Mobile robot path planning method, system, robot and storage medium

Abstract

The present invention discloses a mobile robot path planning method, system, robot and storage medium, and relates to the field of path planning technology. The mobile robot path planning method comprises: using a grid method to divide a map into 1×1 grids, using preset color blocks to represent traversable areas or obstacles; establishing a mathematical model; initializing whale optimization algorithm parameters; initializing the population using the Tent chaotic sequence strategy; performing a linear equidistant interpolation strategy on all whale individuals to add new position vectors; calculating fitness; selecting the whale individual with the smallest fitness as the current global optimal individual; updating the whale individual; when the current number of iterations t reaches the maximum number of iterations T, outputting the current global optimal individual; calculating and generating a cubic uniform B-spline curve to complete the path curve construction. The mobile robot path planning method proposed in the present invention has the characteristics of fast running speed, high solution quality, strong optimization ability, etc., and can better solve practical problems.

Description

Technical Field

[0001] The present invention relates to the technical field of path planning, and more specifically, to a mobile robot path planning method, system, robot and storage medium. Background Art

[0002] Mobile robots are widely used in logistics and transportation, equipment maintenance, emergency rescue, catering, and waste disposal, among other fields. Path planning is a key research topic for mobile robots, addressing both the "where to go" and "how to get there" questions. The quality of path planning significantly impacts the quality of mobile robot services.

[0003] The main content of mobile robot path planning is to find a path from the starting position to the target position that can avoid obstacles and collisions, while optimizing various performance indicators of this route, including distance, time, and energy consumption.

[0004] The Whale Optimization Algorithm (WOA) is a heuristic optimization algorithm. It is an innovative algorithm designed by Mirjalili S based on observations of humpback whales feeding in groups. Whale optimization algorithms have been used in existing technologies for path planning, but they suffer from shortcomings such as slow execution, poor solution quality, and insufficient optimization capabilities. Summary of the Invention

[0005] In order to overcome the defects of the above-mentioned prior art such as slow running speed, poor solution quality and insufficient optimization ability, the present invention provides a mobile robot path planning method, system, robot and storage medium.

[0006] In order to solve the above technical problems, the technical solutions of the present invention are as follows:

[0007] In a first aspect, a mobile robot path planning method comprises the following steps:

[0008] S1. Use the grid method to divide the map into 1×1 squares, and use preset color blocks to represent passable areas or obstacles;

[0009] S2. Establish a mathematical model as follows:

[0010] minE(r)=αV(r)+βL(r)

[0011]

[0012]

[0013]

[0014] stλ(r)>0

[0015]

[0016] Among them, n is the number of nodes that the path passes through; m is the number of turns; b is the number of obstacles; the path r consists of n nodes The composition is: k=1,2,…,n; r=1,2,…,N, where N represents the size of the whale population; E(r) represents the evaluation value of the path based on path safety and transportation distance; V(r) represents the path smoothness of path r; L(r) represents the length of path r; a and β are preset constants, representing the safety factor and distance weight coefficient of path r respectively; (x0, y0), (x n+1 ,y n+1 ) represent the starting point and end point coordinates of the path, (x k-1 ,y k-1 )、(x k ,y k )、(x k+1 ,y k+1 ) represent nodes respectively and The two-dimensional coordinates of Indicates adjacent nodes The Euclidean distance between k Represents the angle variable between two adjacent points; O={O1,O2,…,O b} represents the set of obstacles, O j =(x j ,y j ), j = 1, 2, ..., b; for Equation of a line between two points; Indicates obstacle O j To the straight line distance; sign represents the sign function; λ(r) represents whether a collision occurs on path r. λ(r) = -1 means that the distance between the two objects is negative and a collision has occurred. λ(r) = 0 means that the distance between the two objects is 0, which is also considered a collision. λ(r) = 1 means that the distance between the two objects is greater than 0 and no collision has occurred.

