Quadruped wall-climbing robot for pipeline inner wall and its kinematic analysis method

Abstract

The invention discloses a four-legged wall-climbing robot for the inner wall of a pipeline and a kinematic analysis method thereof. The four-legged wall-climbing robot comprises a waist joint, four legs connected to the waist joint and a controller. The four legs are arranged in groups of two and are distributed on both sides of the waist joint. Each leg is composed of a hip joint, a thigh joint, a calf joint, a connecting frame and a foot end. The hip joint, the thigh joint and the calf joint can be rotatably mounted on the connecting frame, and the hip joint, the thigh joint, the calf joint and the foot end are connected in sequence through the connecting frame, and the two legs in the same group are connected through the connecting frame; the controller is arranged at the waist joint, and the controller connects and controls the joints and the foot end of each leg. The robot of the invention can move flexibly in the pipeline. The invention performs kinematic analysis on the robot, analyzes the position and posture of the robot in the pipeline, and analyzes the single-leg coordinate system of the robot, and obtains the forward and inverse solutions of the robot motion, which can facilitate the motion control of the robot.

Description

Technical Field

[0001] The invention relates to the technical field of robots, and in particular to a pipeline inner wall quadruped wall climbing robot and a kinematic analysis method thereof. Background Art

[0002] Pipelines are widely used in all aspects of our lives, such as large urban sewers, urban power grid pipelines, large gas transmission pipelines, water plant water supply pipelines, industrial oil pipelines, power grid high-voltage GIS pipeline switches, etc. However, when facing various pipeline problems, such as blockage, maintenance, leakage, aging, etc., due to the particularity of the pipeline, the substances in the pipeline are not easy for the human body to touch, and most of them are not suitable for direct contact. The pipeline is also relatively narrow and difficult to operate manually. Therefore, it has caused great difficulties in the maintenance and inspection of the pipeline. Even if it is accessible manually, the efficiency is extremely low. Therefore, many scholars have developed special robots to replace manual operation for pipeline problems.

[0003] Due to its unique structure and multiple degrees of freedom, the quadruped wall-climbing robot can not only realize simple forward, backward, left and right movements, but also realize turning and strong load capacity, so it is increasingly used in pipeline environments. In actual work, the wall surfaces encountered by the wall-climbing robot are generally not flat. Most of them are curved surfaces or uneven surfaces formed by process errors, external forces or impurity deposition. Therefore, how to design a quadruped wall-climbing robot that can move flexibly in pipelines and how to control the motion of the quadruped wall-climbing robot are current research hotspots, among which the kinematic analysis of the quadruped wall-climbing robot is the basis of motion control. Summary of the invention

[0004] The first purpose of the present invention is to overcome the shortcomings and deficiencies of the prior art and to provide a pipeline inner wall four-legged wall-climbing robot that can move flexibly in the pipeline.

[0005] The second purpose of the present invention is to provide a kinematic analysis method for a four-legged wall-climbing robot on the inner wall of a pipe, which can obtain forward and inverse kinematic solutions and facilitate the motion control of the robot.

[0006] The first object of the present invention is achieved by the following technical solutions:

[0007] A four-legged wall-climbing robot for the inner wall of a pipeline comprises a waist joint, four legs connected to the waist joint and a controller. The four legs are arranged in groups of two and are distributed on the left and right sides of the waist joint. Each leg is composed of a hip joint, a thigh joint, a calf joint, a connecting frame and a foot end. The hip joint, the thigh joint and the calf joint can all be rotatably mounted on the connecting frame, and the hip joint, the thigh joint, the calf joint and the foot end are connected in sequence through the connecting frame, and the two legs in the same group are connected through the connecting frame; the controller is arranged at the waist joint, and the controller connects and controls the hip joint, the thigh joint, the calf joint and the foot end of each leg.

