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

Abstract

According to the mathematical modeling method for multi-target-point inspection path planning in the nuclear radiation environment, a grid map of the nuclear radiation environment is prior information, and each grid in the grid map comprises radiation field information and obstacle information; the method comprises the following steps: respectively establishing an inspection path quality evaluation model and a paired path quality evaluation model by considering path length, accumulated radiation dose and turning energy consumption; aiming at the MTIPP problem of the mobile robot in the indoor nuclear environment, the path length, the accumulated radiation dose and the turning energy consumption are comprehensively considered, a double-layer mathematical model is established, an upper layer model (a routing inspection path quality evaluation model) is used for quantitatively evaluating the quality of a routing inspection target point traversal sequence, and a lower layer model (a routing inspection path quality evaluation model) is used for quantitatively evaluating the quality of the routing inspection target point traversal sequence; a lower-layer model (pairwise path cost calculation model) provides a calculation mode of three-dimensional cost values of pairwise paths; therefore, a necessary prerequisite basis is provided for subsequent multi-target-point inspection path planning.

Description

Technical Field

[0001] The invention 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 Art

[0002] In the indoor environment of nuclear power plants, it is often necessary to perform multi-target inspection tasks. Under the premise that the indoor map of the nuclear power plant (the map contains radiation field and obstacle information) is known, planning a suitable inspection path is the basis for the safe and smooth execution of the multi-target inspection tasks. The above multi-target inspection tasks usually adopt the method of manual inspection. The path planning of manual inspection mostly only considers the cumulative radiation dose, and the path planning difficulty is relatively low.

[0003] It is rare to use mobile robots to perform multi-target inspection tasks. Multi-target inspection path planning needs to consider the turning energy consumption of the mobile robot (the number of turns should be as few as possible and the turning angle should be as small as possible), the cumulative radiation dose (as low as possible without exceeding the tolerance limit of the mobile robot) and the path length (the shorter the better), which is very difficult. The first task of multi-target inspection path planning is to accurately describe the MTIPP (multi-target inspection path planning) problem and perform mathematical modeling. Summary of the invention

[0004] The purpose of the present invention 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 realizes the accurate description of the MTIPP (multi-target point inspection path planning) problem and performs mathematical modeling, thus providing the necessary prerequisite for subsequent multi-target point inspection path planning.

[0005] The technical solution of the present invention is: a mathematical modeling method for planning a multi-target inspection path in a nuclear radiation environment, wherein a 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, an inspection path quality evaluation model and a paired path quality evaluation model are established respectively.

[0006] A further technical solution of the present invention is: the process of establishing the inspection path quality evaluation model is as follows: the multi-target point inspection task needs to establish a Hamiltonian circuit that passes each inspection target point only once and finally returns to the starting point, considering the path length, cumulative radiation dose and turning energy consumption, a total of three dimensions, to establish the inspection path quality evaluation model, or the inspection target point traversal sequence quality evaluation model, see formula 1;

[0007] Formula 1:

[0008] Among them, λ is the total cost of the three dimensions of all paired paths in the inspection path; 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 inspection target point T i and T j The path length cost matrix between is the inspection target point T i and T j The cumulative radiation dose cost matrix between is the inspection target point T i and T j The turning energy cost matrix between i,j is a decision variable. If the value is 1, it means that the inspection target point T is selected. i To the inspection target point T j If the value is 0, it means that the inspection target point T is not selected. i To the inspection target point T j The path between; ω1 is the weight coefficient of path length, ω2 is the weight coefficient of cumulative radiation dose, and ω3 is the weight coefficient of turning energy consumption.

[0009] A further technical solution of the present invention is: the process of establishing a paired path cost calculation model is as follows: i and T j are any two inspection target points, let T i to T j The set of grids that the path with the smallest total cost value in the three dimensions passes through in sequence is P, P = {p1, p, p3…p m}, then T i The grid where it is located is p1, then T j The grid is p m ; Considering the three dimensions of path length, cumulative radiation dose and turning energy consumption, a pairwise path cost calculation model is established, as shown in Formula 2;

[0010] Formula 2:

[0011] Where M(P) is the pairwise path T i to T j The total cost of the three dimensions, L(P) is T i to T j The path length cost value, R(P) is T i to T j The cumulative radiation dose cost of T i to T jThe turning energy consumption cost value; ε1 is the weight coefficient of the steering angle variable, ε2 is the weight coefficient of the number of turns, l(p a-1 ,p a ) is the grid p α-1 With grid p α The center point of the line, l(p a ,p a+1 ) is the grid p α With grid p α+1 The center point of the line, ψ[l(p a-1 ,p a ),l(p a ,p a+1 )] is the line segment l(p a-1 ,p a ) and line segment l(p a ,p a+1 ) steering angle variable, N turn is the number of turns; (x α ,y α ) is the grid p α The coordinates of (x α+1 ,y α+1 ) is the grid p α+1 The coordinates of (x α-1 ,y α-1 ) is the grid p α-1 Coordinates of R(p α ,p α+1 ) is the mobile robot from the grid p a Travel to grid p a+1 The cumulative radiation dose received, is the grid p α The average radiation dose rate, is the grid p α+1 The average radiation dose rate of the grid p α to p α+1 If the grid p α With p α+1 If the grid edges are adjacent, then l is equal to 1 times the grid edge length. α With p α+1 End point contact is equal to times the grid side length, v is the length of the grid p α Move to grid p α+1 speed.