[0017] S3. Initialize the parameters of the whale optimization algorithm, specifically: determine the size of the whale population N, initialize the maximum number of iterations T, and the dimension D of the whale individual in the search space; set the iteration counter t, which represents the current number of iterations, and initialize t = 1;

[0018] S4, using the Tent chaotic sequence strategy to initialize the population;

[0019] S5. Execute the linear isometric interpolation strategy to add new position vectors for all whale individuals;

[0020] S6. Calculate the number of whales in the population after linear isometric interpolation. The fitness of the path r represented by is expressed as follows:

[0021] fitness=E(r);

[0022] S7. Select the whale individual with the smallest fitness as the current global optimal individual

[0023] S8. Updating the whale individual further includes:

[0024] S81. Generate a random number ρ uniformly distributed on [0,1] and define the partition coefficient A as follows:

[0025]

[0026] Where g1 is a random value uniformly distributed on [0, 2π], g2 is a random value uniformly distributed on [0, π]; t represents the current number of iterations;

[0027] S82. Update the t+1 generation of whale individuals according to the values ​​of ρ and A.

[0028] S9, the iteration counter is incremented by 1, t=t+1; determine whether the current number of iterations t reaches the maximum number of iterations T: if so, output the current global optimal individual and proceed to step S10; otherwise, return to step S5;

[0029] S10, perform linear isometric interpolation on the current global optimal individual to generate a new individual, and calculate the cubic uniform B-spline curve path based on the position vector of the new individual z (q), a piecewise fitting strategy is adopted to complete the path curve construction; where z = 0, 1, 2, …, 3D-1; the non-decreasing parameter q∈[0,1] represents the curve variable.

[0030] In a second aspect, a path planning system is provided, which applies the mobile robot path planning method proposed in the first aspect, and includes:

[0031] The map acquisition module is used to obtain and rasterize the map, using preset color blocks to represent passable areas or obstacles; it is also used to set the starting and ending points of the path;

[0032] A model building module is used to build a mathematical model with the minimum evaluation value generated based on path safety and transportation distance as the objective function, and to initialize the model parameters;

[0033] An optimization module is used to calculate and solve the mathematical model using the whale optimization algorithm, the Tent chaotic sequence strategy, and the linear equidistant interpolation strategy to generate the global optimal individual;

[0034] The path generation module is used to perform linear equidistant interpolation on the global optimal individual to generate a new individual, and generate a B-spline curve according to the position vector contained in the new individual; the B-spline curve is the path curve.

[0035] In the third aspect, a mobile robot includes a robot body, a control unit and a mobile unit, wherein the output end of the control unit is connected to the input end of the mobile unit, the control unit is equipped with a path planning system proposed in the second aspect, and the control unit controls the mobile unit to execute the path curve generated by the path planning system.

[0036] In a fourth aspect, a computer device includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, it implements a mobile robot path planning method proposed in the first aspect.

[0037] In a fifth aspect, a computer storage medium stores instructions, and when the instructions are executed on a computer, the computer executes a mobile robot path planning method as proposed in the first aspect.

[0038] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0039] The present invention provides a mobile robot path planning method, system, robot, and storage medium. The method proposes an improved whale optimization algorithm, an improved Tent chaotic sequence strategy for mapping the initialization population, and a linear equidistant interpolation strategy to enhance the algorithm's global and local search capabilities. The proposed mobile robot path planning method boasts fast execution, high-quality solutions, and strong optimization capabilities, effectively solving practical problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 Flowchart of the path planning method for a mobile robot;

[0041] Figure 2 This is the optimal path diagram generated in Example 2;

[0042] Figure 3 A schematic diagram comparing paths generated using the path planning method and the basic whale optimization algorithm in Example 2;

[0043] Figure 4 This is an architectural diagram of the path planning system in Example 3. DETAILED DESCRIPTION

[0044] The accompanying drawings are for illustrative purposes only and are not to be construed as limiting this patent;

[0045] In order to better illustrate this embodiment, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product size;

[0046] It is understandable to those skilled in the art that some well-known structures and descriptions thereof may be omitted in the drawings.

