A multi-machine collaborative control system and method for reactor pressure vessel inspection

Abstract

The present invention belongs to the field of cooperative control of multiple underwater robots for nuclear power plant detection, and particularly relates to a multi-robot cooperative control system and method for reactor pressure vessel inspection. It includes a control computer, a network switch, a crawling robot control box, a floating robot control box, a pan-tilt control box, a laser video pan-tilt, a pan-tilt mounting bracket, a container, a floating robot and a crawling robot; the control computer is connected to the network switch, and the network switch is respectively connected to the crawling robot control box, the floating robot control box and the laser video pan-tilt. The laser video pan-tilt is installed on the pan-tilt mounting bracket, and the pan-tilt mounting bracket is installed on the container. The floating robot is connected to the floating robot control box, and the crawling robot is connected to the crawling robot control box. Its advantages are: shortening the operation time, greatly improving the underwater operation efficiency, reducing the maintenance cost, reducing the personnel irradiation intensity and working hours.

Description

Technical Field

[0001] The invention belongs to the field of underwater multi-robot cooperative control for nuclear power plant detection, and particularly relates to a multi-robot cooperative control system and method for reactor pressure vessel inspection. Background Art

[0002] For the underwater inspection and maintenance of the primary equipment reactor pressure vessel in a nuclear power plant, through the research on underwater multi-robot cooperative control technology, key technologies such as multi-sensor information fusion perception, remote control, underwater positioning, spatial intelligent obstacle avoidance and path planning of underwater multi-robots are mastered, a set of underwater multi-robot cooperative operation control platform with strong adaptability and stable performance is formed, and the cooperative operation control of underwater multi-robots is completed. Give full play to the advantages of underwater multi-robot cooperative operation, improve the parallel degree of complex operation and maintenance tasks, enhance the intelligence and functionality of nuclear power robots, shorten the operation time, and reduce the personnel irradiation intensity and working hours. Summary of the Invention

[0003] The purpose of the invention is to provide a multi-robot cooperative control system and method for reactor pressure vessel inspection, which realizes the cooperative control of a nuclear reactor pressure vessel through multiple underwater robots to achieve parallel operation, so as to improve the detection efficiency and safety of the vessel.

[0004] The technical solution of the invention is as follows: A multi-robot cooperative control system for reactor pressure vessel inspection includes a control computer, a network switch, a crawler robot control box, a first floating robot control box, a second floating robot control box, a third floating robot control box, a pan-tilt control box, a laser video pan-tilt, a pan-tilt mounting bracket, a vessel, a first floating robot, a second floating robot, a third floating robot and a crawler robot; the control computer is connected to the network switch, and the network switch is respectively connected to the crawler robot control box, the first floating robot control box, the second floating robot control box and the third floating robot control box. The crawler robot control box, the first floating robot control box, the second floating robot control box and the third floating robot control box are respectively connected to the laser video pan-tilt. The laser video pan-tilt is installed on the pan-tilt mounting bracket, and the pan-tilt mounting bracket is installed on the vessel. The first floating robot is connected to the first floating robot control box, the second floating robot is connected to the second floating robot control box, the third floating robot is connected to the third floating robot control box, and the crawler robot is connected to the crawler robot control box. The first floating robot, the second floating robot, the third floating robot and the crawler robot are all arranged inside the vessel.

[0005] A multi-robot cooperative control method for reactor pressure vessel inspection includes the following steps:

[0006] Step 1: Establish formation parameters, including formation type, formation scale, formation spacing, and formation operation rhythm;

[0007] Step 2: Set the geometric shape of the robot formation and the logical relationship of relative positions;

[0008] Step 3: Complete the specific formation tasks of the robots, including formation generation / reconfiguration, formation maintenance, formation obstacle avoidance / collision avoidance, and accidental collaboration tasks;

[0009] Step 4: Evaluate the formation effect during the collaborative work of multiple underwater robots, and quantitatively and qualitatively evaluate the formation effect from two directions: path length rate and formation maintenance rate.