[0008] Preferably, the hip joint, thigh joint, and calf joint all contain a steering wheel and a joint servo motor mounted on the steering wheel. The steering wheel is mechanically connected to the connecting frame, and the steering wheel is connected to the output shaft of each joint servo motor and rotates with the rotation of the output shaft. Each joint servo motor is connected to the controller via a cable.

[0009] Preferably, the two groups of legs are symmetrically distributed on the waist joint, and for the two hip joints at the front and rear ends of the waist joint, the plane where their axis lines are located is parallel to the upper surface of the waist joint; the joint axis lines of the thigh joints and the hip joints intersect and are perpendicular to each other; the joint axis lines of the thigh joints and the calf joints are parallel to each other; the joint axis lines of the calf joints and the axis line of the symmetry axis of the foot end are parallel to each other.

[0010] Preferably, a camera is installed on the waist joint, and the camera is connected to a controller and controlled by the controller.

[0011] Preferably, the foot end is a vacuum suction cup device.

[0012] The second object of the present invention is achieved by the following technical solutions:

[0013] A kinematic analysis method for a four-legged wall-climbing robot on the inner wall of a pipeline comprises the following steps:

[0014] S1. Construct the pipeline basic coordinate system {O} and the robot body coordinate system {E};

[0015] S2. Determine the position of the quadruped wall-climbing robot in the pipeline by the rotation change of the pipeline base coordinate system and the robot body coordinate system;

[0016] S3. According to the joint positions of the quadruped wall-climbing robot, multiple single-leg coordinate systems are established: the single-leg coordinate system {A0} coincides with the robot body coordinate system {E}; the single-leg coordinate system {A1} is established on the axis of the joint servo motor of the hip joint, and the three-axis directions are the same as those of the coordinate system {A0}; the single-leg coordinate system {A2} is established on the axis of the joint servo motor of the thigh joint, and its y A2 The axis is parallel to the left and right surfaces of the thigh joint motor; the single-leg coordinate system {A3} is established on the axis of the joint servo motor of the calf joint, A3 The axis is parallel to the left and right surfaces of the calf joint motor; the single-leg coordinate system {A4} is established at the end of the calf joint, and the directions of the three axes are the same as those of the single-leg coordinate system {A3}; the single-leg coordinate system {A5} is established at the foot end, and the directions of the three axes are the same as those of the single-leg coordinate system {A4};

[0017] S4. The forward kinematics solution of the quadruped wall-climbing robot is obtained through the rotation change between the single-leg coordinate systems. The joint and foot positions of the quadruped wall-climbing robot can be determined based on the forward kinematics solution.

[0018] S5. Then transform the formula of the forward kinematics solution to obtain the inverse kinematics solution of the quadruped wall-climbing robot. Based on the inverse kinematics solution, the rotation angles of the hip joint, thigh joint, and calf joint that need to be controlled can be solved given the target position of the foot end.

[0019] Preferably, in step S1, a pipeline basic coordinate system {O} is established with the center position of the pipeline as the origin, the pipeline axial direction as the x-axis direction, the vertical upward direction as the y-axis, and the z-axis being perpendicular to the x-axis and the y-axis;

[0020] The mechanical center of the quadruped wall-climbing robot is taken as the origin, the x-axis is collinear with the forward direction of the quadruped wall-climbing robot, the y-axis is perpendicular to the body surface, and the z-axis is perpendicular to the x-axis and y-axis. The robot body coordinate system {E} is established.