[0047] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0048] Example 1

[0049] This embodiment proposes a mobile robot path planning method, see Figure 1 , including the following steps:

[0050] S1. Use the grid method to divide the map into 1×1 squares, and use preset color blocks to represent passable areas or obstacles;

[0051] S2. Establish a mathematical model as follows:

[0052] minE(r)=αV(r)+βL(r)

[0053]

[0054]

[0055]

[0056] stλ(r)>0

[0057]

[0058] Among them, n is the number of nodes that the path passes through; m is the number of turns; b is the number of obstacles; the path r consists of n nodes The composition is: k=1,2,…,n; r=1,2,…,N, where N represents the size of the whale population; E(r) represents the evaluation value of the path based on path safety and transportation distance; V(r) represents the path smoothness of path r; L(r) represents the length of path r; a and β are preset constants, representing the safety factor and distance weight coefficient of path r respectively; (x0, y0), (x n+1 ,y n+1 ) represent the starting point and end point coordinates of the path, (x k-1 ,y k-1 )、(x k ,y k )、(x k+1,y k+1 ) represent nodes respectively and The two-dimensional coordinates of Indicates adjacent nodes The Euclidean distance between k Represents the angle variable between two adjacent points; O={O1,O2,…,O b} represents the set of obstacles, O j =(x j ,y j ), j = 1, 2, ..., b; for Equation of a line between two points; Indicates obstacle O j To the straight line distance; sign represents the sign function; λ(r) represents whether a collision occurs on path r. λ(r) = -1 indicates that the distance between the two objects is negative and a collision has occurred. λ(r) = 0 indicates that the distance between the two objects is 0 and a collision has occurred. λ(r) = 1 indicates that the distance between the two objects is greater than 0 and no collision has occurred.

[0059] S3. Initialize the parameters of the whale optimization algorithm, specifically: determine the size of the whale population N, initialize the maximum number of iterations T, and the dimension D of the whale individual in the search space; set the iteration counter t, which represents the current number of iterations, and initialize t = 1;

[0060] S4, using the Tent chaotic sequence strategy to initialize the population;

[0061] S5. Execute the linear isometric interpolation strategy to add new position vectors for all whale individuals;

[0062] S6. Calculate the number of whales in the population after linear isometric interpolation. The fitness of the path r represented by is expressed as follows:

[0063] fitness=E(r);

[0064] S7. Select the whale individual with the smallest fitness as the current global optimal individual

[0065] S8. Updating the whale individual further includes:

[0066] S81. Generate a random number ρ uniformly distributed on [0,1] and define the partition coefficient A as follows:

[0067]

[0068] Where g1 is a random value uniformly distributed on [0, 2π], g2 is a random value uniformly distributed on [0, π]; t represents the current number of iterations;

[0069] S82. Update the t+1 generation of whale individuals according to the values ​​of ρ and A.

[0070] S9, the iteration counter is incremented by 1, t=t+1; determine whether the current number of iterations t reaches the maximum number of iterations T: if so, output the current global optimal individual and proceed to step S10; otherwise, return to step S5;

[0071] S10, perform linear isometric interpolation on the current global optimal individual to generate a new individual, and calculate the cubic uniform B-spline curve path based on the position vector of the new individual z (q), a piecewise fitting strategy is adopted to complete the path curve construction; where z = 0, 1, 2, …, 3D-1; the non-decreasing parameter q∈[0,1] represents the curve variable.

[0072] The Whale Optimization Algorithm (WOA) is a heuristic optimization algorithm. It is an innovative thinking algorithm designed by Mirjalili S based on observing the feeding behavior of humpback whale groups. It has the characteristics of simple principles and parameter settings and strong function optimization capabilities. In this embodiment, each individual whale represents a path; the tent chaotic sequence strategy is used to initialize the population, which can enrich the population diversity.

[0073] In a preferred embodiment, in step S4, the population is initialized using the Tent chaotic sequence strategy, including:

[0074] S41. Randomly generate a whale individual in D-dimensional space

[0075] S42, calculating the position vectors of the remaining N-1 whale individuals;

[0076] S43. Map the whale's individual position vector to the solution space. The mapping process expression is as follows:

[0077]

[0078] Where ub v lb v They represent the upper and lower bounds of the solution space, v=1,2; ub1 and lb1 are the upper and lower bounds of the x-coordinate value, and ub2 and lb2 are the upper and lower bounds of the y-coordinate value.

