An APA type under-actuated robot arm control method and a patrol device using the same

By using the APA-type underactuated robotic arm control method and the fuzzy sliding mode variable structure controller, the problems of blind spots and inconsistent control in inspection robots were solved, enabling omnidirectional image acquisition and efficient inspection of belt conveyors.

CN117754597BActive Publication Date: 2026-07-31TAIYUAN UNIVERSITY OF TECHNOLOGY
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
TAIYUAN UNIVERSITY OF TECHNOLOGY
Filing Date
2024-02-06
Publication Date
2026-07-31

AI Technical Summary

Technical Problem

Existing inspection robots have blind spots, and the control process of the three-link underactuated robotic arm is discontinuous and takes a long time.

Method used

The APA-type underactuated robotic arm control method is adopted. By establishing a planar three-degree-of-freedom active-passive-active kinematic and dynamic model, the expected forward and reverse trajectories are designed and stitched together. Combined with a fuzzy sliding mode variable structure controller, the camera can realize omnidirectional image acquisition between the upper and lower belts of the belt conveyor.

Benefits of technology

It enables all-round inspection of belt conveyors, covering the original blind spots, improving inspection efficiency and effectiveness, with a smooth and efficient control process, and a compact robotic arm structure that avoids collisions with the support frame.

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Abstract

This invention discloses an APA-type underactuated robotic arm control method, comprising the following steps: establishing a planar three-degree-of-freedom active-passive-active underactuated robotic arm kinematic and dynamic model; designing two desired trajectories (positive and negative) for the two active links respectively, and splicing the positive and negative trajectories of the passive link to plan a robotic arm end-effector trajectory from the starting position to the desired position; designing a fuzzy sliding mode variable structure controller to track the planned trajectory, using the absolute value of the sliding mode surface function s as the input of the fuzzy control, and the approach rate parameter ε,k as the fuzzy control output. The control strategy proposed in this invention does not require order reduction, the control process is not segmented, the control process is coherent, and the efficiency is relatively high. Simultaneously, a vision extension device for a belt conveyor inspection robot is also provided, employing the APA-type underactuated robotic arm control method to control a planar three-link system. The acquired image range is expanded to the area between the upper and lower belts, covering the original blind spot and avoiding collisions with supports, etc.
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Description

Technical Field

[0001] The present invention relates to the technical field of an APA-type underactuated robotic arm control method and an inspection device using the method. Background Technology

[0002] Belt conveyors are a key component in coal mine transportation. They often operate under harsh conditions and are subject to long hours and high loads, which makes them prone to belt slippage, longitudinal tearing, misalignment, and even belt breakage. These problems can range from minor shutdowns and production stoppages that disrupt normal mining operations to serious threats to the lives of coal miners.

[0003] Currently, track-mounted inspection robots equipped with cameras and sensors are commonly used to collect five types of information: gas, temperature, smoke, sound, and images, to locate and predict faults in belt conveyors. However, most of the inspection robots currently under research are positioned above the conveyor belt and run along the direction of the conveyor belt. Their visual perception cannot detect the lower surface of the conveyor belt, resulting in blind spots.

[0004] The invention patent with publication number CN115892923B discloses an intelligent inspection robot for belt conveyors (such as...). Figure 5 As shown, the system includes a detection unit and a base unit. When the base unit moves along the conveyor direction of the belt conveyor via double-track rails and wheels, it drives the detection unit to perform mobile inspections of the belt conveyor. Simultaneously, as the base unit moves, it drives a roller ring via a transmission mechanism to rotate on the lower part of the base plate through support rods and sliding sleeves. Since the roller ring is fitted outside the conveyor belt and its inner ring surface has multiple acquisition terminals arranged in a ring array, the roller ring can simultaneously roll outside the belt conveyor as the base unit moves along the conveyor direction. This causes the acquisition terminals to rotate around the belt conveyor, resulting in a spiral trajectory for the acquisition terminals when capturing original images of the belt conveyor. This significantly increases the image acquisition range of the acquisition terminals, enabling the intelligent inspection robot to perform comprehensive inspections of the belt conveyor. However, since its rolling ring is fitted outside the conveyor belt, its diameter must be large enough; it is easily obstructed during actual operation due to the influence of the belt conveyor support and the coal accumulation at the bottom of the conveyor belt; the fixed spiral detection trajectory makes the field of view angle fixed, which also means that there are still blind spots in the field of view.

