Permanent magnet synchronous linear motor multi-rotor path planning method based on ant colony algorithm

Abstract

The invention discloses a permanent magnet synchronous linear motor multi-rotor path planning method based on an ant colony algorithm, and the method comprises the following steps: A, forming a grid map of rotor motion according to a grid method, and coding the position of a grid; b, initializing basic parameters of the improved ant colony algorithm; c, calculating initialized pheromones in differentiated distribution; d, forming expected heuristic information according to the next to-be-selected grid and the end point of the ant; e, forming a transition probability according to the pheromone, the expected heuristic information and the corner heuristic function; f, judging whether all the broken ants arrive at the end point or not; if yes, ending the iteration, and updating the global pheromones and the local pheromones; otherwise, skipping to the step D; g, judging whether the current number of iterations is the maximum number of iterations, and if yes, outputting the current optimal solution; otherwise, skipping to the step C; according to the method, the defects in the prior art can be overcome, and the efficiency and accuracy of the ant colony algorithm in multi-mover path planning are optimized and improved.

Description

Technical Field

[0001] The present invention relates to the technical field of underground logistics path planning, in particular to a method for multi-motor path planning of a permanent magnet synchronous linear motor based on an ant colony algorithm. Background Art

[0002] With the accelerating pace of urbanization and the growing demand for urban logistics, traditional ground-based delivery methods face numerous challenges, including traffic congestion, pollution emissions, and low delivery efficiency. Underground logistics systems, as emerging urban logistics infrastructure, enable efficient and automated transportation of goods within cities by constructing independent underground transportation networks. This is expected to effectively alleviate ground traffic pressure and improve urban delivery efficiency. In underground logistics systems, permanent magnet linear synchronous motors (PMLSMs) are widely used to drive multi-motor systems due to their high thrust density, fast response speed, simple structure, and ease of multi-motor control. A "multi-motor" refers to multiple independent motor units that can operate on the primary track of the same motor. Each motor can serve as an independent transport platform to complete starting and ending points. However, as the number of motors increases, the system's scheduling and path planning problems become increasingly complex. Especially in underground environments with limited space resources, avoiding path conflicts and ensuring transportation efficiency are key issues that need to be addressed.

[0003] In the early stages, researchers primarily relied on graph theory and mathematical programming models for path search. Classic algorithms such as Dijkstra's algorithm and the A* algorithm (heuristic search algorithm) were widely used. These methods discretize the environment into a graph structure of nodes and edges and solve the problem by calculating the shortest path from the starting point to the target point. These methods work well in static environments, but are less efficient in dynamic environments or complex and changing scenarios, and lack the ability to adapt to environmental changes. With the development of technology, path planning problems have gradually taken into account more complex scenarios, including dynamic obstacles and unstructured environments. At this time, the research on path planning algorithms began to introduce some heuristic search and simulation optimization techniques, such as ant colony algorithms. These algorithms can not only handle static path problems, but also cope with some uncertain and dynamically changing environments. The ant colony algorithm imitates the process by which ants search for food paths and is suitable for solving complex path planning problems. It has shown good performance in multi-actuator collaborative path planning.

[0004] However, traditional ant colony algorithms also have some significant shortcomings in path planning. First, due to the fixed nature of pheromone volatility, the algorithm is prone to search stagnation and premature convergence during the search process. That is, after finding a relatively good path, the algorithm finds it difficult to jump out of that path to conduct a global search, thus limiting the algorithm's search capabilities and the diversity of solutions. Second, when choosing the next movement direction, traditional ant colony algorithms rely primarily on the pheromone concentration at the current location and a heuristic function. However, the heuristic function often only considers the distance between the next two nodes to be traveled. This results in the ants lacking a clear goal during their movement, increasing the blindness and time-consuming nature of the search. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a multi-movement path planning method for a permanent magnet synchronous linear motor based on an ant colony algorithm, which can solve the shortcomings of the existing technology and optimize and improve the efficiency and accuracy of the ant colony algorithm in multi-movement path planning.

[0006] In order to solve the above technical problems, the technical inventions adopted by the present invention are as follows.

[0007] A method for multi-movement path planning of a permanent magnet synchronous linear motor based on an ant colony algorithm comprises the following steps:

[0008] A. A grid map of the mover motion is formed according to the grid method. One grid represents one position node. The position of the grid is encoded from left to right and from top to bottom. The calculation formula for the sequence encoding of the mover in the grid map is: Among them, the coordinates of the mover are (x i ,y i ); X is the number of rows of the grid map; Y is the number of columns of the grid map; a is the side length of a grid; % is the redundant operator symbol; i is the grid code number occupied by the mover in the grid map.

