Path planning method based on multi-strategy fusion improved dung beetle optimization algorithm

Abstract

The invention relates to the technical field of path planning, in particular to a path planning method based on a multi-strategy fusion improved dung beetle optimization algorithm. The method comprises the following steps: A, inputting an environment map, and setting a starting point and an ending point; b, initializing parameters of an algorithm; c, an initial population generation process in the dung beetle optimization algorithm is optimized through improved Tent chaotic mapping, and the fitness value of each dung beetle is calculated. The invention provides a path planning method based on a multi-strategy fusion improved dung beetle optimization algorithm. An initial solution of a multi-strategy fusion improved dung beetle optimization algorithm is diversified by adopting a Tent chaos strategy, a penalty term of a turning angle is added into a fitting function, an inertia weight is adaptively updated by using a sine algorithm, and an Ivre flight strategy and a local search mechanism are introduced, so that when a mobile robot moves, the accuracy of the movement of the robot is improved, and the accuracy of the movement of the robot is improved. A simpler and shorter path is obtained, the path efficiency is improved, the search capability in the steering behavior and the smoothness of the planned path are improved, and the convergence speed is accelerated.

Description

Technical Field

[0001] The present invention relates to the technical field of path planning, and in particular to a path planning method based on a multi-strategy fusion-improved dung beetle optimization algorithm. Background Art

[0002] In recent years, mobile robots have been widely used in indoor and outdoor environments. Among them, path planning of mobile robots is a basic and important issue because it directly affects the efficiency and safety of mobile robots. Therefore, the research on path planning of mobile robots has become a hot topic in the research fields of control, robotics, artificial intelligence, etc.

[0003] For the path planning of mobile robots, there are some graph-based algorithms that are more efficient in relatively simple scenarios, such as the A* algorithm, Dijkstra algorithm, breadth-first search algorithm, and rapidly exploring random trees (RRT) algorithm. However, in complex environments, these algorithms also face some challenges, such as slow convergence and easy occurrence of local optimality.

[0004] In addition, some swarm intelligence optimization algorithms, including particle swarm optimization (PSO), genetic algorithm (GA), ant colony optimization (ACO), sparrow search algorithm (SSA) and dung beetle optimization (DBO), have also been used to plan paths for mobile robots and have shown excellent effectiveness in complex environments. However, the performance of these algorithms depends heavily on parameters, and even improper settings can affect the quality of the solution and lead to premature convergence.

[0005] Cui et al. proposed a multi-strategy adaptive ant colony optimization algorithm (MSAACO) to alleviate the inefficiency of traditional ant colony optimization algorithm.

[0006] Huang et al. developed an integrated method for path mapping of autonomous underwater vehicles (AUVs).

[0007] Wang et al. proposed an improved firefly optimization algorithm (FA) for unmanned aerial vehicle path planning and an autonomous navigation and obstacle avoidance algorithm (ANOA) for unmanned surface vehicle obstacle avoidance.

[0008] The novel Dung Beetle Optimizer (DBO) algorithm has the advantages of fast convergence, simple implementation, and short optimization period, and has been applied to various multi-objective optimization and path planning scenarios. In addition, several DBO variants have been proposed.

[0009] Gupta et al. added population similarity mutation strategy and reverse learning strategy to the DBO algorithm for three-dimensional mountain path planning of UAVs.

[0010] Zhang et al. proposed an improved trajectory planning method based on DBO, combining the Levy strategy and lateral intersection with policy adaptation.

[0011] Ji et al. proposed a hybrid method combining Tent chaotic mapping and DBO hybrid algorithm to plan the trajectory of underwater robots.

[0012] However, the improved methods proposed in these studies may still encounter limitations in the search process and have difficulty overcoming local optimality. In addition, the efficiency of these methods may decrease when dealing with high-dimensional complex problems such as robot path planning.

[0013] To this end, a path planning method based on a multi-strategy fusion improved dung beetle optimization algorithm was designed to provide another technical solution to the above technical problems. Summary of the invention

[0014] Based on this, it is necessary to provide a path planning method based on a multi-strategy fusion improved dung beetle optimization algorithm to solve the technical problems raised in the above background technology.

[0015] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0016] A path planning method based on multi-strategy fusion to improve the dung beetle optimization algorithm, the steps are as follows:

[0017] A. Input environment map (specifically similar to the environment picture, and finally form Figure 4 etc.), and set the starting point and end point;

[0018] B. Initialize the algorithm parameters;

[0019] C. Optimize the initial population generation process in the dung beetle optimization algorithm by improving the Tent chaotic mapping, and calculate the fitness value of each dung beetle;

[0020] D. Sort the dung beetle individuals according to their fitness values ​​and assign roles to them;

[0021] E. Perform global search (search all dung beetles) and local search (search the N dung beetles with the highest fitness values) on the dung beetles after role assignment, and select the one with the highest fitness value for saving based on the comparison of fitness values;

[0022] F. Determine whether the convergence accuracy is reached. If so, the path and fitness value of the dung beetle with the highest fitness value among the N dung beetles are output as the optimal path and the optimal fitness value. If not, execute step G;

[0023] G: Determine whether the maximum number of iterations has been reached. If so, the path and fitness value of the dung beetle with the highest fitness value among the N dung beetles are output as the optimal path and optimal fitness value. If not, execute step C and proceed to the next round of iteration.

[0024] As a preferred implementation of the path planning method based on the multi-strategy fusion improved dung beetle optimization algorithm provided by the present invention, in step B, the parameters of the algorithm are initialized by setting the parameters of rolling, dancing, foraging, and the number of thief dung beetles in the dung beetle optimization algorithm.