[0010] The above-mentioned Step 1 includes:

[0011] Step 11: Set the formation type: Set the supported formation types according to the specific task scenario. The project plan supports 4 formation types: parallel, serial, V-shaped, and circular;

[0012] Step 12: Set the formation scale: Set the number of underwater robots in the formation. The formation scale of the robots needs to be set according to the actual task nature and environmental constraints;

[0013] Step 13: Set the formation spacing: Used to set the relative position relationship between adjacent two robots during the formation process, including the linear distance and angle, and dynamically set according to needs;

[0014] Step 14: Set the formation operation rhythm: Used to set the synchronization time of the coordinated action steps between the robots. For the formation method based on the leader method, the leader must continuously plan sub-goal points for each follower, and then the leader and the followers rush towards their respective goal points at the same time, repeating until the final goal point is reached, then this formation operation ends. The formation operation rhythm is the time interval for the leader to plan sub-goal points for the followers.

[0015] The above-mentioned Step 2 includes: Use a four-element ordered array and a control matrix to achieve the accurate shaping of the formation. The four-element ordered array is used to determine the relationship of the connecting edges of the formation; the control matrix is used to determine the hierarchical relationship between the robots in the entire formation system.

[0016] The above-mentioned Step 2 includes:

[0017] Step 21: There is exactly one leader in the collaborative formation system;

[0018] Step 22: For the leader, its tracking degree d L = 0. For the follower, its tracking degree d F = 1. For the trailing robot, its being-tracked degree d T= 0, the tracking degree is defined as: whether a certain underwater robot has a preceding underwater robot. If there is a preceding underwater robot, the tracking degree is 1; otherwise, it is 0. The being-tracked degree is defined as: whether a certain underwater robot has a following underwater robot. If there is no following underwater robot, its being-tracked degree is 0.

[0019] Step 23: In the formation system of N underwater robots, there are N - 1 connecting edges in the hierarchical structure of the formation.

[0020] Step 24: The connecting edge is represented by a four-tuple ordered array E N denotes, V i denotes the node, R ij , σ ij respectively represent the straight-line distance and azimuth angle between two nodes of the formation:

[0021] E n = {(V1, V2, R 12 , σ 12 ), (V2, V3, R 23 , σ 23 ),..., (V N-1 , V N-1 , R (N-1)N , σ (N-1)N )}

[0022] Step 25: Derive the corresponding formation control matrix through the four-tuple ordered array. According to the logical relationship between each node, define the formation control matrix as follows:

[0023]

[0024] where, i, j = 1, 2,..., N, i ≠ j

[0025] The element characteristics of the control matrix are:

[0026] ① If the i-th underwater robot is the leader, then

[0027] ② If the i-th underwater robot is a follower, then

[0028] ③ If the i-th ROV is a trailer, then

[0029] The said step 3 includes:

[0030] Step 31: Formation generation / reconfiguration adopts the leader-follower formation model. The leader automatically runs to the target point according to the task assignment. At the same time, it will assign sub-target points to the followers according to the four-element ordered array and the control matrix. Then the followers run from the current actual position to the sub-target points, repeating the cycle until the final formation is formed. The artificial potential field control method is adopted. The gravitational function is defined as a function of the relative distance and azimuth between the actual position point of the underwater robot and the new sub-target point. The gravitational function and the potential function are shown as follows:

[0031]

[0032]

[0033] In the formula, ||d jj' || represents the relative distance between the actual position of the follower underwater robot and the actual ideal position planned by the leader underwater robot, φ jj' is the azimuth difference between the actual heading and the ideal heading of the underwater robot, φ jj' =|α i -α j' |; ρ PA is the positive gain to reach the sub-target point; d is the motion vector of each underwater robot, α is the heading of each underwater robot. When ||d jj' || and φ jj' are 0, the follower will reach the assigned sub-target point.