[0009] B. Set the starting point S and end point E of the mover and initialize the basic parameters of the improved ant colony algorithm;

[0010] C. Initialization pheromones with differentiated distribution based on the ant’s starting point S and end point E as well as obstacle information;

[0011] D. Place m ants at the starting point S and start this iteration; form the expected heuristic information based on the ants' next candidate grid j and the end point E;

[0012] E. Forming transition probabilities based on pheromones, expected heuristic information, and corner heuristic functions;

[0013] F. Randomly select the next candidate grid j based on the transition probability; determine whether all m ants have reached the end point E; if so, end this iteration, update the global pheromone and local pheromone, and proceed to the next step; otherwise, jump to step D;

[0014] G. Determine whether the current number of iterations is the maximum number of iterations. If so, output the current optimal solution; otherwise, jump to step C.

[0015] Preferably, in step A, the positions of the grids are encoded from left to right and from top to bottom. The calculation formula for the sequence encoding of the mover in the grid map is: Among them, the coordinates of the mover are (x i ,y i ); X is the number of rows of the grid map; Y is the number of columns of the grid map; a is the side length of a grid; % is the redundant operator symbol; i is the grid code number occupied by the mover in the grid map.

[0016] Preferably, in step B, the mover is regarded as an individual ant, and the basic parameters include the total amount of pheromone Q released by the ant in one cycle, the pheromone factor α, the heuristic factor β, the global pheromone volatility factor adjustment coefficient r, the number of ants m, the maximum number of iterations Nmax, the local pheromone volatility factor σ, and the constant λ related to the grid map size.

[0017] As a preference, in step C, the initialization pheromone calculation formula is: where τ' ij (0) is the pheromone at time 0, i.e., the initialization pheromone; d is the distance from the next candidate network j of the ant to the line connecting the starting point S and the end point E; λ is a constant related to the size of the grid map, and its value is In the range of , W is the maximum length or width of the grid map size; τ0 is the initial pheromone of the environment; d m The grid map environment comprehensive evaluation value is calculated as follows:

[0018] As a preference, in step D, the calculation formula for the expected heuristic information is: Among them, η ij (t) is the heuristic information from the ant’s network i to the next candidate network j at time t; x j (t), y j (t) is the coordinate of the next selected grid j at time t; (x E ,y E ) are the coordinates of the end point E.

[0019] As an example, in step E, the calculation formula for the transition probability is:

[0020] , where τ′ ij (t) is the pheromone at time t, η ij (t) is the expected heuristic information, W ij is the corner heuristic function, and the calculation formula is j is the next candidate grid selected by the ant, allowed k is the set of grids to be selected by ants, is the probability that the mth ant selects the next candidate grid j from the current grid i at time t.

[0021] As a preferred method, in step F, the method for updating the global pheromone is:

[0022] Among them J gbest is the length of the current global optimal path; J best is the optimal path length in this iteration; J worst is the worst path length of this iteration; p bs is the current optimal path grid node information; p wS is the grid node information of the worst path in the current iteration; τ′ ij (t) is the pheromone at time t, τ′ ij (t+1) is the pheromone at time t+1; ρ is the global pheromone volatility factor, which ranges from [0,1], k is the adjustment coefficient, which is a positive number less than 1. SE is the Euclidean distance from the starting point S to the end point E.

[0023] As a preference, in step F, the method for updating the local pheromone is τ ij ′(t+1)=(1-σ)τ ij ′(t)+σQ, where τ′ ij (t) is the pheromone at time t, τ′ ij (t+1) is the pheromone at time t+1, and σ is the local pheromone volatility factor, which ranges from [0,1].

[0024] Preferably, in each iteration, the total amount Q of pheromones released by the ants in one cycle is updated in real time. The updating method is to set a first influencing factor and a second influencing factor, wherein the first influencing factor has a first weight, the second influencing factor has a second weight, and the sum of the first weight and the second weight is 1. J is the length of the path the ant has traveled this time. When the average pheromone concentration on the path the ant has traveled is greater than the average pheromone concentration on the grid map, the first impact factor is assigned a negative value. When the average pheromone concentration on the path the ant has traveled is less than the average pheromone concentration on the grid map, the first impact factor is assigned a positive value. The absolute value of the first impact factor is proportional to the deviation between the average pheromone concentration on the path the ant has traveled and the average pheromone concentration on the grid map. When the pheromone concentration of the ant's current path segment is greater than the pheromone concentration of the path segment closest to it, the second impact factor is assigned a negative value. When the pheromone concentration of the ant's current path segment is less than the pheromone concentration of the path segment closest to it, the second impact factor is assigned a positive value. The total impact factor K is obtained by weighted summing the first and second impact factors. The updated total pheromone amount is Q′=Q(1+K), |K|<1.