[0025] As a preferred implementation of the path planning method based on the multi-strategy fusion improved dung beetle optimization algorithm provided by the present invention, in step C, the initial population generation process in the dung beetle optimization algorithm is optimized by improving the Tent chaotic mapping, so that the dung beetle population is evenly distributed;

[0026] Improve the Tent chaos map, the expression is as follows:

[0027]

[0028] In the formula, a is the chaotic mapping parameter, rand is a random number between 0 and 1, and k represents the kth point of the chaotic sequence path;

[0029] Effectively generate a series of values ​​that meet specific distribution characteristics P = [P (1) ,P (2) ,...,P (n) ], the generated value is used as the parameter value for population initialization, and the expression is as follows:

[0030] X=P·(ub-lb)+lb

[0031] To ensure that the resulting positions fall within the bounds, the following truncation is performed:

[0032]

[0033] The initialization method can effectively ensure that the generated position solution is within the specified boundary, thereby improving the effectiveness and exploration ability of the optimization algorithm in the solution space.

[0034] As a preferred implementation of the path planning method based on the multi-strategy fusion improved dung beetle optimization algorithm provided by the present invention, the Tent chaotic mapping is improved, and the steps are as follows:

[0035] First generate an initial random number P (1) , the value is in the range [0,1];

[0036] Generate subsequent values ​​through an iterative process, and in each iteration, judge P(k) Is it greater than or less than a?

[0037] If the current value P (k) is less than the preset parameter a, then the next value P (k+1) By calculating 2*(P (k) +0.1*rand) to get;

[0038] If the current value is greater than or equal to a, then by calculating 2*(1-P (k) +0.1*rand)) to generate the next value;

[0039] Until the maximum number of iterations is reached, a series of values ​​P that meet the specific distribution characteristics are effectively generated. (1) ,P (2) ,...,P (n) ].

[0040] As a preferred implementation of the path planning method based on the multi-strategy fusion improved dung beetle optimization algorithm provided by the present invention, the maximum steering angle and the number of turns of the robot in the planned route are added to the fitness function as penalty conditions, and the expression is as follows:

[0041]

[0042] Where: x i and i are the location information of the path nodes. is the steering angle coefficient, N is the number of turns, and M is the size of the driving environment map;

[0043] The direction vector of the robot moving from node i to node j is recorded as The direction vector from node j to the next node d is recorded as Maximum steering angle θ max The calculation formula is as follows:

[0044]

[0045] As a preferred implementation of the path planning method based on the multi-strategy fusion improved dung beetle optimization algorithm provided by the present invention, the path with the minimum fitness value is stored as the current global optimal path x_best, and its fitness value is stored as the current global optimal fitness value f_best.

[0046] As a preferred implementation of the path planning method based on the multi-strategy fusion improved dung beetle optimization algorithm provided by the present invention, in the step D, the dung beetle individuals are sorted according to the fitness values, and the roles of the dung beetles are assigned, and the steps are as follows:

[0047] By updating the population, the global search is completed and the fitness value of each updated dung beetle is calculated;

[0048] Sort by fitness value and reassign roles to the dung beetle population.

[0049] As a preferred implementation of the path planning method based on the multi-strategy fusion improved dung beetle optimization algorithm provided by the present invention, in the step E, the dung beetles after role assignment are searched globally and locally, and the ones with the highest fitness values ​​are selected and saved according to the comparison of fitness values, and the steps are as follows:

[0050] 1) For the N dung beetles with the highest fitness, they are randomly re-initialized and the position of each dung beetle is updated to complete the local search;

[0051] 11). Update the location of each dung beetle to complete the local search. The steps are as follows:

[0052] 12). Get the number of rows and columns of the map and the feasible domain of the grid;

[0053] 13). Randomly explore each feasible area in the path dimension and calculate the fitness value of the new path;

[0054] 14). Determine the fitness value, select the smaller fitness value as the new path and add the node;

[0055] 2). Calculate the fitness value of the N dung beetles;

[0056] 3) Compare N dung beetles, and by comparing the fitness values ​​of local search and global search, select the one with the larger fitness value and save it.

[0057] As a preferred implementation of the path planning method based on the multi-strategy fusion improved dung beetle optimization algorithm provided by the present invention, the steps of updating the position of each dung beetle are as follows:

[0058] The position of the breeding dung beetles is updated, and the expression is as follows:

[0059] X t+1 =X * +b1×(X t -Lb * )+b2×(X t -Ub * );

[0060] Among them, X * represents the optimal position from the beginning to this iteration, Lb * is the lower bound of the spawning area, Ub * It is the upper boundary of the spawning area;

[0061] The position of the rolling dung beetle is updated as follows:

[0062]

[0063] Where: δ is a random number between [0,1], ST∈(0.5,1], when δ>ST, it means that the rolling ball dung beetle is in the global exploration stage, and the dung beetle will roll along the predetermined path to find the optimal solution;

[0064] The position of the thief dung beetle is updated as follows:

[0065] X t+1 =(X b +S×g×(|X t -X * |+|X t -X b |))·s;

[0066] Among them, X t-1 Record the position state of the last iteration, S is a constant value, g is a 1×D random vector, X * Represents the optimal position from the beginning to this iteration;

[0067] The position of the foraging dung beetle is updated as follows:

[0068] X t+1 =X t +C1×(X t -Lb b )+C2×(X t -Ub b )

[0069] Among them, C1 and C2 are random numbers and (0,1) random vectors that obey normal distribution, respectively, and Lb b is the lower bound of the optimal foraging area, Ub b is the upper bound of the optimal foraging area.

