Mathematical modeling method for multi-target point inspection path planning in nuclear radiation environment

Abstract

The nuclear radiation environment multi-target point inspection path planning mathematical modeling method, the grid map of the nuclear radiation environment is prior information, each grid in the grid map contains radiation field information and obstacle information;The method is as follows: considering the path length and the cumulative radiation dose and the turning energy consumption, the inspection path evaluation model and the pair path cost calculation model are established respectively.The present application is aimed at the mobile robot MTIPP problem in indoor nuclear environment, considering the path length and the cumulative radiation dose and the turning energy consumption, a double-layer mathematical model is established, the upper model (inspection path evaluation model) is used for quantitative evaluation of the pros and cons of the inspection target point traversal sequence, the lower model (pair path cost calculation model) puts forward the calculation method of the three dimension value of the pair path;Thus, the necessary prerequisite foundation is provided for the subsequent multi-target point inspection path planning.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of path planning, in particular to a mathematical modeling method for multi-target point inspection path planning in a nuclear radiation environment. BACKGROUND

[0002] Multi-target point inspection tasks often need to be performed in the indoor environment of a nuclear power plant. Under the premise that the indoor map of the nuclear power plant (which contains radiation field and obstacle information) is known, planning a suitable inspection path is the basis for the safe and smooth execution of multi-target point inspection tasks. The above-mentioned multi-target point inspection tasks are usually performed by manual inspection. The path planning for manual inspection mostly only considers the cumulative radiation dose, and the path planning difficulty is relatively low.

[0003] It is rare to see mobile robots performing multi-target point inspection tasks. Multi-target point inspection path planning needs to consider the turning energy consumption of the mobile robot (as few turns as possible and as small a turning angle as possible), the cumulative radiation dose (as low as possible under the premise that it does not exceed the bearing limit of the mobile robot), and the path length (the shorter the better). The difficulty is very great. The primary task of multi-target point inspection path planning is to accurately describe the MTIPP (multi-target point inspection path planning) problem and perform mathematical modeling. SUMMARY

[0004] The purpose of the present application is to overcome the shortcomings of the prior art and provide a mathematical modeling method for multi-target point inspection path planning in a nuclear radiation environment, which accurately describes the MTIPP (multi-target point inspection path planning) problem and performs mathematical modeling, providing a necessary prerequisite for subsequent multi-target point inspection path planning.

[0005] The technical solution of the present application is: a mathematical modeling method for multi-target point inspection path planning in a nuclear radiation environment, the grid map of the nuclear radiation environment is prior information, and each grid in the grid map contains radiation field information and obstacle information; the method is as follows: considering the path length, cumulative radiation dose, and turning energy consumption, a path quality evaluation model and a pair-wise path cost calculation model are established respectively.

[0006] The further technical solution of the present application is: the process of establishing the path quality evaluation model is as follows: the multi-target point inspection task needs to establish a Hamiltonian circuit for each inspection target point to pass through only once and finally return to the starting point, considering the three dimensions of path length, cumulative radiation dose, and turning energy consumption, a path quality evaluation model, or an inspection target point traversal order quality evaluation model, is established, see formula 1.

[0007] Formula 1:

[0008] Wherein, λ is the total value of all pairs of path in the inspection path; T is the set of inspection target points, T={T1, T2, T3, …, Tn}, and the subscript n is the total number of inspection target points; n}; is the path length cost matrix between the inspection target points T i and T j , is the cumulative radiation dose cost matrix between the inspection target points T i and T j , is the turning energy consumption cost matrix between the inspection target points T i and T j ; τ i,j is a decision variable, if the value is 1, it indicates that the path between the inspection target points T i and T j is selected, if the value is 0, it indicates that the path between the inspection target points T i and T j is not selected; ω1 is the weight coefficient of the path length, ω2 is the weight coefficient of the cumulative radiation dose, and ω3 is the weight coefficient of the turning energy consumption.

