is a No. 1 signal transmission line, 15 is a No. 2 signal transmission line, 16 is a No. 3 signal transmission line, 17 is a pressure signal processing and conversion system, 18 is a high-pressure jet pump, 19 is a data transmission line, 20 is a fiducial mark, and 21 is a binocular camera. Detailed Embodiment

[0027] To make the content of the present invention easier to understand, the technical solution of the present invention will be further explained below in conjunction with specific embodiments. The examples are only used to illustrate the present invention, but the present invention is not limited to this content.

[0028] Embodiment

[0029] The present invention includes a silt removal pool 1, a silt removal robot deck platform 2, a first high-pressure nozzle 3, a second high-pressure nozzle 4, a third high-pressure nozzle 5, a fourth high-pressure nozzle 6, a first pressure sensor 7, a second pressure sensor 8, a third pressure sensor 9, a first high-pressure water pipe 10, a second high-pressure water pipe 11, a third high-pressure water pipe 12, a fourth high-pressure water pipe 13, a first signal transmission line 14, a second signal transmission line 15, a third signal transmission line 16, a pressure signal processing and conversion system 17, a high-pressure jet pump 18, a data transmission line 19, a base mark 20, and a binocular camera 21. The silt removal robot is arranged on the silt removal robot deck platform 2; the silt removal robot platform deck 2 is horizontally structured, and when the silt removal robot lands on the horizontal plane, the distances from each point on the platform deck to the horizontal plane are equal; the first high-pressure nozzle 3, the second high-pressure nozzle 4, the third high-pressure nozzle 5, and the fourth high-pressure nozzle 6 are arranged at equal intervals on the silt removal robot deck platform 2; the first pressure sensor 7, the second pressure sensor 8, and the third pressure sensor 9 are respectively arranged at the central positions of the two side edges and the rear central position of the robot platform deck 2; the pressure signal processing and conversion system 17 and the high-pressure jet pump 18 are also arranged on the silt removal robot platform deck 2. The high-pressure jet pump 18 is connected to the first high-pressure nozzle 3, the second high-pressure nozzle 4, the third high-pressure nozzle 5, and the fourth high-pressure nozzle 6 through the first high-pressure water pipe 10, the second high-pressure water pipe 11, the third high-pressure water pipe 12, and the fourth high-pressure water pipe 13 respectively; the pressure signal processing and conversion system 17 and the high-pressure jet pump 18 are connected through the data transmission line 19, and the pressure signal processing and conversion system 17 is connected to the first pressure sensor 7, the second pressure sensor 8, and the third pressure sensor 9 through the first signal transmission line 14, the second signal transmission line 15, and the third signal transmission line 16 respectively.

[0030] During the implementation of the present invention, the silt removal robot is completely submerged in the water body in the silt removal pool, and due to the turbidity of the water body during the silt removal operation, it is difficult to directly observe the position of the robot with the naked eye.

[0031] There are three pressure sensors in total, which are respectively arranged at the central positions of the two side edges and the rear central position of the robot platform deck. The water depths measured by the three pressure sensors are h1, h2, and h3 respectively. Then the overlying water depth h of the robot is h = (h1 + h2) / 2; the distance between the first pressure sensor 7 and the second pressure sensor 8 is d 12 , and the distance between the midpoint of the line connecting the first pressure sensor 7 and the second pressure sensor 8 and the third pressure sensor 9 is d 123 .

[0032] Taking the robot's traveling direction as the positive direction, the postures of the robot are divided into left tilt, right tilt, forward tilt, and backward tilt. The left and right tilt angles are calculated as shown in formula (1); when the calculated value is positive, it indicates a left tilt, and when the calculated value is negative, it indicates a right tilt. The forward and backward tilt angles are calculated as shown in formula 2; when the calculated value is positive, it indicates a forward tilt, and when the calculated value is negative, it indicates a right tilt. Thus, the posture information of the underwater dredging robot can be obtained.