[0070] As a preferred implementation mode of the path planning method based on the multi-strategy fusion improved dung beetle optimization algorithm provided by the present invention, in step G, when no new path is found after 20 consecutive iterations, it is judged that the convergence accuracy is reached, and the global optimal path x_best and its fitness value f_best are output; if a new path is found in less than 20 iterations, it is judged that the convergence accuracy is not reached, and step G is executed.

[0071] It can be seen without a doubt that the above-mentioned technical solution of the present application can definitely solve the technical problem to be solved by the present application.

[0072] At the same time, through the above technical solutions, the present invention has at least the following beneficial effects:

[0073] The present invention provides a path planning method based on a multi-strategy fusion improved dung beetle optimization algorithm. In the process of population initialization, the tent chaos strategy is used to diversify the initial solution of MIDBO to avoid local optimum. Then, a penalty term of the turning angle is added to the fitting function to minimize the frequency and amplitude of the turns, thereby obtaining a simpler and shorter path and improving the path efficiency. Then, a sinusoidal algorithm is used to adaptively update the inertia weight to accelerate the convergence speed and enhance the robustness of the algorithm. Meanwhile, a Levy flight strategy and a local search mechanism are introduced to improve the search capability in the turning behavior and the smoothness of the planned path. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0075] Figure 1 This is a population ratio diagram of dung beetles of the present invention;

[0076] Figure 2 It is a schematic diagram of the implementation process of the local search optimization mechanism of the present invention;

[0077] Figure 3 It is a schematic diagram of the MIDBO algorithm flow of the present invention;

[0078] Figure 4 A schematic diagram of a simulated robot map environment model of the present invention;

[0079] Figure 5 Schematic diagram of the best paths of seven DBOs of the present invention;

[0080] Figure 6 A schematic diagram showing the comparison between the MIDBO and improved PSO paths of the present invention;

[0081] Figure 7 A schematic diagram showing the comparison between the MIDBO and DBO paths of the present invention;

[0082] Figure 8 A schematic diagram showing the comparison between the MIDBO and GAACO pathways of the present invention;

[0083] Fig. 9 A schematic diagram showing the comparison between the MIDBO and ISSA paths of the present invention;

[0084] Fig.10 A schematic diagram showing the path comparison between the MIDBO of the present invention and the improved PSO, DBO and ISSA.

[0085] Fig.11 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0086] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0087] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings.

[0088] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features and technical solutions in the embodiments may be combined with each other.

[0089] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0090] Reference Figure 1-Figure 11 , a path planning method based on multi-strategy fusion to improve the dung beetle optimization algorithm.

[0091] 1. Dung beetle optimization algorithm

[0092] The main idea of ​​the dung beetle optimization algorithm is to imitate the ball rolling, dancing, foraging and reproduction behaviors of dung beetles to conduct global and local searches. The algorithm includes four types of dung beetle individuals: ball rolling dung beetles, dancing dung beetles, foraging dung beetles and breeding dung beetles. Among them, the individual solution in each solution space is each dung beetle individual, represented by X = (x1, x2, ..., xn). The proportion of each dung beetle is set as follows Figure 1 As shown;

[0093] 1.1 Rolling ball and dancing behavior

[0094] The ball rolling behavior of dung beetles refers to their rolling of spherical objects to their nests or suitable locations, usually for the purpose of food storage or reproduction. When encountering obstacles, dung beetles will adjust their routes by dancing. The dancing behavior is simulated by the tangent function. After determining the new direction, the individual position will continue to be updated. The next iteration position update of an individual dung beetle is associated with the individual position in this iteration and the previous iteration. Let X t+1 For X t The position state at the next iteration, X t-1 The position state of the last iteration is recorded, and the randomness of α between 1 and -1 is used to simulate the environment. In summary, the rolling behavior of the ball without obstacles can be expressed as:

[0095] X t+1 =X t +α×k×X t-1 +b×Δx (1)

[0096] Where k is the disturbance factor, with a value between (0, 0.2], b is a random number between (0, 1), α is -1 or 1 depending on the situation, and Δx simulates the light intensity. Δx represents the change in light intensity in the environment, X w The global worst position formula is expressed as:

[0097] Δx=|X t -X w | (2)

[0098] If an obstacle is encountered, dance to find a new direction:

[0099] X t+1 =X t +tanθ|X t -X t-1 | (3)

[0100] 1.2 Reproductive behavior

[0101] Usually, dung beetles will place their eggs in a safe area. The so-called safe area refers to the location of the optimal solution in the solution space. The boundary selection strategy can be used to simulate the area where dung beetles lay eggs. The selection formula for the egg-laying area is expressed as:

[0102] Lb * =max(X * ×(1-R),Lb) (4)

[0103] Ub * =min(X * ×(1+R),Ub) (5)

[0104] Where X * represents the optimal position from the beginning to this iteration, that is, the current global optimal position. Lb and Ub are two vectors, representing the upper and lower bounds of the optimization path, respectively. R = 1-t / T, T is the total number of iterations. From the two formulas, it can be seen that the upper and lower bounds are dynamically updated, which means that as the iterations increase, the dung beetle's egg-laying area will continue to optimize and move closer to a safer area, which can encourage the dung beetle population to move closer to the optimal solution. After determining the current safe area, the baby dung beetles will hatch. The formula for updating the egg-laying position is as follows, where b1 and b2 are two independent random vectors:

[0105] X t+1 =X * +b1×(X t -Lb* )+b2×(X t -Ub * ) (6)

[0106] Among them, X * represents the optimal position from the beginning to this iteration, Lb * is the lower bound of the spawning area, Ub * It is the upper boundary of the spawning area.