[0009] The further technical solution of the present application is: the process of establishing the pair path cost calculation model is as follows: T i and T j are any two inspection target points, and the grid set successively passed by the path with the minimum total value of three dimensions between T i and T j is P, P={p1, p, p3…p m}, then the grid where T i is located is p1, and the grid where T j is located is p m ; considering the path length, the cumulative radiation dose and the turning energy consumption, the pair path cost calculation model is established, as shown in formula 2.

[0010] Formula 2:

[0011] Wherein, M(P) is the total value of three dimensions of the pair path T i and T j , L(P) is the path length value of T i and T j , R(P) is the cumulative radiation dose value of T i and T j , and E(P) is the turning energy consumption value of T i and T jturning energy consumption equivalent value; ε1 is a weight coefficient of the turning angle variable, ε2 is a weight coefficient of the turning frequency, l(p a-1 , p a ) is a line segment connecting the center point of the grid p α-1 and the center point of the grid p α , l(p a , p a+1 ) is a line segment connecting the center point of the grid p α and the center point of the grid p α+1 , ψ[l(p a-1 , p a ), l(p a , p a+1 )] is a turning angle variable of the line segment l(p a-1 , p a ) and the line segment l(p a , p a+1 ), N turn is the turning frequency; (x α , y α ) is the coordinate of the grid p α , (x α+1 , y α+1 ) is the coordinate of the grid p α+1 , (x α-1 , y α-1 ) is the coordinate of the grid p α-1 ; R(p α , p α+1 ) is the cumulative radiation dose received by the mobile robot when moving from the grid p a to the grid p a+1 , is the average radiation dose rate of the grid p α , is the average radiation dose rate of the grid p α+1 , l is the distance from the grid p α to the grid p α+1 , if the grid p α is adjacent to the grid p α+1 , then l is equal to 1 times the grid edge length, if the grid p α is in contact with the grid p α+1 , then l is equal to times the grid edge length, and v is the speed of moving from the grid p α to the grid p α+1 .

[0012] A further technical solution of the present application is that the grid in the grid map is a square; the radiation field information is the average radiation dose rate recorded in each grid in a real number coding manner, and the obstacle information is identified as "not passable" and "allowable to pass" in each grid in a binary coding manner of "1" and "0".

[0013] The present application has the following advantages compared with the prior art:

[0014] 1. It is aimed at the mobile robot MTIPP (multi-target point inspection path planning) problem in indoor nuclear environment, and a double-layer mathematical model (inspection path advantage and disadvantage evaluation model and pair path cost calculation model) is established by comprehensively considering path length, cumulative radiation dose and turning energy consumption. The upper model (inspection path advantage and disadvantage evaluation model) is used for quantitatively evaluating the advantages and disadvantages of the inspection target point traversal sequence, and the lower model (pair path cost calculation model) proposes a calculation method of three-dimensional value of the pair path; thus providing necessary prerequisite basis for subsequent multi-target point inspection path planning.

[0015] 2. The grid map as the basis for establishing the mathematical model is a multi-information double-layer hybrid map, in which the passability information (i.e. environmental obstacle information) and environmental radiation field information are fused, thus providing a reliable environmental map which can index multi-element information value for the mathematical modeling of the MTIPP (multi-target point inspection path planning) problem and subsequent multi-target point inspection path planning.

[0016] The present application is further described below in combination with the drawings and embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 A schematic diagram for the mobile robot MTIPP problem in indoor nuclear environment is shown.

[0018] Figure 2 A schematic diagram for the eight-direction search strategy adopted by the mobile robot is shown. DETAILED DESCRIPTION

[0019] Embodiment 1:

[0020] The nuclear radiation environment multi-target point inspection path planning mathematical modeling method, the map of the indoor nuclear environment is prior information. The map is in the form of a grid map, and the grid in the grid map is a square; each grid in the grid map contains radiation field information and obstacle information, the radiation field information is the average radiation dose rate recorded in each grid in the form of real number coding, and the obstacle information is identified by binary coding "1" and "0" in each grid to represent "not passable" and "allowed to pass", respectively.