[0005] Therefore, there is an urgent need for an auxiliary detection device that can effectively solve the problem of blind spots in the inspection of inspection robots and realize detailed local inspection of belt conveyors.

[0006] Chinese patent application CN109262612A discloses a method for optimizing joint angles of an underactuated manipulator based on an improved particle swarm optimization algorithm. The method includes: establishing a planar three-degree-of-freedom passive-active-active (PAA) type underactuated manipulator dynamic model; then, for the underactuated manipulator dynamic model with nonholonomic constraints, using the inverse control concept, reducing it to two passive-active (PA) type subsystems, and clarifying the relationship between joint angles and the end effector position; finally, using the difference between the end effector position and the target position as the objective function, based on the optimization principle of the particle swarm optimization algorithm, introducing the Metropolis acceptance criterion of simulated annealing and the crowding factor of the artificial fish swarm algorithm, to solve for the optimal joint angle corresponding to reaching the target position. This invention can reduce the probability of the optimization algorithm getting trapped in local optima and improve the solution accuracy when controlling the position of an underactuated manipulator. However, it is essentially still the control of a planar two-link underactuated arm. Applying it to a planar three-link underactuated manipulator requires two order reduction controls, and the control process is sequential, discontinuous, and relatively time-consuming. Summary of the Invention

[0007] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0008] In view of the aforementioned existing problems, the present invention is proposed.

[0009] Therefore, the technical problem solved by the present invention is that existing inspection robots have blind spots in detection, and the control process of existing three-link underactuated robotic arms is sequential, discontinuous, and takes a long time.

[0010] To address the problems of sequential, discontinuous, and time-consuming control processes in existing three-bar underactuated robotic arms, this invention provides the following technical solution:

[0011] An APA-type underactuated robotic arm control method includes the following steps:

[0012] Step 1: Establish the kinematics and dynamics model of a planar three-degree-of-freedom active-passive-active (APA type) underactuated manipulator;

[0013] Step 2: Design two desired trajectories for the two active levers, one positive (from the starting position to the middle position) and the other negative (from the desired position to the middle position). Then, splice the positive and negative trajectories of the passive lever to plan a robotic arm end-effector running trajectory from the starting position to the desired position.

[0014] Step 3: Design a fuzzy sliding mode variable structure controller to track the planned trajectory. Combine sliding mode variable control with fuzzy control, using the absolute value of the sliding surface function s as the input to the fuzzy control, and the approach rate parameter. For fuzzy control output, the parameters are adaptively adjusted based on the comparison between the current motion state and the desired motion state of the system.

[0015] As a preferred embodiment of the present invention, the kinematic model of the APA-type underactuated robotic arm is as follows:

[0016] (1).

[0017] As a preferred embodiment of the present invention, the dynamic model of the APA-type underactuated robotic arm is as follows:

[0018] (2)

[0019] in

[0020]

[0021]

[0022]

[0023] In the formula: -No. The mass of the connecting rod, -No. The length of the connecting rod, -No. The distance from the center of mass of the connecting rod to the previous rotating joint. -No. The moment of inertia of the connecting rod rotating about its own center of mass. -No. root link rotation angle ( 1, 2, 3).

[0024] As a preferred embodiment of the present invention,

[0025] The expected positive trajectories of the two active links are as follows:

[0026] (3)

[0027] (4)

[0028] In the formula, q i0 -No. The initial angle of the connecting rod, q im -No. The midpoint angle of the connecting rod. As a time factor, .

[0029] As a preferred embodiment of the present invention,

[0030] The expected trajectories of the two active levers in opposite directions are as follows:

[0031] (5)

[0032] (6)

[0033] In the formula, q id -No. The desired angle of the connecting rod. As a time factor, .

[0034] As a preferred embodiment of the present invention, the passive rod trajectory is solved using the fourth-order Runge-Kutta method according to equation (2), and the specific solution formula is as follows:

[0035] (7)

[0036] The trajectory of the passive lever is determined by the planned trajectory of the active lever, and mainly depends on... , , , The trajectory of the passive lever changes with the magnitude of the value; a suitable trajectory is found using the particle swarm optimization algorithm. , , , This allows the two trajectories of the passive rod, one forward and one reverse, to be pieced together into a smooth and complete trajectory.