[0079] Demonstration, ub v lb v is a real number.

[0080] In an optional embodiment, in step S42, the position vectors of the remaining N-1 individual whales are calculated using the following formula:

[0081]

[0082] Among them, if or Then reassign it according to the following formula:

[0083]

[0084] Where v = 1, 2, Represents the sth position vector of the whale individual before the update The vth dimension in They represent the x and y coordinate values ​​of the s-th position vector of the whale individual before the update; s = 1, 2, ..., D.

[0085] In a preferred embodiment, in step S5, a linear equidistant interpolation strategy is performed on all whales to add new position vectors, including:

[0086] For each individual whale Linearly interpolate 2D new position vectors to obtain the new individual after interpolation

[0087] Among them, the new position vector Calculate as follows:

[0088]

[0089] Where, s = 1, 2, ..., D.

[0090] In a preferred embodiment, in step S82, the t+1 generation whale individuals are updated according to the values ​​of ρ and A. Specifically:

[0091] If ρ<0.5 and |A|<1, update the individual whale as follows

[0092]

[0093] If ρ<0.5 and |A|≥1, update the individual whale as follows

[0094]

[0095] If ρ≥0.5, the golden sine strategy is used to update the whale individual

[0096] in, represents the tth generation of whale individuals, represents the t+1 generation of whale individuals, represents the current global optimal individual, Represents a whale individual randomly selected from N whales.

[0097] In an optional embodiment, in step S82, if ρ≥0.5, the golden sine strategy is used to update the whale individual. The update method is as follows:

[0098]

[0099] c1=aτ+b(1-τ)

[0100] c2=a(1-τ)+bτ

[0101] in, represents the tth generation of whale individuals, represents the t+1 generation of whale individuals, represents the current global optimal individual, Represents a whale randomly selected from N whales, c1 and c2 are the golden section numbers The obtained coefficients, a, u1, u2 and b are uniformly distributed random values ​​of (0,π) and (-π,0) respectively.

[0102] In a preferred embodiment, in step S10, a cubic uniform B-spline curve path is calculated based on the position vector of the new individual. z (q) A segmented fitting strategy is used to complete the path curve construction, including:

[0103] S101. Generate a cubic uniform B-spline curve path based on the position vector of the new individual z (q), which is a sequence Q of non-decreasing parameters q: 0≤q1≤q2≤...≤q 10 The cubic polynomial determined by ≤1 is expressed as follows:

[0104]

[0105] Where q∈[0,1], the preset values ​​q1,q2,...,q 10 is an increasing arithmetic progression on [0,1], and q1,q2,...,q 10 Substitute the value of path into z In (q), the obtained point set is connected to obtain a cubic uniform B-spline curve, z = 0, 1, 2, ..., 3D-1, The global optimal individual New individuals after linear isometric interpolation The z-th position vector of ;

[0106] S102, adopt the segmented fitting strategy to The four adjacent position vectors draw the zth B-spline curve, and a total of 3D curve segments are drawn. Then, the drawn curve segments are smoothly connected to form a smooth curve with continuous curvature, which is the final path Path. The expression of the final path Path is a piecewise function composed of the cubic B-spline curves fitted by the 3D segments, and the expression is as follows:

[0107]

[0108] Where x0, x1, …, x 3D+2 for The x-coordinate of .

[0109] Example 2

[0110] This embodiment applies a mobile robot path planning method proposed in Example 1, see Figure 1 ,include:

[0111] S1. Use the grid method to divide the 20×40 map into 1×1 squares. The preset white blocks represent the passable areas, and the preset black blocks represent obstacles.