[0021] In combination with Figures 1-2 The mobile robot MTIPP problem in the nuclear radiation environment is described. Figure 1The grid map of the indoor kernel environment is displayed in the middle. In order to more intuitively display the radiation field information, different colors are used to distinguish the average radiation dose rate of different grids (the average radiation dose rate gradually increases according to the change rule of light blue-beige-bright yellow-pink-deep red), and in order to more intuitively display the obstacle information, black is used to represent the "non-passable" grid, and other grids except black are "passable". Figure 2 In the middle, 11 inspection target points (T1, T2, T3…T 11 ) are labeled. The 11 inspection target points are connected in a specific traversal order to form a Hamiltonian circuit. Figure 2 In the middle, the mobile robot adopts an eight-direction search strategy for path search, that is, when the mobile robot moves from the current grid point to the adjacent grid, it can only move along the straight line path of "current grid center point-adjacent grid center point".

[0022] The method is as follows:

[0023] Considering the path length, cumulative radiation dose, and turning energy consumption, an inspection path evaluation model and a pair-wise path cost calculation model are respectively established.

[0024] The process of establishing the inspection path evaluation model is as follows: a Hamiltonian circuit is needed for a multi-target inspection task, which passes through each inspection target point only once (the start and end inspection target points are the same point, which is equivalent to passing through twice, so it is the only exception), and finally returns to the starting point. Considering the path length, cumulative radiation dose, and turning energy consumption, an inspection path evaluation model (this model takes the minimum value as the target) or an inspection target point traversal order evaluation model is established, refer to formula 1.

[0025] Formula 1:

[0026] Where λ is the total value of the three dimensions of all pairs of paths in the inspection path (the path between the two inspection target points connected in front and back is called a pair of paths); T is the set of inspection target points, T = {T1, T2, T3, …, T n}, the subscript n is the total number of inspection target points; is the path length cost matrix between the inspection target points T i and T j , is the cumulative radiation dose cost matrix between the inspection target points T i and T j , is the turning energy consumption cost matrix between the inspection target points T i and T j ; τ i,j is the decision variable, if the value is 1, it means that the inspection target point Ti to the inspection target point T j , if the value is 0, indicating that the inspection target point T i to the inspection target point T j ; ω1 is the weight coefficient of the path length importance, ω2 is the weight coefficient of the cumulative radiation dose importance, and ω3 is the weight coefficient of the turning energy importance.

[0027] The process of establishing the pair path cost calculation model is as follows: T i and T j are any two inspection target points, and it is assumed that P is the grid set successively passed by the path with the minimum total value of three dimensions from T i to T j , P = {p1, p, p3…p m}, then the grid where T i is located is p1, and the grid where T j is located is p m ; considering the path length, the cumulative radiation dose, and the turning energy consumption, a pair path cost calculation model (the model aims to find the minimum value) is established, as shown in formula 2.

[0028] Formula 2:

[0029] wherein M(P) is the total value of three dimensions of the pair path (the path between two inspection target points is called a pair path) from T i to T j , L(P) is the path length value of T i to T j , R(P) is the cumulative radiation dose value of T i to T j , E(P) is the turning energy consumption value of T i to T j ; ε1 is the weight coefficient of the turning angle variable, ε2 is the weight coefficient of the turning frequency, l(p a-1 , p a ) is the center point connecting line of the grid p α-1 and the grid p α , l(p a , p a+1 ) is the center point connecting line of the grid p α and the grid p α+1 , and ψ[l(p a-1 , p a ), l(p a , p a+1 )] is the line segment l(p a-1 , p a ) and the line segment l(p a , pa+1 ) the steering angle variable of the mobile robot, N turn is the number of turns; (x α , y α ) is the (map coordinate system) coordinate of the grid p α ; (x α+1 , y α+1 ) is the (map coordinate system) coordinate of the grid p α+1 ; (x α-1 , y α-1 ) is the (map coordinate system) coordinate of the grid p α-1 ; R(p α , p α+1 ) is the cumulative radiation dose received by the mobile robot from the grid p a to the grid p a+1 , is the average radiation dose rate of the grid p α , is the average radiation dose rate of the grid p α+1 , l is the distance from the grid p α to the grid p α+1 , if the grid p α is adjacent to the grid p α+1 at the side, then l is equal to 1 times the grid side length, if the grid p α is in contact with the grid p α+1 at the end point, then l is equal to times the grid side length, v is the speed from the grid p α to the grid p α+1 (the initial speed of the mobile robot at the position of the grid p α and the final speed of the mobile robot at the position of the grid p α+1 are consistent, and the speed of the mobile robot during the movement also remains unchanged). The average radiation dose rate of a certain grid refers to the average radiation dose rate in the space formed by the ground 1 m above the grid.