[0107] 1.3 Foraging behavior

[0108] The foraging behavior is mainly aimed at the small dung beetles in the egg-laying area. They are stipulated that the small dung beetles will be restricted to move in a safe area, so they still need to be restricted within the upper and lower boundaries. The regional formula is expressed as:

[0109] Lb b =max(X b ×(1-R),Lb) (7)

[0110] Ub b =min(X b ×(1+R),Ub) (8)

[0111] All hatched dung beetles forage for food in a safe area, so b represents the local optimal position of the current population, R is defined in the same way as in formula (4) above. It can be seen from the formula that the position of the dung beetle is also updated continuously with iterations. C1 and C2 are random numbers and (0,1) random vectors that obey the normal distribution, respectively. The position update formula of the dung beetle in the region is:

[0112] X t+1 =X t +C1×(X t -Lb b )+C2×(X t -Ub b ) (9)

[0113] Among them, C1 and C2 are random numbers and (0,1) random vectors that obey normal distribution, respectively, and Lb b is the lower bound of the optimal foraging area, Ub b is the upper bound of the optimal foraging area.

[0114] 1.4 Theft

[0115] Stealing behavior is a very important part of the entire dung beetle optimization algorithm. Some dung beetles in the population will steal dung balls from other dung beetles. This behavior can effectively make the algorithm jump out of the local optimum as much as possible. The formula is as follows:

[0116] X t+1=X b +S×g×(|X t -X * |+|X t -X b |) (10)

[0117] Where S is a constant value and g is a 1×D random vector.

[0118] 2. Improved path planning of dung beetle optimization algorithm based on multi-strategy fusion

[0119] 2.1 Improved population initialization generation of Tent chaotic mapping

[0120] The original DBO uses random numbers to generate the initial population in the search space. This method will make the generated initial solution individuals unevenly distributed and the prediction efficiency is low. Tent chaos mapping is a nonlinear dynamic system that can generate sequences with random and chaotic properties. By applying Tent chaos mapping to the initial population generation process of the dung beetle optimization algorithm, it can ensure that the dung beetle population is evenly distributed, improve the convergence speed and optimization accuracy of the algorithm, and lay the foundation for global optimization. The formula of Tent chaos mapping is:

[0121]

[0122] Where: a is the chaotic mapping parameter, which is usually set to 0.499 to ensure that the generated initial population will not have large differences. Although the differences using this method are small, the ergodicity is low and lacks randomness, making it difficult to maintain the diversity of the population, which will have a certain impact on the algorithm's optimization performance. The improved Tent chaotic mapping formula designed by the present invention is as follows:

[0123]

[0124] In the formula, a is the chaotic mapping parameter, rand is a random number between 0 and 1, and k represents the kth point of the chaotic sequence path. This method first generates an initial random number P (1) , which is in the range [0,1]. Then, the subsequent values ​​are generated through an iterative process. In each iteration, if the current value P (k) is less than the preset parameter a, then the next value P (k+1) By calculating 2*(P (k) +0.1*rand), this process makes the generated value show an expansion trend; otherwise, if the current value is greater than or equal to a, then by calculating 2*(1-P (k) +0.1*rand)) to generate the next value. This mapping process continues until the maximum number of iterations is reached. Effectively generates a series of values ​​that meet the specific distribution characteristics P = [P (1) ,P(2) ,...,P (n) ], the generated values ​​are used as parameter values ​​for population initialization:

[0125] X=P·(ub-lb)+lb (13)

[0126] To ensure that the generated positions fall within the bounds, we perform the following truncation:

[0127]

[0128] This initialization method effectively ensures that the generated position solution is within the specified boundaries, thereby improving the effectiveness and exploration ability of the optimization algorithm in the solution space.

[0129] The improved Tent chaotic mapping enhances the quality of the optimal individuals in the initial population, increases population diversity, and realizes the exploration of more high-quality search areas. It can help the algorithm start searching from a wider solution space, and help increase the possibility of the algorithm finding the global optimal solution while improving the convergence performance of the algorithm.

[0130] 2.2 Improvement of fitness function

[0131] In the actual driving process of the robot, it is usually necessary to avoid driving paths with large turning angles, because when the physical car makes a large angle turn during driving, the car body may tilt due to the sudden increase in lateral force, increasing the risk of overturning, and even if the angle is small, a path with too many turns will increase the energy consumption of the robot. Therefore, when planning the path, not only the length of the driving path must be considered, but also the steering angle limitation of the robot. The fitness of the traditional path planning algorithm is only related to the path length and cannot be directly applied to the path planning of the robot. For this reason, the fitness function is redesigned, and it is proposed to add the maximum steering angle and number of turns of the robot in the planned route as penalty conditions to the fitness function. The calculation formula of the improved fitness function is as follows:

[0132]

[0133] Where: x i and i are the location information of the path nodes. is the steering angle coefficient, N is the number of turns, and M is the size of the driving environment map. The direction vector of the robot moving from node i to node j is recorded as The direction vector from node j to the next node d is recorded as Design maximum steering angle θ max The calculation formula is:

[0134]

[0135] It can be seen from formula (14) that the maximum steering angle, the number of turns and the improved fitness value are proportional, that is, when the path length is the same, the smaller the maximum steering angle and the fewer the number of turns, the smaller the fitness value. In the end, the robot will choose the driving route with the smallest fitness value, thereby obtaining a path with better performance indicators such as path length, maximum steering angle and number of turns, which makes it more in line with the actual navigation requirements of the robot.