[0112] S2. Establish mathematical model:

[0113] minE(r)=αV(r)+βL(r) (1)

[0114]

[0115]

[0116]

[0117] stλ(r)>0

[0118]

[0119] Among them, the number of nodes passed by the path is n = 14, the number of turns is m = 14, the number of obstacles is b = 40, the safety factor of the path r is a = 0.3, the distance weight coefficient is β = 0.67, and the path r consists of n nodes. composition, k=1,2,…,n,r=1,2,…,N,N is the size of the whale population; E(r) represents the evaluation value of the path based on path safety and transportation distance, V(r) (unit: radian) represents the path smoothness of path r, L(r) (unit: meter) represents the length of path r; (x k-1 ,y k-1 )、(xk ,y k )、(x k+1 ,y k+1 ) represent nodes respectively and The two-dimensional coordinates of the path are (1,1) and (19,39). Indicates adjacent nodes The Euclidean distance between k Represents the angle variable between two adjacent points; O={O1,O2,…,O b} represents the set of obstacles, O j =(x j ,y j ), j = 1, 2, ..., b; for Equation of a line between two points; Indicates O j To the straight line distance; sign represents the sign function, λ(r) represents whether a collision occurs along path r. When λ(r) = -1, it indicates that the distance between the two objects is negative and a collision has occurred. When λ(r) = 0, it indicates that the distance between the two objects is 0, which is also considered a collision. When λ(r) = 1, it indicates that the distance between the two objects is greater than 0 and no collision has occurred.

[0120] S3. Initialization of whale optimization algorithm parameters: set the whale population size N = 100, the maximum number of iterations T = 100, the dimension D = 4, and the current number of iterations t = 1.

[0121] S4. Initializing the population using the Tent chaotic sequence strategy, further including:

[0122] S41. Randomly generate a whale individual in D-dimensional space

[0123] S42. Calculate the position vectors of the remaining N-1 whale individuals according to formula (6):

[0124]

[0125] if or Then re-assign according to formula (7):

[0126]

[0127] Where v = 1, 2, Represents the sth position vector of the whale individual before the update The vth dimension in They represent the x and y coordinate values ​​corresponding to the s-th position vector of the whale individual before the update; s = 1, 2, ..., D.

[0128] S43. Map the whale's individual position vector to the solution space according to formula (8):

[0129]

[0130] In the formula, v=1,2,ub1=20,ub2=40,lb1=0,lb2=0.

[0131] S5. Execute linear equidistant interpolation strategy: for each individual whale Linearly interpolate 2D new position vectors, and the new individual after interpolation is

[0132] Among them, the new position vector Calculate according to formula (9):

[0133]

[0134] Where r=1,2...,N,s=1,2...,D, is the sth position vector of the current global optimal whale individual, and Respectively in The left and right position vectors for the two side insertions.

[0135] S6. Calculate the number of whales in the population after linear isometric interpolation. The fitness of the path r represented by is calculated according to formula (10), that is, the evaluation value of the path is used as the fitness of the individual whale in the population:

[0136] fitness=E(r) (10)

[0137] S7. Sort by the fitness of each whale and take the whale with the smallest fitness as the current global optimal individual

[0138] S8. Updating the whale individual further includes:

[0139] S81. Determine ρ and A: Generate a uniformly distributed random number ρ on [0,1] and calculate the partition coefficient A according to formula (11):

[0140]

[0141] Where g1 is a random value uniformly distributed on [0, 2π], g2 is a random value uniformly distributed on [0, π], and t is the current number of iterations.

[0142] S82, update all whale individuals in generation t+1 Specifically include:

[0143] If ρ<0.5 and |A|<1, update the individual whales according to formula (12)

[0144]

[0145] If ρ<0.5 and |A|≥1, update the individual whales according to formula (13)

[0146]

[0147] If ρ ≥ 0.5, the golden sine strategy is used to update the whale individuals according to formula (14)

[0148]

[0149] c1=aτ+b(1-τ) (15)

[0150] c2=a(1-τ)+bτ (16)

[0151] in, represents the tth generation of whale individuals, represents the t+1 generation of whale individuals, represents the current global optimal individual, Represents a whale randomly selected from N whales, c1 and c2 are the golden section numbers The obtained coefficients, a, u1, u2 and b are uniformly distributed random values ​​of (0,π) and (-π,0) respectively.

[0152] S9, the iteration counter is incremented by 1 to determine whether the current number of iterations t reaches the maximum number of iterations T. If so, the current global optimal individual is output. And execute step S10; otherwise, return to execute step S5.