[0034] Step 32: During the formation maintenance stage, each underwater robot must continuously track the positions of their respective sub-target points. The positions of the sub-target points are calculated according to the leader-follower formation model. Maintaining the formation shape is to determine the linear velocity and angular velocity of the follower, so as to eliminate the error values of the distance and angle between the current position and the desired position of the follower:

[0035]

[0036]

[0037] Among them, L ij and ψ ij are the actual distance and angle between the leader and the follower, L ij d and ψ ij d are the desired distance and angle. When the sum of the distance deviations and the sum of the angle deviations of all underwater robots are 0, the system will maintain the formation shape and run;

[0038] Step 33: Adopt a distributed obstacle avoidance / collision avoidance detection algorithm. Each robot is the main body of the obstacle avoidance / collision avoidance detection algorithm and runs the obstacle avoidance / collision avoidance detection algorithm with the same architecture.

[0039] Accidental collaboration means that when multiple underwater robots are operating in formation and one of them fails, the other robots can still maintain normal functions. In the leader-follower formation model, there are two cases: the leader fails and the follower fails.

[0040] The said Step 34 includes:

[0041] Step 341: The leader fails

[0042] When the leader fails, a new leader is re-elected. During the operation of multiple underwater robots, each underwater robot is assigned an ID. The leader ID is set to 1, and the IDs of other underwater robots are arranged in ascending order according to their distance from the leader. When the leader fails, the robot with the ID closest to the leader ID will be elected as the new leader, and other robots will dynamically adjust the formation according to the new leader.

[0043] Step 342: The follower fails

[0044] When a follower fails during the formation operation of multiple underwater robots, other follower robots continue to run according to the sub-goal positions assigned by the leader, and the position of the faulty follower will remain vacant.

[0045] The said Step 4 includes,

[0046] Step 41: Path length ratio R path_lengh It is defined as the ratio of the average distance traveled by all underwater robots to the straight-line distance between the target point and the starting point:

[0047]

[0048] In the formula, d i is the distance traveled by the i-th underwater robot during the entire formation operation, and d sg is the straight-line distance between the starting point and the target point.

[0049] Step 42: Formation maintenance rate is defined as the proportion of the time when the underwater robots are at the expected positions during the entire movement process:

[0050]

[0051] In the formula, m iLet \(n_i\) be the actual number of times the \(i\)-th underwater robot is at the sub-goal point during the entire formation operation, and \(m\) be the planned number of times each underwater robot is at the sub-goal point during the entire formation operation.

[0052] The \(d\) in step 41 sg The value range is from 1 to ∞.

[0053] The \(m\) in step 42 i The value is in the range of [0, 1].

[0054] The beneficial effects of the present invention are as follows: The present invention can realize the cooperative operation control of multiple robots during the inspection and maintenance of nuclear power underwater containers, improve the parallelism and intelligence of the operation and maintenance tasks of nuclear power robots in complex environments, shorten the operation time, can greatly improve the underwater operation efficiency, reduce the maintenance cost, reduce the radiation intensity and working hours of personnel. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 FIG. is a schematic diagram of a multi-robot cooperative control system for reactor pressure vessel inspection provided by the present invention;

[0056] Figure 2 FIG. is an example diagram of formation types;

[0057] Figure 3 FIG. is a schematic diagram of a leader / follower formation model;

[0058] Figure 4 FIG. is a schematic diagram for explaining the safe area of underwater robots;

[0059] Figure 5 FIG. is a schematic diagram of a failure of the formation leader;

[0060] Figure 6 FIG. is a schematic diagram of a failure of the formation follower.

[0061] In the figure, 1 is a control computer, 2 is a network switch, 3 is a crawling robot control box, 4 is a first floating robot control box, 5 is a second floating robot control box, 6 is a third floating robot control box, 7 is a pan-tilt control box, 8 is a laser video pan-tilt, 9 is a pan-tilt mounting bracket, 10 is a container, 11 is a first floating robot, 12 is a second floating robot, 13 is a third floating robot, and 14 is a crawling robot. DETAILED DESCRIPTION OF THE INVENTION