[0025] Preferably, the method for evaporating pheromones in a path segment is to set a basic pheromone evaporation rate, set a sliding window on a grid map to traverse the grid map, calculate the average pheromone concentration in the sliding window area, reduce the pheromone evaporation rate for path segments where the pheromone concentration in the sliding window is lower than the average pheromone concentration, and increase the pheromone evaporation rate for path segments where the pheromone concentration in the sliding window is higher than the average pheromone concentration.

[0026] The beneficial effects brought about by the above-mentioned technical invention are as follows: the present invention realizes efficient planning of multi-motor collaborative paths of permanent magnet synchronous linear motors in underground logistics by improving the ant colony algorithm, thereby optimizing path selection, reducing energy consumption, and improving system operation efficiency and intelligence level. The present invention accelerates the convergence of the algorithm and avoids local optimal solutions by using non-uniform initialization pheromone concentration and an enhanced direction guidance mechanism, while also using a new dynamic update algorithm for pheromones. In addition, the present invention also adds the distance from the candidate node to the target point to the heuristic function, thereby improving the purposefulness and efficiency of the path search. Finally, the present invention adopts a strategy that combines multiple transfer strategies for transfer, and ultimately can obtain the optimal path with a shorter distance and a relatively smooth path more quickly. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 Flowchart of the present invention.

[0028] Figure 2 This is a flow chart of adjusting the total amount of pheromones in the ant colony algorithm adopted in the present invention.

[0029] Figure 3 This is a flow chart of pheromone evaporation rate regulation in the ant colony algorithm adopted in the present invention.

[0030] Figure 4 This is a result diagram of the simulation experiment of the present invention.

[0031] Figure 5 This is a convergence curve diagram of the invention simulation experiment. DETAILED DESCRIPTION

[0032] A method for multi-movement path planning of a permanent magnet synchronous linear motor based on an ant colony algorithm comprises the following steps:

[0033] A. A grid map of the mover motion is formed according to the grid method. One grid represents one position node, and the position of the grid is encoded.

[0034] B. Set the start point S and end point E of the mover and initialize the basic parameters of the improved ant colony algorithm. Consider the mover as an individual ant. The basic parameters include the total amount of pheromone released per cycle Q, the pheromone factor α, the heuristic factor β, the global pheromone volatility adjustment coefficient r, the number of ants m, the maximum number of iterations Nmax, the local pheromone volatility factor σ, and the constant λ related to the grid map size.

[0035] C. The initialization pheromone is formed based on the starting point S and end point E of the ant and the obstacle information. The calculation formula of the initialization pheromone is: where τ′ ij (O) is the pheromone at time 0, i.e., the initialization pheromone; d is the distance from the next candidate network j of the ant to the line connecting the starting point S and the end point E; λ is a constant related to the size of the grid map, and its value is In the range of , W is the maximum length or width of the grid map size; τ0 is the initial pheromone of the environment; d m The grid map environment comprehensive evaluation value is calculated as follows:

[0036] D. Place m ants at the starting point S and start this iteration; form the expected heuristic information based on the ants' next selected grid j and the end point E. The calculation formula for the expected heuristic information is Among them, η ij (t) is the heuristic information from the ant’s network i to the next candidate network j at time t; x j (t), y j (t) is the coordinate of the next selected grid j at time t; (x E ,y E ) are the coordinates of the end point E.

[0037] E. Form the transition probability based on pheromone, expected heuristic information and corner heuristic function. The calculation formula of transition probability is: , where τ′ ij (t) is the pheromone at time t, η ij (t) is the expected heuristic information, W ij is the corner heuristic function, and the calculation formula is j is the next candidate grid selected by the ant, allowed k is the set of grids to be selected by ants, is the probability that the mth ant selects the next candidate grid j from the current grid i at time t.

[0038] F. Randomly select the next candidate grid j according to the transition probability; determine whether all m ants have reached the end point E; if so, end this iteration, update the global pheromone and local pheromone, and proceed to the next step; otherwise, jump to step D.

[0039] The method for updating global pheromone is

[0040] Among them J gbest is the length of the current global optimal path; J best is the optimal path length in this iteration; J worst is the worst path length of this iteration; p bs is the current optimal path grid node information; p wS is the grid node information of the worst path in the current iteration; τ′ ij (t) is the pheromone at time t, τ′ ij (t+1) is the pheromone at time t+1; ρ is the global pheromone volatility factor, which ranges from [0,1], k is the adjustment coefficient, which is a positive number less than 1. SE is the Euclidean distance from the starting point S to the end point E.