[0037] As a preferred embodiment of the present invention, the conditions to be followed for splicing the forward and reverse trajectories of the passive rod and the fitness function of the particle swarm optimization algorithm are as follows:

[0038] (8)

[0039] (9)

[0040] After finding a suitable solution , , , Then, the time reversal method is used to convert the reverse trajectory into a trajectory from the middle position to the desired position. The equation of the reverse trajectory is as follows:

[0041] (10)

[0042] (11)

[0043] In the formula:

[0044] Will , , , Substituting equations (3) and (4) into equations (10) and (11) yields the desired trajectory of the active rod. The active rod drives the passive rod to move through the coupling relationship, which can realize the requirement of the APA type underactuated robot arm to reach the desired position from the starting position.

[0045] As a preferred embodiment of the present invention, the sliding surface and the approach rate function in step three are as follows:

[0046] (12)

[0047] (13)

[0048] In the formula, It is a constant. It is the system tracking position error. It is the system tracking speed error.

[0049] To address the issue of blind spots in existing inspection robots, this invention provides the following technical solution:

[0050] A vision extension device for a belt conveyor inspection robot includes:

[0051] A bracket installed on the inspection robot of the belt conveyor;

[0052] The detection unit, power supply unit, and control unit are installed inside the bracket;

[0053] The detection unit consists of a vertical push rod and a planar three-bar linkage. The vertical push rod is responsible for movement in the Z direction, and the planar three-bar linkage rotates in the horizontal plane. The reachable space is a semicircle whose radius is the sum of the lengths of the three rods. At the same time, the inverse kinematics of the planar three-bar linkage has multiple solutions. The end of the linkage is equipped with a sensing device such as a camera to collect images and transmit the collected images to the host computer.

[0054] The power supply unit provides an independent power source for the entire vision extension device of the belt conveyor inspection robot;

[0055] The control unit consists of a microcontroller and three stepper motor drivers, which drive the vertical electric push rod motor and the first and third joint motors of the planar three-link, respectively. The control unit uses an APA-type underactuated robotic arm control method to control the planar three-link.

[0056] As a preferred embodiment of the present invention, two carbon steel plates are arranged above the support, and the support is magnetically attached to the belt conveyor inspection robot and moves together with the inspection robot.

[0057] The beneficial effects of this invention are:

[0058] (1) When the track inspection robot moves along the conveyor direction of the belt conveyor for inspection, the present invention can achieve image acquisition between the upper and lower belts of the belt conveyor through the cooperation of the electric push rod and the APA-type underactuated robotic arm. Compared with the existing track inspection robot, the present invention expands the image range of the inspection robot to between the upper and lower belts when collecting image information of the belt conveyor, covering the original blind spot, and realizes the track inspection robot to perform all-round inspection of the belt conveyor, improving its inspection efficiency and effect; compared with the patent mentioned in the background, the visual extension device control unit, power supply unit and detection unit of the inspection robot proposed in the present invention have a compact structure and the size of the robotic arm is more reasonable; the extension and retraction of the robotic arm can avoid collision with the support, etc., and the operation is unobstructed; the camera shooting angle can be changed by the rotation angle of the robotic arm to achieve all-round shooting, with a wider field of view and no blind spot.

[0059] (2) This invention discloses an APA (Active-Passive-Active) type underactuated manipulator control strategy, which transforms the position control of the manipulator into trajectory planning + trajectory tracking. By pre-planning a trajectory from the initial position to the target position, trajectory tracking is then performed to achieve direct control of the planar three-bar underactuated manipulator. Compared with the patent described in the background, the control strategy proposed in this invention does not require order reduction, the control process is not segmented, and the two active arms are directly controlled simultaneously, thereby driving the entire manipulator to move according to the planned trajectory. The control process is coherent and has relatively high efficiency. Attached Figure Description

[0060] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0061] Figure 1 A three-dimensional schematic diagram of a vision extension device for a belt conveyor inspection robot.

[0062] Figure 2 This is a schematic diagram of the APA type underactuated robotic arm.

[0063] Figure 3 This is a flowchart of the control method for an APA-type underactuated robotic arm.

[0064] Figure 4 This is a schematic diagram of the main modules of the APA-type underactuated robotic arm fuzzy sliding mode variable structure controller.

[0065] Figure 5 This is a schematic diagram of the structure of an intelligent inspection robot for a belt conveyor.