[0153] S10, for the current global optimal individual Linear isometric interpolation to generate new individuals Calculate the cubic uniform B-spline curve path based on the position vector of the new individual z (q), adopting a piecewise fitting strategy to complete the path curve construction; where z = 0, 1, 2, ..., 3D-1; the non-decreasing parameter q∈[0,1] represents the curve variable; specifically:

[0154] S101. Generate a cubic uniform B-spline curve path based on the position vector of the new individual z(q), which is a sequence Q of non-decreasing parameters q: 0≤q1≤q2≤...≤q 10 The cubic polynomial determined by ≤1 is expressed as follows:

[0155]

[0156] Where q∈[0,1], the preset values ​​q1,q2,...,q 10 is an increasing arithmetic progression on [0,1], where q1=0.1,q2=0.2,...,q9=0.9,q 10 =1, and q1,q2,...,q 10 Substitute the value of path into z In (q), the obtained point set is connected to obtain a cubic uniform B-spline curve, z=0,1,2,…,3D-1, The global optimal individual New individuals after linear isometric interpolation The z-th position vector of ;

[0157] Where q∈[0,1], the preset values ​​q1,q2,...,q 10 is an increasing arithmetic progression on [0,1], and q1,q2,...,q 10 Substitute the value of path into z In (q), the obtained point set is connected to obtain a cubic uniform B-spline curve, z = 0, 1, 2, ..., 3D-1, The global optimal individual New individuals after linear isometric interpolation The z-th position vector of ;

[0158] S102, adopt the segmented fitting strategy to The four adjacent position vectors draw the zth B-spline curve, and a total of 3D curve segments are drawn. Then, the drawn curve segments are smoothly connected to form a smooth curve with continuous curvature, which is the final path Path. The expression of the final path Path is a piecewise function composed of the cubic B-spline curves fitted by the 3D segments. That is, Path is calculated as follows:

[0159]

[0160] Where x0, x1, …, x 3D+2 They are The x-coordinate of .

[0161] The optimal individual or optimal path finally outputted by this embodiment is as follows Figure 2 shown.

[0162] The mobile robot path planning method used in this embodiment adopts an improved Tent chaotic sequence strategy mapping initialization population, an improved golden sine strategy, and proposes a linear equidistant interpolation strategy, which improves the global search capability and local search capability of the algorithm.

[0163] In addition, this embodiment also conducts a comparative experiment on the path planning method using only the basic whale optimization algorithm. The comparison results are as follows: Figure 3 and

[0164] As shown in Table 1.

[0165] Table 1 Effect comparison list

[0166]

[0167] It can be seen that compared with only using the basic whale optimization algorithm, the mobile robot path planning method applied in this embodiment has a faster path generation speed, higher solution quality, and stronger optimization ability.

[0168] Example 3

[0169] This embodiment proposes a path planning system, and applies the mobile robot path planning method proposed in Example 1. Figure 4 ,include:

[0170] The map acquisition module is used to obtain and rasterize the map, using preset color blocks to represent passable areas or obstacles; it is also used to set the starting and ending points of the path;

[0171] A model building module is used to build a mathematical model with the minimum evaluation value generated based on path safety and transportation distance as the objective function, and to initialize the model parameters;

[0172] An optimization module is used to calculate and solve the mathematical model using the whale optimization algorithm, the Tent chaotic sequence strategy, and the linear equidistant interpolation strategy to generate the global optimal individual;

[0173] The path generation module is used to perform linear equidistant interpolation on the global optimal individual to generate a new individual, and generate a number of B-spline curves according to the position vectors contained in the new individual, and obtain the path curve by smoothly connecting the B-spline curves.

[0174] Example 4

[0175] This embodiment proposes a mobile robot, including a robot body, a control unit and a mobile unit. The output end of the control unit is connected to the input end of the mobile unit. The control unit is equipped with a path planning system proposed in Example 2. The control unit controls the mobile unit to execute the path curve generated by the path planning system.

[0176] Example 5

[0177] A computer device includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, it implements a mobile robot path planning method proposed in Example 1.

[0178] In a specific implementation process, the computer device is a cloud device.

[0179] Example 6

[0180] A computer storage medium stores instructions, which, when executed on a computer, enable the computer to execute a mobile robot path planning method proposed in Example 1.