[0062] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0063] As Figure 1As shown in the figure, a multi-robot collaborative control system for reactor pressure vessel inspection includes a control computer 1, a network switch 2, a crawling robot control box 3, a first floating robot control box 4, a second floating robot control box 5, a third floating robot control box 6, a pan-tilt control box 7, a laser video pan-tilt 8, a pan-tilt mounting bracket 9, a container 10, a first floating robot 11, a second floating robot 12, a third floating robot 13, and a crawling robot 14. The control computer 1 is connected to the network switch 2, and the network switch 2 is respectively connected to the crawling robot control box 3, the first floating robot control box 4, the second floating robot control box 5, and the third floating robot control box 6. The crawling robot control box 3, the first floating robot control box 4, the second floating robot control box 5, and the third floating robot control box 6 are respectively connected to the laser video pan-tilt 8. The laser video pan-tilt 8 is installed on the pan-tilt mounting bracket 9, and the pan-tilt mounting bracket 9 is installed on the container 10. The first floating robot 11 is connected to the first floating robot control box 4, the second floating robot 12 is connected to the second floating robot control box 5, the third floating robot 13 is connected to the third floating robot control box 6, and the crawling robot 14 is connected to the crawling robot control box 3. The first floating robot 11, the second floating robot 12, the third floating robot 13, and the crawling robot 14 are all arranged inside the container 10.

[0064] A multi-robot collaborative control method for reactor pressure vessel inspection divides the underwater multi-robot collaboration formation into four levels: mission planning level, formation design level, behavior control level, and formation evaluation level for design and implementation. The mission planning level mainly realizes the determination of formation parameters. The formation design level mainly realizes the specific geometric shape and the relative logical relationship between robots. The behavior control level mainly realizes the specific formation tasks of robots, including formation generation / reconfiguration, formation maintenance, formation obstacle avoidance / collision avoidance, accidental collaboration, etc. The formation evaluation level mainly qualitatively and quantitatively evaluates the performance of each robot in the formation system during the entire formation task according to certain evaluation indicators to determine whether the formation has achieved the expected effect.

[0065] A multi-robot collaborative control method for reactor pressure vessel inspection includes the following steps:

[0066] Step 1: The mission planning level should first establish appropriate formation parameters, including formation type, formation scale, formation spacing, formation operation rhythm, formation reference point, etc. The setting of these parameters is often related to the self-configuration and performance of underwater robots and environmental constraints, etc.

[0067] Step 11: Set the formation type: The supported formation types can be set according to the specific task scenario. The project plan supports 4 formation types: parallel, serial, V-shaped, and circular, as Figure 2 shown.

[0068] Step 12: Set the formation scale: Set the number of underwater robots in the formation. The formation scale of the robots needs to be set according to the actual mission nature and environmental constraints.

[0069] Step 13: Set the formation spacing: It is used to set the relative position relationship between two adjacent robots during the formation process, including the straight-line distance and the angle. These two parameters are strongly related to the mission nature, formation type, robot volume, etc., and are dynamically set according to needs.

[0070] Step 14: Set the formation operation rhythm: It is used to set the synchronization time of the coordinated action pace between robots. For the formation method based on the leader method, the leader must continuously plan sub-goal points for each follower, and then the leader and the followers rush towards their respective goal points at the same time, repeating until the final goal point is reached, then this formation operation ends. The formation operation rhythm is the time interval for the leader to plan sub-goal points for the followers, and the interval size is strongly related to the robot speed and the operating environment.

[0071] Step 2: The formation design layer is used to set the geometric shape of the robot formation and the logical relationship of the relative positions.

[0072] Use a four-element ordered array and a control matrix to achieve the accurate shaping of the formation: The four-element ordered array is used to determine the relationship of the connecting edges of the formation; the control matrix is used to determine the hierarchical relationship between the robots in the entire formation system.

[0073] Step 21: There is exactly one leader in the cooperative formation system;

[0074] Step 22: For the leader, its tracking degree d L = 0. For the followers, their tracking degree d F = 1. For the trailers, their being-tracked degree d T = 0. The tracking degree is defined as: whether there is a preceding underwater robot for a certain underwater robot. If there is a preceding underwater robot, the tracking degree is 1, otherwise it is 0; the being-tracked degree is defined as: whether there is a subsequent underwater robot for a certain underwater robot. If there is no subsequent underwater robot, its being-tracked degree is 0.