[0136] 2.3 Local Search Optimization Mechanism

[0137] In MIDBO, the global optimal individual plays an important role in guiding the overall exploration direction of the population and has a vital impact on the fitness of the population. Therefore, a local search optimization mechanism is designed for individuals with the best fitness to improve the quality of the global optimal individual and lay the foundation for subsequent population fitness optimization. The design ideas of the local search optimization mechanism are as follows: Figure 2 As shown in the figure, the shaded part is the obstacle area, and the rest is the passable area. The paths obtained before and after the local search optimization mechanism is used between nodes are represented by dotted lines and solid lines respectively. The specific steps are as follows:

[0138] Get the number of rows and columns (dimensions) of the map and the feasible domain of the grid;

[0139] Randomly explore each feasible area in the path dimension, as shown in the solid line in the figure, and calculate the fitness value of the new path.

[0140] Determine the fitness value, select the smaller fitness value as the new path and add the node.

[0141] Figure 2 The fitness value of the new path obtained by searching is higher, so the solid line new path obtained by searching replaces the original dotted line path. If the fitness of the searched path is lower, the search is abandoned and the original path is retained.

[0142] 2.4 Position update strategy of thief dung beetles

[0143] Analysis of the original DBO position update strategy of dung beetles (Equation (10)) shows that this behavior tends to search locally at the optimal location (best food source), but this strategy may lead to rapid assimilation of dung beetles during the iteration process, that is, rapid aggregation to the area near the optimal location, which may cause the population to fall into a local optimum and stagnate the search. Therefore, it is hoped that the search range can be expanded as much as possible in the early stage of the iteration to increase the diversity of the population, and more accurate optimization can be performed in the area near the optimal solution in the later stage of the iteration.

[0144] From the motion characteristics of Levy flight, we can see that its small step length and occasional long jump alternation mechanism can achieve global exploration and local development at the same time. Therefore, incorporating this strategy into the stealing behavior not only balances the need for optimization, but its random movement can also improve the algorithm's ability to jump out of the local optimum. The formula for the Levy flight strategy is:

[0145]

[0146] Where: σ v =1,γ=3 / 2,l is the step length control parameter, its value is l=0.01(x i (t)-x p ). The position update formula of the thief dung beetle after the introduction of the levy flight strategy is:

[0147] X t+1 =(X b +S×g×(|X t -X * |+|X t -X b |))·s (17)

[0148] 2.5 Update the adaptive inertia weight coefficient based on the sine algorithm

[0149] The inertia weight coefficient is an important parameter in the dung beetle optimization algorithm. It determines the degree of inertia of the dung beetle individual during the search process. Improving the inertia weight coefficient using the improved sine algorithm MSA can improve the performance and search ability of the algorithm. In the initial stage of the algorithm, the idea of ​​MSA is introduced, and the inertia weight coefficient is set to a randomly generated value to increase the diversity of the population and improve the global search ability. In the iterative process of the algorithm, the inertia weight coefficient is dynamically adjusted to improve the convergence accuracy and speed of the standard DBO. The position update formula of the improved sine algorithm is as follows:

[0150] X(t+1)=R t X(t)+r1×sin(r2)×[r3p(t)-X(t)] (18)

[0151] Among them, R t is the improved inertia weight coefficient, r1 is a nonlinear decreasing function, r2 is a random number in the interval [0,2π], r3 is a random number in the interval [-2, 2], and p(t) is the optimal position in the tth iteration. Use nonlinear decreasing to set the value of r1, and use the cosine function between [0,π] to determine the change of r1. The formula is as follows:

[0152]

[0153] Where R max and R min is the maximum and minimum value of the variable inertia weight coefficient, which is defined at initialization. For the setting that the inertia weight coefficient decreases linearly with the increase of the number of iterations, the inertia weight R = 1-t / T of the standard dung beetle optimization algorithm is improved, and the formula is as follows:

[0154]

[0155] In order to further optimize the DBO algorithm, referring to the safety value-warning value mechanism of the sparrow optimization algorithm, we introduced a sinusoidal guidance mechanism to the rolling ball stage, modified the dancing strategy of the rolling ball dung beetle stage, and used MSA for sinusoidal guidance improvement to coordinate the capabilities of global exploration and local development. The improved formula is as follows:

[0156]

[0157] Where δ is a random number between [0,1], ST∈(0.5,1], when δ<ST, it means that the rolling ball dung beetle is in the global exploration stage, and the dung beetle will roll along the predetermined path to find the optimal solution. When a certain condition is met (such as reaching a certain threshold), the dung beetle will enter the sine guidance stage. In the sine guidance stage, the dung beetle does not have a clear rolling target, but will search and move in a sinusoidal function. This improved sinusoidal guidance mechanism can greatly improve the problem of the DBO algorithm's position update strategy being too random. This is because after adding the MSA strategy, the dung beetle individual will exchange information with the current optimal individual, promote the rapid spread of information in the population, and thus improve the defect of lack of information exchange between individuals in the original algorithm.

[0158] Formula (18) is used to control the search distance and direction of the rolling dung beetle, and formula (15) is used to gradually narrow the search space of the inertia weight coefficient. As the number of iterations increases, the inertia weight decreases. In the early stage of the algorithm iteration, the relatively large inertia weight enables the algorithm to have a strong global exploration ability; while in the later stage of the algorithm iteration, the relatively small inertia weight helps to improve its local development ability.