[0021] Preferably, step S2 specifically comprises:

[0022] Set the waist joint length of the quadruped wall-climbing robot to 2a, width 2b, height 2c, hip joint L1, thigh joint length L2, calf joint length L3, and foot end joint length L4;

[0023] Define the origin O of the robot body coordinate system E The position in the pipeline base coordinate system {O} is (L X ,L Y ,L Z ), the three angle parameters of its coordinate system rotating along the x, y, and z axes relative to the pipeline base coordinate system are α, β, and γ;

[0024] The transformation matrix of coordinate system {E} relative to {O} coordinate system is:

[0025]

[0026] Where: R(z,γ), R(y,β), and R(x,α) represent the rotation angles of the coordinate system around the z, y, and x axes, respectively. X ,L Y ,L Z ) represents the displacement of the coordinate system;

[0027] The position and posture matrix of the robot body can be obtained through three known rotation angles and displacements to quantify the position and posture of the robot in the pipeline;

[0028] During the motion of the quadruped wall-climbing robot, given a specific robot starting posture, the origin of the robot body coordinate system O E At the origin O of the pipeline world coordinate system O Directly below, the deflection angles α, β, and γ are all zero, and the transformation matrix of the coordinate system {E} relative to the coordinate system {O} is:

[0029]

[0030] In the formula, R represents the inner radius of the pipe; is the coordinate difference between the origins of the two coordinate systems on the z-axis.

[0031] Furthermore, the process of solving the forward kinematic solution is as follows:

[0032] Combine the rotation transformations of the single-leg coordinate system {A5} and {A0}, and the rotation matrix of the single-leg coordinate system {A0} relative to the coordinate system {A5} is:

[0033]

[0034] In the formula, θ A1 ,θ A2 ,θ A3 Respectively represent the rotation angles of the hip joint, thigh joint, and calf joint of a single leg; is the rotation matrix of {A4} relative to the coordinate system {A5}; is the rotation matrix of {A3} relative to the coordinate system {A4}; is the rotation matrix of {A2} relative to the coordinate system {A3}; is the rotation matrix of {A1} relative to the coordinate system {A2}; is the rotation matrix of {A0} relative to the coordinate system {A1};

[0035] The forward kinematic solution is obtained:

[0036]

[0037]

[0038] in, A0 P is the positive kinematic solution of {A0}; A5 P is the positive kinematic solution of {A5}; x A0 ,y A0 , z A0 Refers to the coordinate value of the foot end position.

[0039] Furthermore, the forward kinematics solution is transformed to obtain the inverse kinematics solution:

[0040]

[0041] in, n A =x A0 -a-L1.

[0042] Compared with the prior art, the present invention has the following advantages and effects:

[0043] (1) In the quadruped wall-climbing robot of the present invention, the four legs are distributed on the sides of the waist joint, and each leg is provided with three joints. The rotation angle of the joints is not limited by the body, and the rotation range is large, so the robot can move flexibly in the pipeline.

[0044] (2) In the quadruped wall-climbing robot of the present invention, two legs in the same group are connected together by a connecting frame, so that the two legs and the waist joint form a closed loop together, which can reduce the deformation of the connecting frame and further improve the control accuracy of the joint.

[0045] (3) The kinematic analysis method of the present invention constructs the pipeline coordinate system and the robot body coordinate system, analyzes their coordinate transformation, and obtains the relationship between the transformation law and the robot posture, thereby determining the axial and radial positions of the robot and the deflection angle of the robot body. According to the position of the joints, multiple single-leg coordinate systems are established, and the forward and inverse solutions of the robot are obtained through the transformation between the coordinate systems, which can provide a theoretical basis for subsequent robot control. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a schematic diagram of the pipeline inner wall four-legged wall-climbing robot of the present invention.

[0047] Figure 2 It is a top view of the pipeline inner wall four-legged wall-climbing robot of the present invention.

[0048] Figure 3 It is a schematic diagram of the pipeline basic coordinate system and the robot body coordinate system.

[0049] Figure 4 It is a schematic diagram of the robot body coordinate system in the initial state.

[0050] Figure 5 It is a schematic diagram of a monopedal coordinate system.