[0075] Step 23: In the formation system of N underwater robots, there are N - 1 connecting edges in its formation hierarchical structure.

[0076] Step 24: The connecting edge is represented by a four-element ordered array E N where V i represents the node, and R ij , σ ij respectively represent the straight-line distance and the azimuth angle between two nodes of the formation:

[0077] E n={(V1, V2, R 12 , σ 12 ), (V2, V3, R 23 , σ 23 ),..., (V N-1 , V N-1 , R (N-1)N , σ (N-1)N )}

[0078] Step 25: The corresponding formation control matrix can be derived from the four - tuple ordered array. According to the logical relationship between each node, the formation control matrix is defined according to the following idea:

[0079]

[0080] where i, j = 1, 2,..., N, i ≠ j

[0081] The element characteristics of the control matrix are as follows:

[0082] ④ If the i - th underwater robot is the leader, then

[0083] ⑤ If the i - th underwater robot is a follower, then

[0084] ⑥ If the i - th ROV is a trailer, then

[0085] Step 3: The behavior control layer mainly realizes the specific formation tasks of the robot, including formation generation / reconfiguration, formation maintenance, formation obstacle avoidance / collision avoidance, accidental cooperation and other tasks.

[0086] Step 31: The leader - follower formation model is adopted for formation generation / reconfiguration. The leader will automatically run to the target point according to the task assignment, and at the same time, it will assign sub - target points to the followers according to the four - tuple ordered array and the control matrix in the formation shape design layer. Then the followers will run from the current actual position to the sub - target points, and repeat the cycle until the final formation shape is formed. To ensure the formation of the final formation shape, the artificial potential field control method is adopted. The gravitational function is defined as a function of the relative distance and azimuth between the actual position point of the underwater robot and the new sub - target point. The gravitational function and the potential function are shown as follows:

[0087]

[0088]

[0089] In the formula, ||d jj' || represents the relative distance between the actual position of the follower underwater robot and the actual ideal position planned by the leader underwater robot, φjj' is the azimuth difference between the actual heading and the ideal heading of the underwater robot, φ jj' = |α i - α j' |; ρ PA is the positive gain to reach the sub-goal point

[0090] ; d is the motion vector of each underwater robot, and α is the heading of each underwater robot. Thus, it can be seen that when ||d jj' || and φ jj' are 0, the follower will reach the assigned sub-goal point.

[0091] Step 32: During the formation maintenance stage, each underwater robot must continuously track the position of its corresponding sub-goal point. The position of the sub-goal point is calculated according to the leader-follower formation model. The formation shape is maintained by keeping the distance and attitude angle required between the follower and the leader. Maintaining the formation shape is to determine the linear velocity and angular velocity of the follower, so as to eliminate the error values of the distance and angle between the current position and the desired position of the follower:

[0092]

[0093]

[0094] where L ij , ψ ij are the actual distance and angle between the leader and the follower, L ij d , ψ ij d are the desired distance and angle. When the sum of the distance deviations and the sum of the angle deviations of all underwater robots are 0, the system will maintain the formation shape and operate.

[0095] Step 33: Formation obstacle avoidance / collision avoidance is mainly used to solve the interference problem of the surrounding environment during the collaborative work of the robots. A distributed obstacle avoidance / collision detection algorithm is adopted. Each robot is the main body of the obstacle avoidance / collision detection algorithm and runs the obstacle avoidance / collision detection algorithm with the same architecture.

[0096] To solve the obstacle avoidance / collision avoidance problem, we define 3 cylindrical regions for each underwater robot, as Figure 4 shown:

[0097] Collision-occurrence cylinder: As shown by the light yellow cylinder in the figure, its radius is r c and its height is h r , indicating that when an obstacle enters this cylindrical region, a collision will surely occur.

[0098] Horizontal safety zone cylinder: As shown by the light green cylinder in the figure, its radius is r r and its height is h r , indicating that when an obstacle enters this cylinder area, a collision will occur in the horizontal direction.