[0033]

[0034] Among them, θ 左右 is the inclination angle of the dredging robot in the lateral direction (the robot's traveling direction is the longitudinal direction); the unit is radian; θ 前后 is the inclination angle of the dredging robot in the longitudinal direction (the robot's traveling direction is the longitudinal direction), and the unit is radian; h1, h2, and h3 are the water depths measured by the first pressure sensor, the second pressure sensor, and the third pressure sensor respectively, and the unit is m; d 12 is the distance between the first pressure sensor and the second pressure sensor, d 123 is the distance between the midpoint of the line connecting the first pressure sensor and the second pressure sensor and the third pressure sensor, and the unit is m.

[0035] One end of the pressure signal processing and conversion system 17 is connected to the pressure sensor, and the other end is connected to the high-pressure jet pump 18; the pressure signal processing and conversion system 17 receives the pressure sensor signal and processes the signal, and outputs a control signal to the high-pressure jet pump 18 according to the magnitude of the pressure signal measurement value to control the rotation speed of the high-pressure jet pump 18. The rotation speed of the high-pressure jet pump 18 is directly proportional to the magnitude of the pressure value measured by the pressure sensor.

[0036] The fiducial mark 20 is arranged above the dredging pool 1 and emits laser light to the water surface, forming a characteristic light circle on the water surface, and its planar position information (x0, y0) is known.

[0037] The binocular camera 21 is arranged on the shore of the dredging pool 1, and its visual range can cover the entire dredging pool 1 and the fiducial mark 20.

[0038] There are a total of four high-pressure nozzles, which are arranged equidistantly on the deck platform of the dredging robot. The high-pressure nozzles are connected to the high-pressure jet pump 18 through pipes, and the high-pressure nozzles are vertically upward. After the high-pressure jet pump 18 is started, the high-pressure nozzles spray water columns upward.

[0039] After the high-pressure jet pump 18 is started, the high-pressure nozzles spray water columns upward, forming four vortices with prominent centers on the water surface.

[0040] The binocular camera 21 acquires an image containing the water surface vortex and the fiducial mark 20, and transmits the image information to the image processing system through a data cable; the image processing system extracts the image feature information to obtain the position information of the four vortex points relative to the fiducial mark.

[0041]

[0042] Among them, x0 and y0 are the coordinate values in the X-axis direction and Y-axis direction of the base point, with the unit of m; x1, x2, x3, and x4 are the coordinate values in the X direction of the 4 vortex points respectively, with the unit of m; y1, y2, y3, and y4 are the coordinate values in the Y direction of the 4 vortex points respectively; Δx1, Δx2, Δx3, and Δx4 are the coordinate differences between the 4 vortex points in the X direction and the base point respectively, with the unit of m; Δy1, Δy2, Δy3, and Δy4 are the coordinate differences between the 4 vortex points in the Y direction and the base point respectively, with the unit of m.

[0043] According to the relative position relationship between the pressure sensor and the high-pressure nozzle and the characteristics of the rigid body, the water depths at the four high-pressure nozzles can be obtained as follows:

[0044]

[0045] Among them, H1, H2, H3, and H4 are the water depths at the four high-pressure nozzles respectively, with the unit of m; h1, h2, and h3 are the water depths measured by the first pressure sensor, the second pressure sensor, and the third pressure sensor respectively, with the unit of m.

[0046] Based on the inclination angle obtained from Formula 1 and Formula 2, the vortex point coordinates obtained from Formula 3, and the water depths at the 4 high-pressure nozzles obtained from Formula 4, the planar coordinates of the 4 high-pressure nozzles can be obtained, as shown in Formula 5:

[0047]

[0048] Among them, x′1, x'2, x'3, and x'4 are the coordinate values in the X direction of the 4 high-pressure nozzles respectively, with the unit of m; y′1, y'2, y'3, and y'4 are the coordinate values in the Y direction of the 4 high-pressure nozzles respectively, with the unit of m; x1, x2, x3, and x4 are the coordinate values in the X direction of the 4 vortex points respectively, with the unit of m; y1, y2, y3, and y4 are the coordinate values in the Y direction of the 4 vortex points respectively, with the unit of m; θ 左右 is the inclination angle of the dredging robot in the lateral direction (the traveling direction of the robot is the longitudinal direction); the unit is radian; θ 前后 is the inclination angle of the dredging robot in the longitudinal direction (the traveling direction of the robot is the longitudinal direction).