[0159] 2.6MIDBO Algorithm

[0160]

[0161]

[0162] 3. Simulation experiment and analysis

[0163] In order to verify the effectiveness of MIDBO, the host operating system of the experimental software platform of the present invention is Windows 10 64bit, the processor is AMD Ryzen 758008-Core Processor, the memory is 16GB, the graphics card is NVIDIA GeForceRTX 3050, and the platform used by the software is Matlab R2023a. Design two groups of map environments for comparative experiments, and compare them with the improved A* algorithm, the improved ant colony algorithm (GAACO), the improved sparrow algorithm (ISSA), and the original DBO. The improved A*, GAACO and ISSA algorithms are all currently more representative excellent path planning algorithms, among which the improved A* algorithm can plan high-quality paths, and the search speed is faster, and the GAACO algorithm has good robustness and environmental adaptability; ISSA has strong search and convergence capabilities. Comparing MIDBO with these algorithms can more comprehensively evaluate the comprehensive performance of MIDBO in robot path planning.

[0164] 3.1 Environmental Modeling

[0165] The robot driving environment can be regarded as a two-dimensional space. The present invention uses the grid method to model the environment. The size of each grid depends on the size of the robot. The obstacles in the environment model are represented by black grids, and the starting point and end point of the path planning are represented by blue circles and red hexagons respectively. Figure (4) shows the working environment constructed by the present invention, and the grid size is 20×20.

[0166] 3.2 Comprehensive performance index

[0167] In order to more comprehensively evaluate the overall performance of the improved algorithm, the present invention uses a comprehensive performance index to evaluate the quality of the algorithm path planning. Four indicators are selected as the basis for path evaluation, namely, path length D, maximum steering angle θ max , the number of turns N and the time t used for path planning, the comprehensive performance index ε can be expressed as:

[0168] ε=ω1D+ω2θ max +ω3N+ω4t (22)

[0169] Where: ω1, ω2, ω3, ω4 are weight coefficients, which can be determined according to actual conditions; D, θ maxThe four indicators N, t, and N are all normalized and standardized to prevent the improved algorithm from obtaining a higher comprehensive performance index due to better performance on a single indicator. The present invention evaluates the path quality of the robot, so the safety of the driving path and the low energy consumption brought by the small number of turns are the main considerations. The present invention designs the weight factor of the path length to be ω1=0.4, the weight factor of the maximum turning angle to be ω2=0.2, the weight factor of the number of turns to be ω3=0.2, and the weight factor of the path acquisition time to be ω4=0.2.

[0170] 3.3 Simulation experiment 1: Verification of the effectiveness of five improvement strategies

[0171] In this part, five strategies, namely, chaos mapping mechanism, fitness function improvement, local search optimization mechanism, levy flight strategy and adaptive inertia weight coefficient, are tested and analyzed to verify their effectiveness.

[0172] In addition, the five proposed strategies are combined with the original DBO and the transition variants of the five DBOs, DBO1, DBO2, DBO3, DBO4, and DBO5, as shown in Table (1). The effectiveness of the five strategies is verified by embedding the five improved strategies into the original DBO algorithm in turn. Under the same experimental conditions, the five algorithms DBO, DBO1, DBO2, DBO3, DBO4, DBO5, and MIDBO were run, and the values ​​of the main parameters were: max_gen = 1000; num_polution = 120; dim = number of map columns - 2; lb = 2; ub = number of map rows; chaos coefficient a = 0.499; w_max = 1; w_min = 0; In addition, in order to reduce random errors, each algorithm was repeatedly run ten times in the path planning environment map model. The optimal path generation is shown in Figure (5), and the statistical results are shown in Table 2.

[0173] The statistical results in Table (2) show that compared with the original DBO algorithm, the DBO1 algorithm has a shorter optimal path length (30.569670 < 30.698111; 31.0000609 < 31.5043918) and fewer turns (7 < 8; 7.3 < 8.8) in both the optimal value and the average value. The results show that the introduction of the Tent chaotic mapping mechanism can effectively improve the quality of the solution of the initial node of the dung beetle individual and improve the search efficiency of the dung beetle algorithm.

[0174] In addition, the performance of the dung beetle algorithm DBO1 was further improved by the adaptive weight mechanism. DBO2 has a shorter average path length (30.912627 < 31.0000609) and fewer turns (7.2 < 7.3) than DBO1. This shows that the adaptive weight mechanism can make the dung beetle algorithm more stable.

[0175] After introducing new strategies in the transitional variants of DBO, it was found that the optimal path length, average path length, optimal number of turns, and average number of turns of MIDBO and DBO5 were gradually reduced compared with DBO4, DBO3, and DBO2. This shows that while these strategies may weaken the convergence of the algorithm while improving the path planning performance of the dung beetle algorithm, they generally improve the path planning performance of the algorithm, with significant effects.

[0176] Table 1: Different variants of DBO combined with different strategies.

[0177]

[0178] Table 2: Statistical results of seven DBOs.

[0179]

[0180] 3.4 Simulation Experiment 2

[0181] In order to prove the superiority of the proposed MIDBO, it is compared with the improved particle swarm algorithm, the improved PSO algorithm in the spatial environment model, the original DBO, the GAACO algorithm and the ISSA algorithm. As can be seen from Figure (6), the size of the grid environment map model is 20×20. The coordinates of the starting node and the target node are (0.5, 19.5) and (19.5, 0.5) respectively. In order to avoid random errors, MIDBO and these algorithms are tested independently 10 times. Table (3) lists the statistical results of MIDBO, DBO, GAACO and ISSA algorithms.