[0051] Description of the symbols in the accompanying drawings:

[0052] 1: Calf joint; 2: Thigh joint; 3: Steering wheel; 4: Waist joint; 5: Connecting frame No. 2; 6: Connecting frame No. 3; 7: Connecting frame No. 4; 8: Connecting frame No. 5; 9: Connecting frame No. 1; 10: Fixed frame; 11: Vacuum suction cup; 12: Camera. DETAILED DESCRIPTION

[0053] The present invention is further described in detail below in conjunction with embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0054] This embodiment discloses a pipeline inner wall four-legged wall climbing robot. Figure 1 and Figure 2 As shown, it includes a waist joint 4, four legs connected to the waist joint and a controller.

[0055] The waist joint is the main body of the machine, and the four legs are arranged in pairs, symmetrically distributed on the left and right sides of the waist joint. The waist joint can be formed by cutting and assembling metal plates such as 5052 aluminum plates.

[0056] Each leg is composed of a hip joint, a thigh joint 2, a calf joint 1, a connecting frame and a foot end. The hip joint, the thigh joint and the calf joint can be rotatably mounted on the connecting frame, and the hip joint, the thigh joint, the calf joint and the foot end are sequentially connected through the connecting frame. The connecting frame can be made of a metal plate such as a 5052 aluminum plate.

[0057] For the two hip joints at the front and back ends of the waist joint, the plane where the joint axis is located is parallel to the upper surface of the waist joint, the joint axis of the thigh joint is perpendicular to the joint axis of the hip joint, the joint axis of the thigh joint and the joint axis of the calf joint are parallel to each other, and the joint axis of the calf joint and the axis of the symmetry axis of the foot end are parallel to each other.

[0058] The hip joint, thigh joint and calf joint all contain a steering wheel 3 and a joint servo motor. The steering wheel is mechanically connected to the connecting frame, and in this embodiment, it is fixed by bolts. The steering wheel is installed at the end of the output shaft of the joint servo motor. As the output shaft rotates, the steering wheel, the connecting frame connected to the steering wheel and the parts fixed to the connecting frame rotate together.

[0059] The foot end can adopt a vacuum suction cup device. The vacuum suction cup 11 of the vacuum suction cup device can be deflated and inhaled through a vacuum tube. The robot can utilize the vacuum suction cup to reliably adsorb on the inner wall surface of the pipeline.

[0060] In this embodiment, the single leg is connected through a series structure, the hip joint is fixed on the fuselage, the steering wheel of the hip joint output shaft is fixed to the No. 1 connecting frame 9, the No. 1 connecting frame is fixed to the thigh joint, the steering wheel of the thigh joint output shaft is connected to the No. 2 connecting frame 5, the No. 2 connecting frame is connected to the No. 3 connecting frame 6, the No. 3 connecting frame is connected to the steering wheel of the calf joint motor output shaft, the calf joint motor is connected to the No. 4 connecting frame 7, the No. 4 connecting frame is connected to the No. 5 connecting frame 8, and the No. 5 connecting frame is connected to the vacuum suction cup 11 at the foot end.

[0061] The two legs of the same group are also connected by a connecting frame, such as Figure 1 and Figure 2 As shown, the No. 1 connecting frame of the two legs is connected through the fixing frame 10, so that the two legs and the waist joint are connected to form a closed loop, which can reduce the deformation of the connecting frame and thus improve the control accuracy of the joint. In addition, the other connecting frame can also be connected to the fuselage through a fixing rod to play the role of fixing the fuselage. Figure 1As shown, the robot of this embodiment refers to the biological structure of a gecko, and the four legs are directly arranged on the side of the waist joint instead of being located below the waist joint. Therefore, the center of gravity of the body can be set lower, and the rotation of the joint will not be restricted by the body. Therefore, the rotation range is larger and the movement is more flexible.