[0099] Vertical safety zone cylinder: As shown by the light purple cylinder in the figure, its radius is r r and its height is h b , indicating that when an obstacle enters this cylinder area, a collision will occur in the vertical direction.

[0100] During the movement of the underwater robot from the starting point to the target point, the running trajectory is likely to be a curvilinear motion, that is, there are both speed components and angle components in the horizontal X-Y direction and the vertical Z direction. Therefore, according to whether the underwater robot is blocked in the horizontal and vertical directions, the running state machine of the underwater robot can be defined as follows:

[0101] X-Y Free state: The state in which the underwater robot can move freely in the X-Y plane. If the underwater robot is not disturbed by obstacles during the movement towards the target point, it will move to the target point according to the horizontal speed component of the target point; if a conflict in the X-Y plane is detected during the movement, it will switch to the X-Y Avoid state or the X-Y Block state.

[0102] X-Y Avoid state: The underwater robot detects a conflict in the X-Y plane but can avoid the conflict angle detected in the X-Y plane The following method is used to calculate the avoidance direction For each X-Y conflict, assuming that all underwater robots move counterclockwise around the obstacle, the interval is defined as the disabled angle. The avoidance direction is calculated through the range of this disabled angle, and then the underwater robot moves in the avoidance direction to avoid the obstacle; if the underwater robot is surrounded by multiple obstacles at the same time, the calculated avoidance angle may be empty, and at this time the underwater robot will enter the X-Y Block state.

[0103] X-Y Block state: The underwater robot cannot avoid the X-Y plane conflict, and the X-Y plane speed is set to 0. If a conflict is detected in the X-Y plane and the calculated avoidance angle is empty, the horizontal running speed of the underwater robot will be set to 0, and then it will enter the X-Y Block horizontal hover waiting state, but the conflict in the X-Y plane does not affect the vertical movement. When the underwater robot performs vertical obstacle avoidance or the surrounding obstacles are bypassed, it will unlock and leave the X-Y Block state.

[0104] Z Free state: The state where the underwater robot can move freely in the vertical direction. If the underwater robot does not detect a Z-direction conflict, or the existing conflict does not interfere with the target path (for example, the Z-direction conflict is above, but the target of the underwater robot is below), the underwater robot can move up or down.

[0105] Z Block state: The underwater robot does not avoid the Z-plane conflict, and the vertical speed is set to 0. The Z Block state means that an obstacle is detected in the vertical direction and cannot be avoided. At this time, the vertical movement speed of the underwater robot is set to 0, and then it enters the Z Block hover waiting state. When the vertical conflict is resolved, it will unlock and leave the Z Block state.

[0106] Step 34: Unexpected cooperation refers to the ability of multiple underwater robots to maintain normal functions when one of them fails during formation operation. In the leader-follower formation model, there are two cases: the leader fails and the follower fails.

[0107] Step 341: The leader fails

[0108] In the leader-follower formation model, the leader is a key factor in formation operation. When the leader fails, a new leader must be re-elected. During the operation of multiple underwater robots, each underwater robot is assigned an ID. The leader ID is set to 1, and the IDs of other underwater robots are arranged in ascending order according to the distance from the leader. In this way, when the leader fails, the robot with the ID closest to the leader ID will be elected as the new leader, and then other robots will dynamically adjust the formation according to the new leader, as Figure 5 shown.

[0109] Step 342: The follower fails

[0110] When a follower fails during the formation operation of multiple underwater robots, there is no problem of re-electing the leader. At this time, to ensure the normal operation of the system, other follower robots continue to operate according to the sub-goal positions assigned by the leader, and the follower with the problem will remain vacant and stop operating, as Figure 6 shown.

[0111] Step 4: The formation evaluation layer is used to evaluate the formation effect during the collaborative work of multiple underwater robots, and quantitatively and qualitatively evaluate the formation effect from two directions: the path length rate and the formation maintenance rate.

[0112] Step 41: Path length rate R path_lengh Defined as the ratio of the average distance traveled by all underwater robots to the straight-line distance between the target point and the starting point:

[0113]

[0114] where d i is the distance traveled by the i-th underwater robot during the entire formation operation, and d sg is the straight-line distance between the starting point and the target point. The value range of this index is 1 to ∞.