[0182] The best paths generated by these algorithms are shown in Figures (6)-(9). As shown in Table (3), in this experiment, the proposed MIDBO has certain advantages over other path planning algorithms. For the excellent GAACO algorithm, although the experimental results are comparable, the running time of GAACO far exceeds that of the other algorithms, which is not feasible in the actual driving process of the robot. The minimum number of turns generated by MIDBO is 7 times, and the path length is also smaller than that of the other algorithms. Compared with other algorithms, MIDBO's path planning solution is smoother and has fewer turns, which shows that MIDBO can effectively reduce the energy consumption of the robot.

[0183] And from Table (3), we can see that the mean of the proposed MIDBO algorithm is 30.7366084, and the mean square error of the 10 experimental results is also smaller than that of several other algorithms, which shows that it is more stable. Therefore, the statistical results prove that MIDBO has obvious advantages in solving such path planning problems.

[0184] Table 3: Experimental results of different algorithms.

[0185]

[0186] 3.4 Simulation Experiment 3

[0187] Since GAACO has a slower real-time effect, it is not compared with it for the time being. MIDBO is compared with the improved PSO, the original DBO and the ISSA algorithm to verify its excellent performance. In order to ensure the fairness of the experiment, the literature [S.C.Zhang,J.X.Pu,et al.,An adaptive improved ant colony system based on population information entropyfor path p lanning of mobile robot,IEEE Access 9(2021)24933–24945] The grid environment map model in is shown in Figure (10). The size of the grid environment map model is 30×30, and the starting node is (0.5, 0.5), represented by a blue circle. The target node is (29.5, 29.5), represented by a red hexagon. The white grid is the free area, and the black grid represents the obstacle. All experiments were conducted 10 times independently to avoid random errors. In order to maintain the original performance of the comparison algorithm, the parameters of MIDBO and the original DBO are set consistently. The maximum number of iterations, population size, problem dimension, upper and lower limits of all algorithms are the same. The optimal paths generated by these algorithms when solving the environment map model are shown in Figure (10).

[0188] From the experimental results in Table (4), it can be seen that the MIDBO algorithm proposed in the present invention is superior to the other three algorithms in terms of path length, number of turns and algorithm stability. The optimal value (42.106843) and average value (44.4754812) of the path length generated by MIDBO are both smaller than those of the other three algorithms (47.624415, 43.587406, 43.587406) (54.0639708, 52.66456, 55.9374817), and the optimal value (10) and average value (13.4) of the number of turns are smaller than those of the improved PSO (11; 16.1), the original DBO (12; 15.3) and the ISSA (12; 16.4). This shows that MIDBO can effectively reduce the energy consumption of the robot during path planning and driving. It can be seen from the table that through 10 independent experiments, the mean square error of the MIDBO path length and number of turns is the smallest, proving its strong stability. MIDBO's path length, number of turns, and algorithm stability are generally better than other algorithms. Thanks to the improvement of five strategies, it can obtain better path optimal solutions than other algorithms.

[0189] Table 4: Experimental results of different algorithms.

[0190]

[0191] 4. Conclusion

[0192] Aiming at the shortcomings of Dung Beetle Optimization Algorithm (DBO) in robot path planning, a multi-strategy fusion improved Dung Beetle Optimization Algorithm (MIDBO) was proposed by combining the above five effective improvement strategies. Firstly, a tent chaotic map was proposed to initialize the population. Then, the fitness function of path planning was improved by adding penalty items such as the number of path turns and turning angles. In addition, the sine algorithm was used to update the adaptive inertia weight coefficient of the rolling ball dung beetle. Furthermore, the levy flight strategy was proposed for the thief dung beetle. Finally, the algorithm as a whole added a local search mechanism. By optimizing the main parameters of the strategy, these five strategies were combined with the DBO algorithm to propose MIDBO, and its performance was verified through effectiveness simulation experiments. Compared with some advanced excellent algorithms, it verifies the outstanding performance of MIDBO in solving robot path planning. Comprehensive statistical results show that the MIDBO algorithm can obtain better path planning results and has advantages in path length, number of turns and algorithm stability. In addition, the path planning solution obtained by the MIDBO algorithm is smoother and more efficient than other algorithms. Therefore, this algorithm overcomes the shortcomings of the original DBO algorithm and is more suitable for robot path planning problems.

[0193] Among them, we have improved the dung beetle optimization algorithm. The traditional dung beetle optimization algorithm is prone to local optimal solutions during the search process, resulting in low search efficiency. To solve this problem, we introduced random factors of mutation operators and levy flight strategies to make the search process more diverse and avoid falling into local optimal solutions. In addition, we have also adjusted the inertia weight to make the search process more refined and better able to explore the solution space. These improvements enable the improved dung beetle optimization algorithm to find solutions close to the optimal value in a shorter time.

[0194] The preferred embodiments of the present invention disclosed above are only used to help explain the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the present invention to the specific implementation methods described. Obviously, many modifications and changes can be made according to the content of this specification. This specification selects and specifically describes these embodiments in order to better explain the principles and practical applications of the present invention, so that those skilled in the art can understand and use the present invention well. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A path planning method based on multi-strategy fusion to improve the dung beetle optimization algorithm, characterized in that: Here are the steps: A. Input the environment map and set the starting point and end point; B. Initialize the algorithm parameters; C. Optimize the initial population generation process in the dung beetle optimization algorithm by improving the Tent chaotic mapping, and calculate the fitness value of each dung beetle; D. Sort the dung beetle individuals according to their fitness values ​​and assign roles to them; E. Perform global search and local search on the dung beetles after role assignment, and select the one with the highest fitness value for saving according to the comparison of fitness values; F. Determine whether the convergence accuracy is reached. If so, the path and fitness value of the dung beetle with the highest fitness value among the N dung beetles are output as the optimal path and the optimal fitness value. If not, execute step G; G: Determine whether the maximum number of iterations has been reached. If so, the path and fitness value of the dung beetle with the highest fitness value among the N dung beetles are output as the optimal path and optimal fitness value. If not, execute step C and proceed to the next round of iteration.