[0049] Furthermore, the coordinates of the center point of the robot deck platform are obtained to achieve the positioning of the robot.

[0050] It should be noted that the above are only the preferred embodiments of the present invention, and there is no restriction on the present invention in any form. The technical features or the combination of technical features described in the embodiments of the present invention should not be considered isolated. They can be combined with each other to achieve better technical effects. The technologies, methods and devices known to those of ordinary skill in the relevant fields are not discussed in detail, but in appropriate cases, the said technologies, methods and devices should be regarded as part of the authorization specification. In all the examples shown and discussed here, any specific value should be interpreted as merely exemplary, rather than as a limitation. Therefore, other examples of the exemplary embodiments may have different values. Any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention shall fall within the scope of the technical solution of the present invention.

Claims

1. An underwater positioning and attitude monitoring device for a dredging robot used in a pool, comprising a dredging pool and a deck platform of the dredging robot. The dredging robot is arranged on the deck platform of the dredging robot. It is characterized in that, It also includes a first high-pressure nozzle, a second high-pressure nozzle, a third high-pressure nozzle, a fourth high-pressure nozzle, a first pressure sensor, a second pressure sensor, a third pressure sensor, a first high-pressure water pipe, a second high-pressure water pipe, a third high-pressure water pipe, a fourth high-pressure water pipe, a first signal transmission line, a second signal transmission line, a third signal transmission line, a pressure signal processing and conversion system, a high-pressure jet pump, a data transmission line, a reference mark, and a binocular camera; The deck of the dredging robot platform is horizontally structured. When the dredging robot lands on the horizontal plane, the distances from each point on the platform deck to the horizontal plane are equal; The first high-pressure nozzle, the second high-pressure nozzle, the third high-pressure nozzle, and the fourth high-pressure nozzle are arranged vertically at equal intervals on the deck platform of the dredging robot, and the nozzles face upward; The first pressure sensor, the second pressure sensor, and the third pressure sensor are respectively arranged at the central positions of the two side edges and the rear central position of the robot platform deck; The pressure signal processing and conversion system and the high-pressure jet pump are also arranged on the deck platform of the dredging robot. The high-pressure jet pump is connected to the first high-pressure nozzle, the second high-pressure nozzle, the third high-pressure nozzle, and the fourth high-pressure nozzle respectively through the first high-pressure water pipe, the second high-pressure water pipe, the third high-pressure water pipe, and the fourth high-pressure water pipe; The pressure signal processing and conversion system and the high-pressure jet pump are connected through a data transmission line. The pressure signal processing and conversion system is connected to the first pressure sensor, the second pressure sensor, and the third pressure sensor respectively through the first signal transmission line, the second signal transmission line, and the third signal transmission line; The reference mark is arranged above the dredging pool; the binocular camera is arranged on the shore of the dredging pool, and its visual range can cover the entire dredging pool and the reference mark.

2. The underwater positioning and attitude monitoring device for the dredging robot used in the pool according to claim 1, characterized in that The pressure signal processing and conversion system receives the pressure sensor signal, processes the signal, and outputs a control signal to the high-pressure jet pump according to the magnitude of the pressure signal measurement value to control the rotation speed of the high-pressure jet pump. The rotation speed of the high-pressure jet pump is directly proportional to the magnitude of the pressure value measured by the pressure sensor.