[0115] Step 42: The formation maintenance rate defines the proportion of the time when the underwater robot is at the desired position during the entire movement process:

[0116]

[0117] where m i is the actual number of times the i-th underwater robot is at the sub-target point during the entire formation operation, and m is the planned number of times for each underwater robot to be at the sub-target point during the entire formation operation. The value range of this index is [0, 1].

[0118] In the leader-based formation system, each underwater robot tracks the corresponding sub-target point in real time. If it encounters an obstacle constraint at a certain moment and cannot continue to maintain the original formation, the underwater robot will abandon its respective sub-target point and thus deviate from the desired position. During the entire formation operation, the more times each underwater robot deviates from its desired position, the worse the formation maintenance effect will be; conversely, the better. When there are obstacle constraints in the environment, this index can be used to indicate the ability to maintain the formation and can be regarded as a discrete index.

Claims

1. A multi-machine collaborative control method for reactor pressure vessel inspection, characterized in that It includes the following steps: Step 1: Determine formation parameters, including formation type, formation scale, formation spacing, and formation operation rhythm; Step 2: Set the geometric shape of the robot formation and the logical relationship of relative positions; The said Step 2 includes: Using a four - element ordered array and a control matrix to achieve accurate shaping of the formation. The four - element ordered array is used to determine the relationship of the connecting edges of the formation; the control matrix is used to determine the hierarchical relationship between robots in the entire formation system; The said Step 2 includes: Step 21: There is exactly one leader in the cooperative formation system; Step 22: For the leader, its tracking degree d L = 0. For the follower, its tracking degree d F = 1. For the trailer, its being-tracked degree d T = 0. The tracking degree is defined as: whether there is a preceding underwater robot for a certain underwater robot. If there is a preceding underwater robot, the tracking degree is 1; otherwise, it is 0. The being-tracked degree is defined as: whether there is a subsequent underwater robot for a certain underwater robot. If there is no subsequent underwater robot, its being-tracked degree is 0; Step 23: In the formation system of N underwater robots, there are N - 1 connecting edges in its formation hierarchical structure; Step 24: The connecting edge is represented by a four - tuple ordered array E N denotes, V i denotes the node, R ij , σ ij respectively denote the straight - line distance and azimuth angle between two nodes of the formation: E n = {(V1, V2, R 12 , σ 12 ), (V2, V3, R 23 , σ 23 ),..., (V N-1 , V N-1 , R (N-1)N , σ (N-1)N )} Step 25: Derive the corresponding formation control matrix through the four - element ordered array. According to the logical relationship between each node, define the formation control matrix as follows: where i, j = 1, 2,..., N, i ≠ j The element characteristics of the control matrix are: ① If the i-th underwater robot is the leader, then ② If the i-th underwater robot is a follower, then ③ If the i-th ROV is a follower, then Step 3: Complete the specific formation tasks of the robots, including formation generation / reconfiguration, formation maintenance, formation obstacle avoidance / collision avoidance, and unexpected cooperative tasks; Step 4: Evaluate the formation effect during the collaborative work of multiple underwater robots, and quantitatively and qualitatively evaluate the formation effect from two aspects: path length rate and formation maintenance rate.

2. The multi-machine collaborative control method for the inspection of a reactor pressure vessel according to claim 1, wherein The said Step 1 includes: Step 11: Set the formation type: Set the supported formation types according to the specific task scenario. The project plan supports 4 formation types: parallel, serial, V - shaped, and circular; Step 12: Set the formation scale: Set the number of underwater robots in the formation. The formation scale of the robots needs to be set according to the actual task nature and environmental constraints; Step 13: Set the formation spacing: Used to set the relative position relationship between adjacent robots during formation, including linear distance and angle, and set it dynamically according to needs; Step 14: Set the formation operation rhythm: Used to set the synchronization time of the coordinated action pace between robots. In the formation method based on the leader - follower method, the leader must continuously plan sub - target points for each follower, and then the leader and the followers run towards their respective target points at the same time, repeating until the final target point is reached, then this formation operation ends. The formation operation rhythm is the time interval for the leader to plan sub - target points for the followers.