2. The path planning method based on the multi-strategy fusion improved dung beetle optimization algorithm according to claim 1 is characterized in that: In step B, the parameters of the algorithm are initialized by setting the parameters of rolling, dancing, foraging, and the number of thief dung beetles in the dung beetle optimization algorithm.

3. The path planning method based on the multi-strategy fusion improved dung beetle optimization algorithm according to claim 1 is characterized in that: In step C, the initial population generation process in the dung beetle optimization algorithm is optimized by improving the Tent chaotic mapping to make the dung beetle population evenly distributed; Improve the Tent chaos map, the expression is as follows: In the formula, a is the chaotic mapping parameter, rand is a random number between 0 and 1, and k represents the kth point of the chaotic sequence path; Generate a value P of a specific distribution characteristic = [P (1) ,P (2) ,...,P (n) ], the generated value is used as the parameter value for population initialization, and the expression is as follows: X=P·(ub-lb)+lb The generated position falls within the boundary range. The expression is as follows:

4. The path planning method based on the multi-strategy fusion improved dung beetle optimization algorithm according to claim 3 is characterized in that: To improve the Tent chaos mapping, the steps are as follows: First generate an initial random number P (1) , the value is in the range [0,1]; Generate subsequent values ​​through an iterative process, and in each iteration, judge P (k) Is it greater than or less than a? If the current value P (k) is less than the preset parameter a, then the next value P (k+1) By calculating 2*(P (k) +0.1*rand) to get; If the current value is greater than or equal to a, then by calculating 2*(1-P (k) +0.1*rand)) to generate the next value; until the maximum number of iterations is reached.

5. The path planning method based on the multi-strategy fusion improved dung beetle optimization algorithm according to claim 1 is characterized in that: The maximum steering angle and number of turns of the robot in the planned route are added to the fitness function as penalty conditions. The expression is as follows: Where: x i and i are the location information of the path nodes. is the steering angle coefficient, N is the number of turns, and M is the size of the driving environment map; The direction vector of the robot moving from node i to node j is recorded as The direction vector from node j to the next node d is recorded as Maximum steering angle θ max The calculation formula is as follows:

6. The path planning method based on the multi-strategy fusion improved dung beetle optimization algorithm according to claim 5 is characterized in that: The path with the minimum fitness value is stored as the current global optimal path x_best, and its fitness value is stored as the current global optimal fitness value f_best.

7. The path planning method based on the multi-strategy fusion improved dung beetle optimization algorithm according to claim 1 is characterized in that: In the step D, the dung beetle individuals are sorted according to their fitness values, and the roles of the dung beetles are assigned at the same time, the steps are as follows: By updating the population, the global search is completed and the fitness value of each updated dung beetle is calculated; Sort by fitness value and reassign roles to the dung beetle population.

8. The path planning method based on the multi-strategy fusion improved dung beetle optimization algorithm according to claim 7 is characterized in that: In the step E, the dung beetles after the role assignment are searched globally and locally, and the one with the highest fitness value is selected and saved according to the comparison of fitness values. The steps are as follows: For the N dung beetles with the highest fitness, they are randomly re-initialized and the position of each dung beetle is updated to complete the local search; Calculate the fitness value for the N dung beetles; Compare N dung beetles, and by comparing the fitness values ​​of local search and global search, select the one with the larger fitness value to save.

9. The path planning method based on the multi-strategy fusion improved dung beetle optimization algorithm according to claim 8 is characterized in that: Update the location of each dung beetle. The steps are as follows: The position of the breeding dung beetles is updated, and the expression is as follows: X t+1 =X * +b1×(X t -Lb * )+b2×(X t -Ub * ); Among them, X * represents the optimal position from the beginning to this iteration, Lb * is the lower bound of the spawning area, Ub * It is the upper boundary of the spawning area; The position of the rolling dung beetle is updated as follows: Where: δ is a random number between [0,1], ST∈(0.5,1], when δ>ST, it means that the rolling ball dung beetle is in the global exploration stage, and the dung beetle will roll along the predetermined path to find the optimal solution; The position of the thief dung beetle is updated as follows: X t+1 =(X b +S×g×(|X t -X * |+|X t -X b |))·s; Among them, X t-1 Record the position state of the last iteration, S is a constant value, g is a 1×D random vector, X * Represents the optimal position from the beginning to this iteration. The position of the foraging dung beetle is updated as follows: X t+1 =X t +C1×(X t -Lb b )+C2×(X t -Ub b ) Among them, C1 and C2 are random numbers and (0,1) random vectors that obey normal distribution, respectively, and Lb b is the lower bound of the optimal foraging area, Ub b is the upper bound of the optimal foraging area.

10. The path planning method based on the multi-strategy fusion improved dung beetle optimization algorithm according to claim 1, characterized in that: In step G, when no new path is found in 20 consecutive iterations, it is judged that the convergence accuracy is reached, and the global optimal path x_best and its fitness value f_best are output. If a new path is found in less than 20 iterations, it is judged that the convergence accuracy is not reached, and step G is executed.

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