[0062] The controller is located at the waist joint. In this embodiment, it is housed in the waist joint. Each joint servo motor is connected to the controller through a cable. The controller can control the rotation angle of the hip joint, thigh joint, and calf joint of each leg, and the adsorption of the foot end to the ground. Specifically, when the robot does not need to move, the joint servo motor does not work, and the foot end is deflated through the vacuum tube to be adsorbed on the wall; when the robot needs to move, the foot end first takes in air through the vacuum tube, and then the joint servo motor works, so the vacuum state of the vacuum suction cup changes with the movement of the robot.

[0063] In this embodiment, a camera 12 is also installed on the waist joint. The camera is connected to the controller and controlled by the controller. The camera can transmit the environmental images it collects to the controller so as to understand the environment in which the robot is located and better control the robot.

[0064] In addition, this embodiment also discloses a kinematic analysis method for a pipeline inner wall quadruped wall climbing robot, which can be applied to the above quadruped wall climbing robot and specifically includes the following steps:

[0065] S1. Construct the pipeline basic coordinate system {O} and the robot body coordinate system {E}:

[0066] like Figure 3 to Figure 5 As shown, the center of the pipeline is taken as the origin, the pipeline axis is the x-axis direction, the vertical direction is the y-axis, and the z-axis is perpendicular to the x-axis and y-axis to establish the pipeline basic coordinate system {O};

[0067] The mechanical center of the quadruped wall-climbing robot is taken as the origin, the x-axis is collinear with the forward direction of the quadruped wall-climbing robot, the y-axis is perpendicular to the body surface, and the z-axis is perpendicular to the x-axis and y-axis. The robot body coordinate system {E} is established.

[0068] S2. Determine the position of the quadruped wall-climbing robot in the pipeline by the rotation of the pipeline base coordinate system and the robot body coordinate system:

[0069] Set the waist joint length of the quadruped wall-climbing robot to 2a, width 2b, height 2c, hip joint L1, thigh joint length L2, calf joint length L3, and foot joint length L4; define the origin of the robot's coordinate system O E The position in the pipeline base coordinate system {O} is (L X ,L Y ,L Z), the three angle parameters of its coordinate system rotating along the x, y, and z axes relative to the pipeline base coordinate system are α, β, and γ. These data are all known and can be obtained through measurement and calculation;

[0070] The transformation matrix of coordinate system {E} relative to {O} coordinate system is:

[0071]

[0072] Where: R(z,γ), R(y,β), and R(x,α) represent the rotation angles of the coordinate system around the z, y, and x axes respectively; L(L X ,L Y ,L Z ) represents the displacement of the coordinate system.

[0073] The position and posture matrix of the robot body can be obtained through three known rotation angles and displacements to quantify the position and posture of the robot in the pipeline.

[0074] During the motion of the quadruped wall-climbing robot, given a specific robot starting posture, the origin of the robot body coordinate system O E At the origin O of the pipeline world coordinate system O Directly below, the deflection angles α, β, and γ are all zero, and the transformation matrix of the coordinate system {E} relative to the coordinate system {O} is:

[0075]

[0076] Where R represents the inner radius of the pipe. is the coordinate difference of the origins of the two coordinate systems on the z-axis.

[0077] S3. According to the joint positions of the quadruped wall-climbing robot, multiple single-leg coordinate systems are established: Figure 5 As shown in the figure, the single-leg coordinate system {A0} coincides with the robot body coordinate system {E}; the single-leg coordinate system {A1} is established on the axis of the joint servo motor of the hip joint, and the three-axis directions are the same as those of the coordinate system {A0}; the single-leg coordinate system {A2} is established on the axis of the joint servo motor of the thigh joint, and its y A2 The axis is parallel to the left and right surfaces of the thigh joint motor; the single-leg coordinate system {A3} is established on the axis of the joint servo motor of the calf joint, A3 The axis is parallel to the left and right surfaces of the calf joint motor; the single-leg coordinate system {A4} is established at the end of the calf joint, and the directions of the three axes are the same as those of the single-leg coordinate system {A3}; the single-leg coordinate system {A5} is established at the foot end, and the directions of the three axes are the same as those of the single-leg coordinate system {A4};