3. A method for using an underwater positioning and attitude monitoring device of the dredging robot for the pool according to claim 1, characterized in that, It includes the following steps: Step 1: On the premise that the plane position information (x0, y0) of the reference mark is known, control the reference mark to emit laser light towards the water surface, and form a characteristic light circle on the water surface; Step 2: Control the high-pressure jet pump to start, so that the four high-pressure nozzles spray water columns upward, and form four vortices with prominent centers on the water surface; Step 3: Calculate the attitude of the robot according to the following formula: Among them, θ 左右 is the lateral inclination angle of the dredging robot, in radians; θ 前后 is the longitudinal inclination angle of the dredging robot, in radians, and the traveling direction of the robot is longitudinal; h1, h2, and h3 are the water depths measured by the first pressure sensor, the second pressure sensor, and the third pressure sensor, in m; d 12 is the distance between the first pressure sensor and the second pressure sensor, d 123 is the distance between the midpoint of the line connecting the first pressure sensor and the second pressure sensor and the third pressure sensor, in m; Step 4: Obtain an image containing the water surface vortices and the reference mark through the binocular camera, and transmit the image information to the image processing system through the data line; the image processing system extracts the image feature information to obtain the position information of the four vortex points relative to the reference mark: Among them, x0 and y0 are the coordinate values in the X-axis and Y-axis directions of the base point, with the unit of m; x1, x2, x3, and x4 are the coordinate values in the X-direction of the 4 vortex points respectively, with the unit of m; y1, y2, y3, and y4 are the coordinate values in the Y-direction of the 4 vortex points respectively; Δx1, Δx2, Δx3, and Δx4 are the coordinate differences between the 4 vortex points in the X-direction and the base point respectively, with the unit of m; Δy1, Δy2, Δy3, and Δy4 are the coordinate differences between the 4 vortex points in the Y-direction and the base point respectively, with the unit of m. Step Five: According to the relative position relationship between the three pressure sensors and the four high-pressure nozzles and the characteristics of the rigid body, the water depths at the four high-pressure nozzles can be obtained as follows: Among them, H1, H2, H3, and H4 are the water depths at the four high-pressure nozzles respectively, with the unit of m; h1, h2, and h3 are the water depths measured by the first pressure sensor, the second pressure sensor, and the third pressure sensor respectively, with the unit of m. Step Six: After obtaining the inclination angle calculated according to Formula (1) and Formula (2), the vortex point coordinates calculated according to Formula (3), and the water depths at the four high-pressure nozzles calculated according to Formula (4), the planar coordinates of the four high-pressure nozzles are calculated according to the following formula: Among them, x'1, x'2, x'3, x'4 are the coordinate values in the X direction of 4 high-pressure nozzles, with the unit of m; y'1, y'2, y'3, y'4 are the coordinate values in the Y direction of 4 high-pressure nozzles, with the unit of m; x1, x2, x3, x4 are the coordinate values in the X direction of 4 vortex points, with the unit of m; y1, y2, y3, y4 are the coordinate values in the Y direction of 4 vortex points, with the unit of m; θ 左右 is the inclination angle of the dredging robot in the horizontal direction, with the unit of radian; θ 前后 is the inclination angle of the dredging robot in the longitudinal direction, with the unit of radian, and the traveling direction of the robot is longitudinal; Step Seven: Further obtain the coordinates of the center point of the robot deck platform to achieve the positioning of the robot.

4. The method of using the underwater positioning and attitude monitoring device for the dredging robot for the pool according to claim 3, characterized in that In Step Three, the postures of the robot are divided into left inclination, right inclination, forward inclination, and backward inclination. The left and right inclination angles are calculated as shown in Formula (1). When the calculated value is positive, it indicates left inclination, and when the calculated value is negative, it indicates right inclination; the forward and backward inclination angles are calculated as shown in Formula (2). When the calculated value is positive, it indicates forward inclination, and when the calculated value is negative, it indicates right inclination.

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