[0181] The same or similar reference numerals correspond to the same or similar components;

[0182] The terms used in the drawings to describe positional relationships are for illustrative purposes only and should not be construed as limiting this patent;

[0183] Obviously, the above embodiments of the present invention are merely examples for the purpose of clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the claims of the present invention.

Claims

1. A mobile robot path planning method, characterized in that: The following steps are involved: S1. Use the grid method to divide the map into 1×1 squares, and use preset color blocks to represent passable areas or obstacles; S2. Establish a mathematical model as follows: minE(r)=αV(r)+βL(r) stλ(r)>0 Among them, n is the number of nodes that the path passes through; m is the number of turns; b is the number of obstacles; the path r consists of n nodes The composition is: k=1,2,…,n; r=1,2,…,N, where N represents the size of the whale population; E(r) represents the evaluation value of the path based on path safety and transportation distance; V(r) represents the path smoothness of path r; L(r) represents the length of path r; a and β are preset constants, representing the safety factor and distance weight coefficient of path r respectively; (x0, y0), (x n+1 ,y n+1 ) represent the starting point and end point coordinates of the path, (x k-1 ,y k-1 )、(x k ,y k )、(x k+1 ,y k+1 ) represent nodes respectively and The two-dimensional coordinates of Indicates adjacent nodes The Euclidean distance between k Represents the angle variable between two adjacent points; O={O1,O2,…,O b } represents the set of obstacles, O j =(x j ,y j ), j = 1, 2, ..., b; for Equation of a line between two points; Indicates obstacle O j To the straight line distance; sign represents the sign function; λ(r) represents whether a collision occurs on path r. When λ(r) = -1 or 0, it indicates a collision occurs, and when λ(r) = 1, it indicates no collision occurs. S3. Initialize the parameters of the whale optimization algorithm, specifically: determine the size of the whale population N, initialize the maximum number of iterations T, and the dimension D of the whale individual in the search space; set the iteration counter t, which represents the current number of iterations, and initialize t = 1; S4, using the Tent chaotic sequence strategy to initialize the population; S5. Execute the linear isometric interpolation strategy to add new position vectors for all whale individuals; S6. Calculate the number of whales in the population after linear isometric interpolation. The fitness of the path r represented by is expressed as follows: fitness=E(r); S7. Select the whale individual with the smallest fitness as the current global optimal individual S8. Updating the whale individual further includes: S81. Generate a random number ρ uniformly distributed on [0,1] and define the partition coefficient A as follows: Where g1 is a random value uniformly distributed on [0, 2π], g2 is a random value uniformly distributed on [0, π]; t represents the current number of iterations; S82. Update the t+1 generation of whale individuals according to the values ​​of ρ and A. S9, the iteration counter is incremented by 1, t=t+1; determine whether the current number of iterations t reaches the maximum number of iterations T: if so, output the current global optimal individual and proceed to step S10; otherwise, return to step S5; S10, perform linear isometric interpolation on the current global optimal individual to generate a new individual, and calculate the cubic uniform B-spline curve path based on the position vector of the new individual z (q), a piecewise fitting strategy is adopted to complete the path curve construction; where z = 0, 1, 2, …, 3D-1; the non-decreasing parameter q∈[0,1] represents the curve variable.

2. A mobile robot path planning method according to claim 1, characterized in that: In step S4, the population is initialized using the Tent chaotic sequence strategy, including: S41. Randomly generate a whale individual in D-dimensional space S42, calculating the position vectors of the remaining N-1 whale individuals; S43. Map the whale's individual position vector to the solution space. The mapping process expression is as follows: Where ub v lb v They represent the upper and lower bounds of the solution space, v=1,2; ub1 and lb1 are the upper and lower bounds of the x-coordinate value, and ub2 and lb2 are the upper and lower bounds of the y-coordinate value.

3. A mobile robot path planning method according to claim 2, characterized in that: In step S42, the position vectors of the remaining N-1 whale individuals are calculated using the following formula: Among them, if or Then reassign it according to the following formula: Where v = 1, 2, Represents the sth position vector of the whale individual before the update The vth dimension in They represent the x and y coordinate values ​​of the s-th position vector of the whale individual before the update; s = 1, 2, ..., D.