3. A multi-machine collaborative control method for reactor pressure vessel inspection according to claim 1, characterized in that, The said Step 3 includes: Step 31: For formation generation / reconfiguration, adopt the leader - follower formation model. The leader automatically runs to the target point according to the task assignment, and at the same time, it will assign sub - target points to the followers according to the four - element ordered array and the control matrix. Then the followers run from the current actual position to the sub - target points, repeating until the final formation shape is formed. Adopt the artificial potential field control method. Define the gravitational function as a function of the relative distance and azimuth between the actual position point of the underwater robot and the new sub - target point. The gravitational function and the potential function are shown as follows: In the formula, ||d jj' || represents the relative distance between the actual position of the underwater robot and the actual ideal position planned by the leading underwater robot. φ jj' is the azimuth difference between the actual heading and the ideal heading of the underwater robot, φ jj' = |α i - α j' |; ρ PA is the positive gain to reach the sub-goal point; d is the motion vector of each underwater robot, α is the heading of each underwater robot. When ||d jj' || and φ jj' are 0, the follower will reach the assigned sub-goal point. Step 32: During the formation maintenance phase, each underwater robot must continuously track the positions of their respective sub-goal points. The positions of the sub-goal points are calculated based on the leader-follower formation model. Maintaining the formation shape means determining the linear velocity and angular velocity of the followers, thereby eliminating the error values of the distance and angle between the current position and the desired position of the followers: where, L ij and ψ ij are the actual distance and angle between the leader and the follower, and L ij d and ψ ij d are the desired distance and angle. When the sum of the distance deviations and the sum of the angle deviations of all underwater robots are both 0, the system will maintain the formation shape and operate; Step 33: A distributed obstacle avoidance / collision avoidance detection algorithm is adopted. Each robot is the main body of the obstacle avoidance / collision avoidance detection algorithm and runs the obstacle avoidance / collision avoidance detection algorithm with the same architecture; Step 34: Unplanned cooperation refers to the ability of multiple underwater robots to maintain normal functions when one of the underwater robots fails during the formation operation. In the leader-follower formation model, it includes two cases: the leader fails and the follower fails.

4. The multi-machine collaborative control method for reactor pressure vessel inspection according to claim 3, characterized in that The said Step 34 includes: Step 341: The leader fails When the leader fails, a new leader is re-elected. During the operation of multiple underwater robots, each underwater robot is assigned an ID. The leader ID is set to 1, and the IDs of other underwater robots are arranged in ascending order according to their distance from the leader. When the leader fails, the robot with the ID closest to the leader ID will be elected as the new leader, and other robots will dynamically adjust the formation according to the new leader; Step 342: The follower fails When a follower fails during the formation operation of multiple underwater robots, other follower robots continue to operate according to the sub-goal positions assigned by the leader, and the position of the problematic follower will remain vacant.

5. The multi-machine collaborative control method for the inspection of a reactor pressure vessel according to claim 1, characterized in that The said Step 4 includes, Step 41: Path length ratio R path_lengh It is defined as the ratio of the average distance traveled by all underwater robots to the straight-line distance between the target point and the initial point: where d i is the distance traveled by the i-th underwater robot during the entire formation operation, and d sg is the straight-line distance between the starting point and the target point. Step 42: The formation maintenance rate defines the proportion of the time when the underwater robot is at the desired position during the entire movement process: where m i is the actual number of times that the i-th underwater robot is at the sub-goal point during the entire formation operation, and m is the planned number of times that each underwater robot is at the sub-goal point during the entire formation operation.

6. The multi-machine collaborative control method for reactor pressure vessel inspection according to claim 5, characterized in that: d in step 41 described above sg The value range is from 1 to ∞.

7. The multi-machine collaborative control method for reactor pressure vessel inspection according to claim 5, wherein: The m in step 42 described above i takes values in [0, 1].

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