[0066] In the diagram: 1-Carbon steel plate; 2-Electrical control cabinet; 3-Battery; 4-Electric actuator; 5-Servo motor; 6-APA type underactuated robotic arm; 7-Camera. Detailed Implementation

[0067] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0068] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0069] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0070] Example 1

[0071] This invention patent proposes a vision extension device for a belt conveyor inspection robot, such as... Figure 1 As shown. The vision extension device of the belt conveyor inspection robot is attached to the bottom of the inspection robot by carbon steel plate 1 and moves with the inspection robot on the track; the electrical control cabinet 2 includes a microcontroller and a motor driver, which can be remotely controlled by connecting to a host computer; the battery 3 powers the entire vision extension device of the belt conveyor inspection robot; the electric push rod 4 realizes the movement of the APA type underactuated robotic arm 6 in the Z direction; the servo motor 5 is driven by the motor driver in the electrical control cabinet 2 to realize the angle change of the active rod; the APA type underactuated robotic arm 6 moves in the plane and sends the camera 7 to the target detection area; the camera 7 is installed at the end of the APA type underactuated robotic arm 6 to acquire images.

[0072] The initial state of the vision extension device of the belt conveyor inspection robot is that the electric push rod 4 is not extended, the APA-type underactuated robotic arm 6 is folded, and the rods form a 20° angle. The entire inspection process involves determining the inspection target position (x, y, z). First, the electric push rod 4 is extended a specified length. Then, the APA-type underactuated robotic arm rotates. After reaching the target position, the camera 7 captures the image. Next, the APA-type underactuated robotic arm returns to the initial state. Finally, the electric push rod 4 is retracted, completing one inspection cycle.

[0073] The control of the vision extension device for a belt conveyor inspection robot is mainly divided into vertical electric actuator control and horizontal APA-type underactuated robotic arm control. Obviously, in actual control, vertical electric actuator control is easily implemented. Therefore, the vision extension device control method for a belt conveyor inspection robot proposed in this invention patent is specifically an APA-type underactuated robotic arm control method, such as... Figure 3 As shown, it includes the following steps:

[0074] Step 1: Establish the kinematics and dynamics model of a planar three-degree-of-freedom active-passive-active (APA type) underactuated manipulator;

[0075] Step 2: Design two desired trajectories for the two active levers, one positive (from the starting position to the middle position) and the other negative (from the desired position to the middle position). Then, splice the positive and negative trajectories of the passive lever to plan a robotic arm end-effector running trajectory from the starting position to the desired position.

[0076] Step 3: Design a fuzzy sliding mode variable structure controller to track the planned trajectory. Combine sliding mode variable control with fuzzy control, using the absolute value of the sliding surface function s as the input to the fuzzy control, and the approach rate parameter... For fuzzy control output, the parameters are adaptively adjusted based on the comparison between the current motion state and the desired motion state of the system.

[0077] In the above method, the structural parameters of the APA-type underactuated robotic arm 6 are as follows: Figure 2 As shown, the kinematic model of the APA-type underactuated robotic arm 6 is established accordingly, as follows:

[0078] (1)

[0079] The dynamic model of the APA-type underactuated robotic arm 6 is established as follows:

[0080] (2)

[0081] in

[0082]

[0083]

[0084]

[0085] In the formula: -No. The mass of the connecting rod, -No. The length of the connecting rod, -No. The distance from the center of mass of the connecting rod to the previous rotating joint. -No. The moment of inertia of the connecting rod rotating about its own center of mass. -No. root link rotation angle ( 1, 2, 3).

[0086] In the above method, two desired trajectories are designed for the two active links: a forward trajectory (from the starting position to the middle position) and a reverse trajectory (from the desired position to the middle position). The forward and reverse trajectories of the passive link are then spliced ​​together to plan a robotic arm end effector trajectory from the starting position to the desired position, including:

[0087] The desired trajectories of the two active levers in the positive direction (from the starting position to the middle position) are as follows:

[0088] (3)

[0089] (4)

[0090] In the formula, q i0 -No. The initial angle of the connecting rod, q im -No. The midpoint angle of the connecting rod. As a time factor,

[0091] The desired trajectories of the two driving levers in opposite directions (from the starting position to the middle position) are as follows:

[0092] (5)

[0093] (6)

[0094] In the formula, q id -No. The desired angle of the connecting rod. As a time factor,

[0095] After planning the trajectory of the active link, the trajectory of the passive link is solved using the fourth-order Runge-Kutta method according to equation (2). The specific solution formula is as follows:

[0096] (7)

[0097] The trajectory of the passive lever is determined by the planned trajectory of the active lever, and mainly depends on... , , , The trajectory of the passive lever changes with the magnitude of the value; a suitable trajectory is found using the particle swarm optimization algorithm. , , , This allows the two trajectories of the passive rod, one forward and one reverse, to be combined into a smooth and complete trajectory. The conditions for combining the forward and reverse trajectories of the passive rod and the fitness function of the particle swarm optimization algorithm are as follows:

[0098] (8)

[0099] (9)

[0100] After finding a suitable solution , , , Then, the time reversal method is used to convert the reverse trajectory into a trajectory from the middle position to the desired position. The equation of the reverse trajectory is as follows:

[0101] (10)

[0102] (11)

[0103] In the formula:

[0104] Will , , , Substituting equations (3) and (4) into equations (10) and (11) yields the desired trajectory of the active rod. The active rod drives the passive rod to move through the coupling relationship, which can realize the requirement of the APA type underactuated robot arm to reach the desired position from the starting position.

[0105] In the above method, a fuzzy sliding mode variable structure controller is designed to track the planned trajectory. Sliding mode variable control is combined with fuzzy control, using the absolute value of the sliding surface function s as the input to the fuzzy control, and the approach rate parameter... For fuzzy control output, the parameters are adaptively adjusted based on the comparison between the current motion state and the desired motion state of the system, such as... Figure 4 As shown, it includes:

[0106] The sliding surface and the rate of approach function are as follows:

[0107] (12)

[0108] (13)

[0109] In the formula, It is a constant. It is the system tracking position error. It is the system tracking speed error.

[0110] The input and output fuzzy sets are as follows:

[0111] For sliding surface functions , reaching law parameters and Define three fuzzy sets, denoted by "zero" (ZR), "smallest" (PS), "middle" (PM), and "largest" (PB), respectively. Then we have:

[0112]

[0113]

[0114]

[0115] The corresponding fuzzy domain is

[0116]

[0117]

[0118]

[0119] Determine the fuzzy rules:

[0120] Table 1 Fuzzy Control Rules

[0121]

[0122] Described in vague language

[0123] if is ZR, then is ZR and k is PB

[0124] if is PS, then is PS and k is PM

[0125] if is PM, then is PM and k is PS

[0126] if is PB, then is PB and k is ZR

[0127] It is important to note that the constructions and arrangements of this application shown in several different exemplary embodiments are merely illustrative. Although only a few embodiments are described in detail in this disclosure, those who consult this disclosure will readily understand that many modifications are possible (e.g., changes in the size, dimensions, structure, shape, and proportions of various elements, as well as parameter values ​​(e.g., temperature, pressure, etc.), mounting arrangements, use of materials, color, orientation, etc.) without substantially departing from the novel teachings and advantages of the subject matter described in this application). For example, an element shown as integrally formed may be composed of multiple parts or elements, the position of elements may be inverted or otherwise altered, and the nature or number or position of discrete elements may be changed or altered. Therefore, all such modifications are intended to be included within the scope of the invention. The order or sequence of any process or method steps may be changed or rearranged according to alternative embodiments. In the claims, any "device plus function" clause is intended to cover the structure described herein that performs the function, and not only structurally equivalent but also equivalent in structure. Other substitutions, modifications, alterations, and omissions may be made in the design, operation, and arrangement of the exemplary embodiments without departing from the scope of the invention. Therefore, the present invention is not limited to the specific embodiments, but extends to various modifications that still fall within the scope of the appended claims.

[0128] Furthermore, in order to provide a concise description of exemplary embodiments, not all features of actual embodiments (i.e., those features that are not relevant to the currently considered best mode for carrying out the invention, or those features that are not relevant to implementing the invention) may be omitted.

[0129] It should be understood that numerous specific implementation decisions can be made during the development of any practical implementation, such as in any engineering or design project. Such development efforts may be complex and time-consuming, but for those skilled in the art who benefit from this disclosure, the development effort will be a routine work of design, manufacturing, and production without requiring much experimentation.