[0078] S4. Through the rotation changes between the single-leg coordinate systems, the positive kinematic solution of the quadruped wall-climbing robot is obtained:

[0079] Combine the rotation transformations of the single-leg coordinate system {A5} and {A0}, and the rotation matrix of the single-leg coordinate system {A0} relative to the coordinate system {A5} is:

[0080]

[0081] Where: θ A1 ,θ A2 ,θ A3 Respectively represent the rotation angles of the hip joint, thigh joint, and calf joint of a single leg; is the rotation matrix of {A4} relative to the coordinate system {A5}; is the rotation matrix of {A3} relative to the coordinate system {A4}; is the rotation matrix of {A2} relative to the coordinate system {A3}; is the rotation matrix of {A1} relative to the coordinate system {A2}; is the rotation matrix of {A0} relative to the coordinate system {A1};

[0082] The forward kinematic solution is obtained:

[0083]

[0084]

[0085] in, A0 P is the positive kinematic solution of {A0}; A5 P is the positive kinematic solution of {A5}; x A0 ,y A0 , z A0 Refers to the coordinate value of the foot end position.

[0086] S5. Then transform the forward kinematics solution to obtain the inverse kinematics solution of the quadruped wall-climbing robot:

[0087]

[0088] in, n A =x A0 -a-L1.

[0089] Therefore, given the target position of the foot end (i.e., given x A0 ,y A0 , z A0 ), based on the inverse kinematics solution, the rotation angles of the hip joint, thigh joint, and calf joint that need to be controlled can be solved.