[0041] The method for updating local pheromones is τ ij ′(t+1)=(1-σ)τ ij ′(t)+σQ, where τ′ ij (t) is the pheromone at time t, τ′ ij (t+1) is the pheromone at time t+1, and σ is the local pheromone volatility factor, which ranges from [0,1].

[0042] In each iteration, the total amount of pheromone Q released by the ants in one cycle is updated in real time. The updating method is to set the first influencing factor and the second influencing factor. The first influencing factor has a first weight, the second influencing factor has a second weight, and the sum of the first weight and the second weight is 1. J is the length of the path the ant has traveled this time. When the average pheromone concentration on the path the ant has traveled is greater than the average pheromone concentration on the grid map, the first impact factor is assigned a negative value. When the average pheromone concentration on the path the ant has traveled is less than the average pheromone concentration on the grid map, the first impact factor is assigned a positive value. The absolute value of the first impact factor is proportional to the deviation between the average pheromone concentration on the path the ant has traveled and the average pheromone concentration on the grid map. When the pheromone concentration of the ant's current path segment is greater than the pheromone concentration of the path segment closest to it, the second impact factor is assigned a negative value. When the pheromone concentration of the ant's current path segment is less than the pheromone concentration of the path segment closest to it, the second impact factor is assigned a positive value. The total impact factor K is obtained by weighted summing the first and second impact factors. The updated total pheromone amount is Q'=Q(1+K), |K|<1.

[0043] After each iteration, the pheromone is evaporated. The method for pheromone evaporation on a path segment is to set a basic pheromone evaporation rate, set a sliding window on the grid map to traverse the grid map, calculate the average pheromone concentration within the sliding window area, reduce the pheromone evaporation rate for path segments where the pheromone concentration within the sliding window is lower than the average pheromone concentration, and increase the pheromone evaporation rate for path segments where the pheromone concentration within the sliding window is higher than the average pheromone concentration.

[0044] Due to the high density and numerous intersections of underground logistics routes, traditional ant colony algorithms focus on selecting the optimal path, while ignoring the potential interference that can arise when using multiple optimal routes simultaneously. By designing a new pheromone evaporation and update algorithm that dynamically adjusts pheromone concentrations along the route, the ant colony can balance the optimization of a single path and the coordination of multiple paths.

[0045] G. Determine whether the current number of iterations is the maximum number of iterations. If so, output the current optimal solution; otherwise, jump to step C.

[0046] Simulation experiment

[0047] For example Figure 4 The grid map shown above uses the above method to simulate path planning, and the optimal result is as follows: Figure 4 Shown in green path. Figure 5 The convergence curve of this simulation is given. It can be clearly seen that the multi-movement path planning method provided by the present invention can efficiently obtain the optimal path.

[0048] In the description of the present invention, it should be understood that the terms "longitudinal", "transverse", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0049] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for multi-motor path planning of permanent magnet synchronous linear motor based on ant colony algorithm, characterized in that The following steps are involved: A. A grid map of the mover motion is formed according to the grid method. One grid represents one position node, and the position of the grid is encoded. B. Set the starting point S and end point E of the mover and initialize the basic parameters of the improved ant colony algorithm; C. Initialization pheromones with differentiated distribution based on the ant’s starting point S and end point E as well as obstacle information; D. Place m ants at the starting point S and start this iteration; form the expected heuristic information based on the ants' next candidate grid j and the end point E; E. Forming transition probabilities based on pheromones, expected heuristic information, and corner heuristic functions; F. Randomly select the next candidate grid j based on the transition probability; determine whether all m ants have reached the end point E; if so, end this iteration, update the global pheromone and local pheromone, and proceed to the next step; Otherwise, jump to step D; G. Determine whether the current number of iterations is the maximum number of iterations. If so, output the current optimal solution. Otherwise, jump to step C.

2. The method for multi-movement path planning of a permanent magnet synchronous linear motor based on ant colony algorithm according to claim 1, characterized in that: In step A, the positions of the grids are encoded from left to right and from top to bottom. The formula for calculating the sequence encoding of the mover in the grid map is: Among them, the coordinates of the mover are (x i ,y i ); X is the number of rows of the grid map; Y is the number of columns of the grid map; a is the side length of a grid; % is the redundant operator symbol; i is the grid code number occupied by the mover in the grid map.