[0012] A further technical solution of the present invention is that the grids in the grid map are square; the radiation field information is the average radiation dose rate recorded in each grid in real number coding, and the obstacle information is in each grid in binary coding "1" and "0" to indicate "no passage" and "allowed passage" respectively.

[0013] Compared with the prior art, the present invention has the following advantages:

[0014] 1. Aiming at the MTIPP (multi-target point inspection path planning) problem of mobile robots in indoor nuclear environments, it comprehensively considers the path length, cumulative radiation dose and turning energy consumption, and establishes a two-layer mathematical model (inspection path quality evaluation model and paired path quality evaluation model). The upper model (inspection path quality evaluation model) is used to quantitatively evaluate the quality of the inspection target point traversal sequence, and the lower model (paired path cost calculation model) proposes a calculation method for the three-dimensional cost values ​​of paired paths; thus, it provides the necessary prerequisite for the subsequent multi-target point inspection path planning.

[0015] 2. The raster map used as the basis for establishing the mathematical model is a multi-information two-layer hybrid map, which integrates the passability information (i.e., environmental obstacle information) and environmental radiation field information, providing a reliable environmental map that can perform multi-information value indexing for the mathematical modeling of the MTIPP (multi-target point inspection path planning) problem and the subsequent multi-target point inspection path planning.

[0016] The present invention is further described below in conjunction with the figures and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 Schematic diagram of the description of the MTIPP problem for mobile robots in indoor nuclear environments;

[0018] Figure 2 Schematic diagram of the eight-direction search strategy adopted by the mobile robot. DETAILED DESCRIPTION

[0019] Embodiment 1:

[0020] A mathematical modeling method for nuclear radiation environment multi-target inspection path planning, wherein the map of the indoor nuclear environment is prior information. The map is in the form of a grid map, and the grids in the grid map are squares; each grid in the grid map contains radiation field information and obstacle information, and 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 in each grid in binary coding "1" and "0" to indicate "not passable" and "allowed to pass" respectively.

[0021] Combination Figure 1-2 Describe the MTIPP problem of a mobile robot in a nuclear radiation environment. Figure 1The grid map of the indoor nuclear environment is displayed in the figure. In order to display the radiation field information more intuitively, different colors are used to distinguish the average radiation dose rates of different grids (the average radiation dose rate gradually increases according to the change rule of lake blue-beige-bright yellow-pink-dark red). In order to display the obstacle information more intuitively, black is used to indicate that the grid is "inaccessible", and all other grids except black are "allowed to pass". Figure 2 The CPC marked 11 inspection target points (T1, T2, T3…T 11 ), the 11 inspection target points are connected in sequence according to a specific traversal order to form a Hamiltonian circuit. Figure 2 It is shown that the mobile robot uses 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] Here’s how:

[0023] Considering the path length, cumulative radiation dose and turning energy consumption, an inspection path quality evaluation model and a paired path quality evaluation model are established respectively.

[0024] The process of establishing the inspection path quality evaluation model is as follows: the multi-target inspection task needs to establish a Hamiltonian circuit that passes each inspection target point only once (the starting point and the end point inspection target point are the same point, which is equivalent to passing twice, so it is the only exception) and finally returns to the starting point. Considering the three dimensions of path length, cumulative radiation dose and turning energy consumption, the inspection path quality evaluation model is established (the model aims to find the minimum value), or the inspection target point traversal order quality evaluation model, see formula 1;

[0025] Formula 1:

[0026] Where λ is the total cost of the three dimensions of all paired paths in the inspection path (the path between two consecutive inspection target points is called a paired path); 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 inspection target point T i and T j The path length cost matrix between is the inspection target point T i and T j The cumulative radiation dose cost matrix between is the inspection target point T i and T j The turning energy cost matrix between i,j is a decision variable. If the value is 1, it means that the inspection target point T is selected.i To the inspection target point T j If the value is 0, it means that the inspection target point T is not selected. i To the inspection target point T j The path between them; ω1 is the weight coefficient of the importance of path length, ω2 is the weight coefficient of the importance of cumulative radiation dose, and ω3 is the weight coefficient of the importance of turning energy.