4. A mobile robot path planning method according to claim 1, characterized in that: In step S5, a linear equidistant interpolation strategy is performed on all whales to add new position vectors, including: For each individual whale Linearly interpolate 2D new position vectors to obtain the new individual after interpolation in, and Represents the original position vector The left and right position vectors inserted on both sides, and the newly added position vector Calculate as follows: Where, s = 1, 2, ..., D.

5. A mobile robot path planning method according to claim 1, characterized in that: In step S82, the t+1 generation whale individuals are updated according to the values ​​of ρ and A. Specifically: If ρ<0.5 and |A|<1, update the individual whale according to the following formula If ρ<0.5 and |A|≥1, update the individual whale as follows If ρ≥0.5, the golden sine strategy is used to update the whale individual in, represents the tth generation of whale individuals, represents the t+1 generation of whale individuals, represents the current global optimal individual, Represents a whale individual randomly selected from N whales.

6. A mobile robot path planning method according to claim 5, characterized in that: In step S82, if ρ≥0.5, the golden sine strategy is used to update the whale individual The update method is as follows: c1=aτ+b(1-τ) c2=a(1-τ)+bτ in, represents the tth generation of whale individuals, represents the t+1 generation of whale individuals, represents the current global optimal individual, Represents a whale randomly selected from N whales, c1 and c2 are the golden section numbers The obtained coefficients, a, u1, u2 and b are uniformly distributed random values ​​of (0,π) and (-π,0) respectively.

7. A mobile robot path planning method according to claim 1, characterized in that: In step S10, the cubic uniform B-spline curve path is calculated based on the position vector of the new individual. z (q) A segmented fitting strategy is used to complete the path curve construction, including: S101. Generate a cubic uniform B-spline curve path based on the position vector of the new individual z (q), which is a sequence Q of non-decreasing parameters q: 0≤q1≤q2≤...≤q 10 The cubic polynomial determined by ≤1 is expressed as follows: Where q∈[0,1], the preset values ​​q1,q2,...,q 10 is an increasing arithmetic progression on [0,1], and q1,q2,...,q 10 Substitute the value of path into z In (q), the obtained point set is connected to obtain a cubic uniform B-spline curve; z=0,1,2,…,3D-1, The global optimal individual New individuals after linear isometric interpolation The z-th position vector of ; S102, adopt the segmented fitting strategy to The four adjacent position vectors draw the zth B-spline curve, and a total of 3D curve segments are drawn. Then, the drawn curve segments are smoothly connected to form a smooth curve with continuous curvature, which is the final path Path. The expression of the final path Path is a piecewise function composed of the cubic B-spline curves fitted by the 3D segments, and the expression is as follows: Where x0, x1, …, x 3D+2 for The x-coordinate of .

8. A path planning system, applying the method according to any one of claims 1 to 6, characterized in that: include: The map acquisition module is used to obtain and rasterize the map, using preset color blocks to represent passable areas or obstacles; it is also used to set the starting and ending points of the path; A model building module is used to build a mathematical model with the minimum evaluation value generated based on path safety and transportation distance as the objective function, and to initialize the model parameters; An optimization module is used to calculate and solve the mathematical model using the whale optimization algorithm, the Tent chaotic sequence strategy, and the linear equidistant interpolation strategy to generate the global optimal individual; The path generation module is used to perform linear equidistant interpolation on the global optimal individual to generate a new individual, and generate a number of B-spline curves according to the position vectors contained in the new individual, and obtain the path curve by smoothly connecting the B-spline curves.

9. A mobile robot comprising a robot body, a control unit and a mobile unit, wherein the output end of the control unit is connected to the input end of the mobile unit, characterized in that: The control unit is equipped with a path planning system according to claim 7, and the control unit controls the mobile unit to execute the path curve generated by the path planning system.

10. A computer storage medium, characterized in that The computer storage medium stores instructions, which, when executed on a computer, enable the computer to perform the method according to any one of claims 1 to 6.

Images