3. The method for multi-movement path planning of a permanent magnet synchronous linear motor based on ant colony algorithm according to claim 2, characterized in that: In step B, the mover is regarded as an individual ant. The basic parameters include the total amount of pheromone released by the ant in one cycle Q, the pheromone factor α, the heuristic factor β, the global pheromone volatility factor adjustment coefficient r, the number of ants m, the maximum number of iterations Nmax, the local pheromone volatility factor σ, and the constant λ related to the grid map size.

4. The method for multi-movement path planning of a permanent magnet synchronous linear motor based on ant colony algorithm according to claim 3, characterized in that: In step C, the initialization pheromone calculation formula is where τ' ij (O) is the pheromone at time 0, i.e., the initialization pheromone; d is the distance from the next candidate network j of the ant to the line connecting the starting point S and the end point E; λ is a constant related to the size of the grid map, and its value is In the range of , W is the maximum length or width of the grid map size; τ O is the initial pheromone of the environment; d m The grid map environmental comprehensive evaluation value is calculated as follows:

5. The method for multi-movement path planning of a permanent magnet synchronous linear motor based on ant colony algorithm according to claim 4, characterized in that: In step D, the calculation formula for expected heuristic information is Among them, η ij (t) is the heuristic information from the ant’s network i to the next candidate network j at time t; x j (t), y j (t) is the coordinate of the next selected grid j at time t; (x E ,y E ) are the coordinates of the end point E.

6. The method for multi-movement path planning of a permanent magnet synchronous linear motor based on ant colony algorithm according to claim 5, characterized in that: In step E, the calculation formula for the transition probability is where τ' ij (t) is the pheromone at time t, η ij (t) is the expected heuristic information, W ij is the corner heuristic function, and the calculation formula is j is the next candidate grid selected by the ant, allowed k is the set of grids to be selected by ants, is the probability that the mth ant selects the next candidate grid j from the current grid i at time t.

7. The method for multi-movement path planning of a permanent magnet synchronous linear motor based on ant colony algorithm according to claim 6, characterized in that: In step F, the method for updating the global pheromone is: Among them J gbest is the length of the current global optimal path; J best is the optimal path length in this iteration; J worst is the worst path length of this iteration; p bs is the current optimal path grid node information; p wS is the grid node information of the worst path in the current iteration; τ′ ij (t) is the pheromone at time t, τ′ ij (t+1) is the pheromone at time t+1; ρ is the global pheromone volatility factor, which ranges from [0,1], k is the adjustment coefficient, which is a positive number less than 1. SE is the Euclidean distance from the starting point S to the end point E.

8. The method for multi-movement path planning of a permanent magnet synchronous linear motor based on ant colony algorithm according to claim 6, characterized in that: In step F, the method for updating local pheromones is τ ij ′(t+1)=(1-σ)τ ij ′(t)+σQ, where τ′ ij (t) is the pheromone at time t, τ′ ij (t+1) is the pheromone at time t+1, and σ is the local pheromone volatility factor, which ranges from [0,1].

9. The method for multi-movement path planning of a permanent magnet synchronous linear motor based on ant colony algorithm according to claim 7 or 8, characterized in that: In each iteration, the total amount of pheromone Q released by the ants in one cycle is updated in real time. The updating method is to set the first influencing factor and the second influencing factor. The first influencing factor has a first weight, the second influencing factor has a second weight, and the sum of the first weight and the second weight is 1. J is the length of the path the ant has walked this time. When the average pheromone concentration on the path the ant has walked is greater than the average pheromone concentration on the grid map, the first impact factor is assigned a negative value. When the average pheromone concentration on the path the ant has walked is less than the average pheromone concentration on the grid map, the first impact factor is assigned a positive value. The absolute value of the first impact factor is proportional to the deviation between the average pheromone concentration on the path the ant has walked and the average pheromone concentration on the grid map. When the pheromone concentration of the ant's current path segment is greater than the pheromone concentration of the path segment closest to it, the second impact factor is assigned a negative value. When the pheromone concentration of the ant's current path segment is less than the pheromone concentration of the path segment closest to it, the second impact factor is assigned a positive value. The total impact factor K is obtained by weighted summing of the first impact factor and the second impact factor. The total amount of pheromone after update is Q'=Q(1+K), |K|<1.

10. The method for multi-movement path planning of a permanent magnet synchronous linear motor based on ant colony algorithm according to claim 9, characterized in that: The method for pheromone evaporation on path segments is to set the basic pheromone evaporation rate, set a sliding window on the grid map to traverse the grid map, calculate the average pheromone concentration within the sliding window area, reduce the pheromone evaporation rate for path segments where the pheromone concentration in the sliding window is lower than the average pheromone concentration, and increase the pheromone evaporation rate for path segments where the pheromone concentration in the sliding window is higher than the average pheromone concentration.

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