[0130] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A control method of an underactuated manipulator of APA type, characterized in that, Includes the following steps: Step 1: Establish the kinematic and dynamic model of the planar three-degree-of-freedom active-passive-active underactuated manipulator; Step 2: Design two desired trajectories for the two active levers, one forward and one reverse. The forward desired trajectory is from the starting position to the middle position, and the reverse desired trajectory is from the desired position to the middle position. Then, splice the forward and reverse trajectories of the passive lever to plan a robotic arm end effector trajectory from the starting position to the desired position. The passive link trajectory is solved using the fourth-order Runge-Kutta method. The trajectory of the passive link is determined by the planned active link trajectory and depends on... , , , The trajectory of the passive lever changes with the magnitude of the value; a suitable trajectory is found using the particle swarm optimization algorithm. , , , This allows the two trajectories of the passive rod, one forward and one reverse, to be pieced together into a smooth and complete trajectory, q im For the first The midpoint angle of the connecting rod. , As a time factor, after solving for a suitable , , , Then, the reverse trajectory is converted into a trajectory from the middle position to the desired position, and spliced ​​together to obtain the desired trajectory of the active lever; Step 3: Design a fuzzy sliding mode variable structure controller to track the planned trajectory. Combine sliding mode variable control with fuzzy control, using the absolute value of the sliding surface function s as the input to the fuzzy control, and the approach rate parameter. For fuzzy control output, parameters are adaptively adjusted based on a comparison between the system's current motion state and the desired motion state. The sliding surface and the rate of convergence function are as follows: (12) (13) In the formula, It is a constant. It is the system tracking position error. It is the system tracking speed error.

2. The APA-type underactuated robotic arm control method according to claim 1, characterized in that, The kinematic model of the APA-type underactuated robotic arm is as follows: (1), In the formula: -No. The length of the connecting rod, -No. root link rotation angle ( 1, 2, 3).

3. The APA-type underactuated robotic arm control method according to claim 1, characterized in that, The dynamic model of the APA-type underactuated robotic arm is as follows: (2) in In the formula: -No. The mass of the connecting rod, -No. The distance from the center of mass of the connecting rod to the previous rotating joint. -No. The moment of inertia of a connecting rod rotating about its own center of mass.

4. The APA-type underactuated robotic arm control method according to claim 1, characterized in that, The expected positive trajectories of the two active links are as follows: (3) (4) In the formula, q i0 -No. The initial angle of the connecting rod, q im -No. The midpoint angle of the connecting rod. As a time factor, .

5. The APA-type underactuated robotic arm control method according to claim 1, characterized in that, The expected trajectories of the two active levers in opposite directions are as follows: (5) (6) In the formula, q id -No. The desired angle of the connecting rod. As a time factor, .

6. The APA-type underactuated robotic arm control method according to claim 1, characterized in that, The trajectory of the passive rod is solved using the fourth-order Runge-Kutta method according to equation (2). The specific solution formula is as follows: (7)。 7. The APA-type underactuated robotic arm control method according to claim 1, characterized in that, The conditions that must be followed for splicing the forward and reverse trajectories of the passive rod, and the fitness function of the particle swarm optimization algorithm, are as follows: (8) (9) After finding a suitable solution , , , Then, the time reversal method is used to convert the reverse trajectory into a trajectory from the middle position to the desired position. The equation of the reverse trajectory is as follows: (10) (11) In the formula: Will , , , Substituting equations (3) and (4) into equations (10) and (11) yields the desired trajectory of the active rod. The active rod drives the passive rod to move through the coupling relationship, which can realize the requirement of the APA type underactuated robot arm to reach the desired position from the starting position.

8. A vision extension device for a belt conveyor inspection robot, characterized in that, include: A bracket installed on the inspection robot of the belt conveyor; The detection unit, power supply unit, and control unit are installed inside the bracket; The detection unit consists of a vertical push rod and a planar three-bar linkage. The vertical push rod is responsible for movement in the Z direction, and the planar three-bar linkage rotates in the horizontal plane. The end of the linkage is equipped with a sensing device such as a camera to collect images and transmit the collected images to the host computer. The power supply unit provides power to the entire vision extension device of the belt conveyor inspection robot; The control unit consists of a microcontroller and three stepper motor drivers, which drive the vertical electric push rod motor and the first and third joint motors of the planar three-link, respectively. The control unit uses any one of the APA-type underactuated robotic arm control methods as described in claims 1-7 to control the planar three-link.

9. The vision extension device for a belt conveyor inspection robot according to claim 8, characterized in that, Two carbon steel plates are arranged above the support frame. The support frame is magnetically attached to the belt conveyor inspection robot and moves together with the inspection robot.