[0027] The process of establishing the pairwise path cost calculation model is as follows: i and T j are any two inspection target points, let T i to T j The set of grids that the path with the smallest total cost value in the three dimensions passes through in sequence is P, P = {p1, p, p3…p m}, then T i The grid where it is located is p1, then T j The grid is p m ; Considering the three dimensions of path length, cumulative radiation dose and turning energy consumption, a pairwise path cost calculation model is established (the model aims to find the minimum value), as shown in Formula 2;

[0028] Formula 2:

[0029] Among them, M(P) is a paired path (the path between two inspection target points is called a paired path) T i to T j The total cost of the three dimensions, L(P) is T i to T j The path length cost value, R(P) is T i to T j The cumulative radiation dose cost of T i to T j The turning energy consumption cost value; ε1 is the weight coefficient of the steering angle variable, ε2 is the weight coefficient of the number of turns, l(p a-1 ,p a ) is the grid p α-1 With grid p α The center point of the line, l(p a ,p a+1 ) is the grid p α With grid p α+1 The center point of the line, ψ[l(p a-1 ,p a ),l(p a ,p a+1 )] is the line segment l(p α-1 ,p a ) and line segment l(p a ,pa+1 ) steering angle variable, N turn is the number of turns; (x α ,y α ) is the grid p α The (map coordinate system) coordinates, (x α+1 ,y α+1 ) is the grid p α+1 The (map coordinate system) coordinates, (x α-1 ,y α-1 ) is the grid p α-1 (Map coordinate system) coordinates; R(p α ,p α+1 ) is the mobile robot from the grid p a Travel to grid p a+1 The cumulative radiation dose received, is the grid p α The average radiation dose rate, is the grid p α+1 The average radiation dose rate of the grid p α to p α+1 If the grid p α With p α+1 If the grid edges are adjacent, then l is equal to 1 times the grid edge length. α With p α+1 End point contact is equal to times the grid side length, v is the length of the grid p α Move to grid p α+1 The speed of the mobile robot in the grid p α The initial velocity and grid p at the location α+1 The final velocity of the position is consistent, and the speed of the mobile robot during the movement process is also constant). The average radiation dose rate of a grid refers to: the average radiation dose rate in the three-dimensional space formed by the height of 1m above the ground where the grid is located.

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 the path length, cumulative radiation dose and turning energy consumption, an inspection path quality evaluation model and a paired path quality evaluation model are established respectively.

2. The method for mathematical modeling of multi-target inspection path planning in a nuclear radiation environment as claimed in claim 1 is characterized by: establishing The process of the inspection path quality evaluation model is as follows: the multi-target point inspection task requires the establishment of a Hamiltonian circuit that passes each inspection target point only once and finally returns to the starting point. Considering the three dimensions of path length, cumulative radiation dose, and turning energy consumption, the inspection path quality evaluation model, or the inspection target point traversal sequence quality evaluation model, is established, see formula 1; Formula 1: Where λ is the total cost of the three dimensions of all paired paths in the inspection path; 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 inspection target point T i and T j The path length cost matrix between is the inspection target point T i and T j The cumulative radiation dose cost matrix between is the inspection target point T i and T j The turning energy cost matrix between i,j is a decision variable. If the value is 1, it means that the inspection target point T is selected. i To the inspection target point T j If the value is 0, it means that the inspection target point T is not selected. i To the inspection target point T j The path between; ω1 is the weight coefficient of path length, ω2 is the weight coefficient of cumulative radiation dose, and ω3 is the weight coefficient of turning energy consumption.

3. The method for mathematical modeling of multi-target inspection path planning in a nuclear radiation environment as claimed in claim 2 is characterized by: establishing The process of pairwise path cost calculation model is as follows: T i and T j are any two inspection target points, let T i to T j The set of grids that the path with the smallest total cost value in the three dimensions passes through in sequence is P, P = {p1, p, p3…p m }, then T i The grid where it is located is p1, then T j The grid is p m ; Considering the three dimensions of path length, cumulative radiation dose and turning energy consumption, a pairwise path cost calculation model is established, as shown in Formula 2; Formula 2: Where M(P) is the pairwise path T i to T j The total cost of the three dimensions, L(P) is T i to T j The path length cost value, R(P) is T i to T j The cumulative radiation dose cost of T i to T j The turning energy consumption cost value; ε1 is the weight coefficient of the steering angle variable, ε2 is the weight coefficient of the number of turns, l(p a-1 ,p a ) is the grid p α-1 With grid p α The center point of the line, l(p a ,p a+1 ) is the grid p α With grid p α+1 The center point of the line, ψ[l(p a-1 ,p a ),l(p a ,p a+1 )] is the line segment l(p a-1 ,p a ) and line segment l(p a ,p a+1 ) steering angle variable, N turn is the number of turns; (x α ,y α ) is the grid p α The coordinates of (x α+1 ,y α+1 ) is the grid p α+1 The coordinates of (x α-1 ,y α-1 ) is the grid p α-1 Coordinates of R(p α ,p α+1 ) is the mobile robot from the grid p a Travel to grid p a+1 The cumulative radiation dose received, is the grid p α The average radiation dose rate, is the grid p α+1 The average radiation dose rate of the grid p α to p α+1 If the grid p α With p α+1 If the grid edges are adjacent, then l is equal to 1 times the grid edge length. α With p α+1 End point contact is equal to times the grid side length, v is the length of the grid p α Move to grid p α+1 speed.

4. The method for mathematical modeling of multi-target inspection path planning in a nuclear radiation environment as claimed in claim 3 is characterized by: The grids in the grid map are square; the radiation field information is recorded in real-number coding as the average radiation dose rate in each grid, and the obstacle information is recorded in each grid in binary coding "1" and "0" to indicate "no passage" and "passage allowed" respectively.

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