[0090] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A kinematic analysis method for a pipeline inner wall quadruped wall-climbing robot, the pipeline inner wall quadruped wall-climbing robot comprises a waist joint, four legs connected to the waist joint and a controller, the four legs are arranged in groups of two, and are distributed on the left and right sides of the waist joint, each leg is composed of a hip joint, a thigh joint, a calf joint, a connecting frame and a foot end, the hip joint, the thigh joint and the calf joint can be rotatably mounted on the connecting frame, and the hip joint, the thigh joint, the calf joint and the foot end are connected in sequence through the connecting frame, and the two legs in the same group are connected through the connecting frame; the controller is arranged at the waist joint, and the controller connects and controls the hip joint, the thigh joint, the calf joint and the foot end of each leg; the two groups of legs are symmetrically distributed on the waist joint, and the front and rear ends of the waist joint are symmetrically arranged. The plane where the axis of the two hip joints is located is parallel to the upper surface of the waist joint; the joint axis of the thigh joint and the joint axis of the hip joint intersect and are perpendicular; the joint axis of the thigh joint and the joint axis of the calf joint are parallel to each other; the joint axis of the calf joint and the axis of the symmetry axis of the foot end are parallel to each other; the hip joint, thigh joint and calf joint all contain a steering wheel and a joint servo motor installed on the steering wheel, the steering wheel is mechanically connected to the connecting frame, the steering wheel is connected to the output shaft of each joint servo motor, and rotates with the rotation of the output shaft, and each joint servo motor is connected to the controller through a cable; a camera is installed on the waist joint, the camera is connected to the controller and controlled by the controller; the foot end is a vacuum suction cup device; It is characterized in that The steps include: S1. Construct the pipeline basic coordinate system {O} and the robot body coordinate system {E}; S2. Determine the position of the quadruped wall-climbing robot in the pipeline by the rotation change of the pipeline base coordinate system and the robot body coordinate system; S3. According to the joint positions of the quadruped wall-climbing robot, multiple single-leg coordinate systems are established: the single-leg coordinate system {A0} coincides with the robot body coordinate system {E}; the single-leg coordinate system {A1} is established on the axis of the joint servo motor of the hip joint, and the three-axis directions are the same as those of the coordinate system {A0}; the single-leg coordinate system {A2} is established on the axis of the joint servo motor of the thigh joint, and its y A2 The axis is parallel to the left and right surfaces of the thigh joint motor; the single-leg coordinate system {A3} is established on the axis of the joint servo motor of the calf joint, A3 The axis is parallel to the left and right surfaces of the calf joint motor; the single-leg coordinate system {A4} is established at the end of the calf joint, and the directions of the three axes are the same as those of the single-leg coordinate system {A3}; the single-leg coordinate system {A5} is established at the foot end, and the directions of the three axes are the same as those of the single-leg coordinate system {A4}; S4. The forward kinematics solution of the quadruped wall-climbing robot is obtained through the rotation change between the single-leg coordinate systems. The joint and foot positions of the quadruped wall-climbing robot can be determined based on the forward kinematics solution. S5. Then, the forward kinematics solution is transformed into an inverse kinematics solution of the quadruped wall-climbing robot. Based on the inverse kinematics solution, the rotation angles of the hip joint, thigh joint, and calf joint to be controlled can be solved given the target position of the foot end; Step S2 is specifically as follows: The waist joint length of the quadruped wall-climbing robot is set to 2a, 2b, 2c, the hip joint length is L1, the thigh joint length is L2, the calf joint length is L3, and the foot joint length is L4; Define the origin O of the robot body coordinate system E The position in the pipeline base coordinate system {O} is (L X ,L Y ,L Z ), the three angle parameters of its coordinate system rotating along the x, y, and z axes relative to the pipeline base coordinate system are α, β, and γ; The transformation matrix of coordinate system {E} relative to {O} coordinate system is: Where: R(z,γ), R(y,β), and R(x,α) represent the rotation angles of the coordinate system around the z, y, and x axes, respectively. X ,L Y ,L Z ) represents the displacement of the coordinate system; The position and posture matrix of the robot body can be obtained through three known rotation angles and displacements to quantify the position and posture of the robot in the pipeline; During the motion of the quadruped wall-climbing robot, given a specific robot starting posture, the origin of the robot body coordinate system O E At the origin O of the pipeline world coordinate system O Directly below, the deflection angles α, β, and γ are all zero, and the transformation matrix of the coordinate system {E} relative to the coordinate system {O} is: In the formula, R represents the inner radius of the pipe; is the coordinate difference of the origin of the two coordinate systems on the z-axis; In step S1, a pipeline basic coordinate system {O} is established with the center of the pipeline as the origin, the pipeline axial direction as the x-axis direction, the vertical upward direction as the y-axis, and the z-axis being perpendicular to the x-axis and the y-axis; The robot body coordinate system {E} is established with the mechanical center of the quadruped wall-climbing robot as the origin, the x-axis is collinear with the forward direction of the quadruped wall-climbing robot, the vertical body surface is upward as the y-axis, and the z-axis is perpendicular to the x-axis and y-axis; The process of solving the forward kinematic solution is as follows: Combine the rotation transformations of the single-leg coordinate system {A5} and {A0}, and the rotation matrix of the single-leg coordinate system {A0} relative to the coordinate system {A5} is: In the formula, θ A1 ,θ A2 ,θ A3 Respectively represent the rotation angles of the hip joint, thigh joint, and calf joint of a single leg; is the rotation matrix of {A4} relative to the coordinate system {A5}; is the rotation matrix of {A3} relative to the coordinate system {A4}; is the rotation matrix of {A2} relative to the coordinate system {A3}; is the rotation matrix of {A1} relative to the coordinate system {A2}; is the rotation matrix of {A0} relative to the coordinate system {A1}; The forward kinematic solution is obtained: in, A0 P is the positive kinematic solution of {A0}; A5 P is the positive kinematic solution of {A5}; x A0 ,y A0 , z A0 It refers to the coordinate value of the foot end position; The forward kinematics solution is transformed into the inverse kinematics solution: in, n A =x A0 -a-L1.

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