Claims

1. A mathematical modeling method for multi-target inspection path planning in a nuclear radiation environment, characterized by: The grid map of the nuclear radiation environment is prior information, and each grid in the grid map contains radiation field information and obstacle information; the method is as follows: considering path length, accumulated radiation dose and turning energy consumption, a patrol path merit evaluation model and a pair path cost calculation model are respectively established; The process of establishing the patrol path merit evaluation model is as follows: a Hamilton circuit that each patrol target point passes through only once and finally returns to the starting point is needed for a multi-target point patrol task, considering three dimensions of path length, accumulated radiation dose and turning energy consumption, a patrol path merit evaluation model, or a patrol target point traversal sequence merit evaluation model, is established, refer to formula 1; Formula 1: wherein λ is the total value of all pairs of paths in the inspection path; T is a set of inspection target points, T = {T1, T2, T3, …, Tn}, and subscript n is the total number of inspection target points; n}; is a path length cost matrix between inspection target points T i and T j , is a cumulative radiation dose cost matrix between inspection target points T i and T j , is a turning energy consumption cost matrix between inspection target points T i and T j ; τ i,j is a decision variable, if the value is 1, it indicates that the path between inspection target point T i and inspection target point T j is selected, if the value is 0, it indicates that the path between inspection target point T i and inspection target point T j is not selected; ω1 is a weight coefficient of the path length, ω2 is a weight coefficient of the cumulative radiation dose, and ω3 is a weight coefficient of the turning energy consumption. The process of establishing the pair path cost calculation model is as follows: T i and T j are any two inspection target points, T i to T j The grid set successively passed through by the path with the minimum total value of three dimensions is P, P={p1,p,p3…p m}, T i is located in the grid p1, and T j is located in the grid p m ; considering the path length, the cumulative radiation dose and the turning energy consumption, the pair path cost calculation model is established, as shown in formula 2; Equation 2: Wherein, M(P) is the paired path T i to T j The total value of three dimensions, L(P) is the path length value of T i to T j , R(P) is the cumulative radiation dose value of T i to T j , E(P) is the turning energy consumption value of T i to T j ; ε1 is the weight coefficient of the steering angle variable, ε2 is the weight coefficient of the steering frequency, l(p a-1 ,p a ) is the center line of the grid p α-1 and the grid p α , l(p a ,p a+1 ) is the center line of the grid p α and the grid p α+1 , ψ[l(p a-1 ,p a ), l(p a ,p a+1 )] is the steering angle variable of the line segment l(p a-1 ,p a ) and the line segment l(p a ,p a+1 ), N turn is the steering frequency; (x α ,y α ) is the coordinate of the grid p α , (x α+1 ,y α+1 ) is the coordinate of the grid p α+1 , (x α-1 ,y α-1 ) is the coordinate of the grid p α-1 ; R(p α ,p α+1 ) is the cumulative radiation dose received by the mobile robot from the grid p a to the grid p a+1 , is the average radiation dose rate of the grid p α , is the average radiation dose rate of the grid p α+1 , l is the distance from the grid p α to p α+1 , if the grid p α is adjacent to p α+1 edge, then l is equal to 1 times the grid edge length, if the grid p α is in contact with p α+1 end point, then l is equal to times the grid edge length, v is the distance from the grid p α Move to grid p α+1 of the speed.

2. The method of claim 1, wherein the method further comprises: determining a plurality of target points in the nuclear radiation environment; and determining a plurality of paths for the inspection robot to inspect the plurality of target points. The grid in the grid map is a square; the radiation field information is the average radiation dose rate recorded in each grid in a real number coding mode, and the obstacle information is identified as "not passable" and "allowable to pass" in each grid in binary coding "1" and "0" respectively.

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