Mobile robot path planning method
By optimizing the whale optimization algorithm with logistic chaotic mapping, nonlinear convergence factor a, and adaptive spiral shape constant b, combined with bird migration navigation and path pruning, the problems of weak local search ability and poor convergence accuracy of the whale optimization algorithm in path planning are solved, and efficient and smooth path planning is achieved.
Patent Information
- Application Number
- CN202510746819.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-05
- Publication Date
- 2025-09-05
AI Technical Summary
The whale optimization algorithm has problems in path planning, such as weak local search capability and poor convergence accuracy, making it difficult to achieve efficient path planning in complex environments.
Logistic chaotic mapping is used to initialize the population, combined with the nonlinear convergence factor a and the adaptive spiral shape constant b, combined with the bird migration navigation method, and the whale individual position update formula and path pruning processing to optimize path planning.
The algorithm's search range and accuracy are improved, local optimal solutions are avoided, a smooth and short path is obtained, and the quality and feasibility of the path are improved.
Smart Images
Figure CN120593754A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of mobile robot path planning, and in particular to a mobile robot path planning method. Background Art
[0002] Path planning algorithms are a crucial component of robot navigation. They primarily involve the robot automatically planning a path from a starting point to a destination within a specific area. For point-to-point path planning, collision avoidance, low pathfinding cost, and short timescales are crucial. For full-coverage path planning, coverage must also be considered.
[0003] The Whale Optimization Algorithm (WOA) is a new heuristic optimization algorithm. It was inspired by the hunting behavior of humpback whales, which employ a unique spiral bubble web foraging strategy. The Whale Optimization Algorithm mimics this behavior to perform optimal search. This algorithm has advantages such as a simple structure, few parameters, and ease of implementation. Compared to other heuristic algorithms, the Whale Optimization Algorithm can converge to an optimal solution more quickly in certain situations and exhibits superior global search capabilities, making it promising for path planning in complex environments. While the Whale Optimization Algorithm has many advantages, it still suffers from relatively weak local search capabilities and poor convergence accuracy. Summary of the Invention
[0004] In view of the shortcomings of the prior art, the present invention provides a mobile robot path planning method.
[0005] In order to achieve the above object, the technical solution adopted by the present invention is: a mobile robot path planning method, comprising the following steps: S1: Initialize the whale optimization algorithm, set the algorithm parameters, use the Logistic Chaos Map to initialize the population, use the fitness function to obtain the fitness value of the whale at all positions, and determine the initial individual optimal position of the whale population and the global optimal position; S2: Construct the convergence factor a and calculate the coefficient vector A; S3: Update the individual whale positions according to the whale position update formula, use the two-dimensional grid map model to obtain the parameters of the feasible path from the starting point to the target point of the mobile robot, and obtain all feasible initial paths for each whale; S4: Calculate the fitness of the individual whale at the new position and compare it with the fitness of the original position. If the fitness of the new position is better than the fitness of the original position, update the individual optimal position of the whale population and update the global optimal position. S5: Randomly select several individuals from all whale populations as partners of a single whale, calculate the average position of the surrounding partners, and combine it with the individual's own position to obtain the new individual position; S6: Determine whether the algorithm has reached the maximum number of iterations. If so, execute step S7; otherwise, return to execute steps S2-S5; S7: Based on the global optimal position obtained by the whale optimization algorithm, a whale path with the minimum fitness value is selected as the preliminary optimal path for the mobile robot path planning; S8: Prune the preliminary optimal path to obtain the optimal path for mobile robot path planning.
[0006] As a preferred solution, in step S2, the calculation formula of the convergence factor a is: Among them, t is the current iteration number, t max is the maximum number of iterations; The calculation formula of the coefficient vector A is: A=2a×r1-a, where r1 is a random vector on [0, 1].
[0007] As a preferred solution, in step S1, the method for determining the initial individual optimal position and the global optimal position of the whale population is as follows: the position of each whale in the first iteration is set as the initial individual optimal position; and the fitness values of all whale individuals are compared, and the position of the whale individual with the minimum fitness value is taken as the global optimal position.
[0008] As a preferred solution, in step S3, the updating methods of the individual whale positions include shrinking encirclement, spiral predation and random search.
[0009] As a preferred solution, let p be a random number in [0, 1]; When p<0.5 and |A|>1, the update method of the whale's individual position is random search, and the whale's individual position update formula is: X(t+1)=X rand (t)-A×|C×X rand (t)-X(t)|, where t is the current iteration number, X rand (t) represents the position vector of an individual randomly selected from the current group, and the coefficient vector C is defined as: C = 2×r2; where r2 is a random number in [0,1]. When p < 0.5 and |A| ≤ 1, the update method of the whale's individual position is shrinkage and encirclement, and the update formula of the whale's individual position is: X(t+1) = X best (t)-A×|C×X best (t)-X(t)|, where X best Represents the current global optimal individual position vector; When p≥0.5, the update method of the whale's individual position is spiral predation, and the whale's position update formula is: X(t+1)=|X best (t)-X(t)|×e bl ×cos(2πl)+X best (t); where X best represents the current global optimal individual position vector, b is a constant used to limit the logarithmic spiral shape, and l is a random number between [-1, 1].
[0010] As a preferred solution, b is calculated using the following formula: Among them, b max is 2, b min is 0.1, t is the current iteration number, t max is the maximum number of iterations.
[0011] As a preferred solution, step S5 includes the following steps: Let the position of a random whale be z r , randomly select n individuals from all individuals as companions of this whale individual, and the position of the companion is z j ,j=(1,2...n), calculate the average position Z of all peers j . The weighted coefficient w is used to adjust the influence of the average position of the companions on the individual whale and update the individual whale position. The specific formula is as follows: z j =(1-w)z j +w×Z j Wherein, w is a constant between [0, 1].
[0012] The beneficial effects of this application are as follows: 1. The present invention uses logistic chaotic mapping to initialize the population, making the initialization population of the whale optimization algorithm more random and improving the population quality. The present invention uses a nonlinear convergence factor a to search for optimal solutions as much as possible in the early and middle stages of the algorithm to prevent the algorithm from falling into a local optimal solution; and then uses a bracketing search phase in the later stage of the algorithm to find the optimal solution of the algorithm and improve the convergence accuracy of the algorithm.
[0013] 2. The present invention uses an adaptive spiral shape constant, assigning a larger b value at the beginning of the iteration to expand the search range. As the number of iterations increases, the b value gradually decreases, favoring a more localized, precise search and improving algorithm accuracy. Finally, by integrating the bird's migratory navigation method, individual whales can determine their own movement direction based on the positions of their surrounding companions, avoiding blind searches in areas far from the optimal solution and improving the quality and stability of the algorithm.
[0014] 3. By pruning the initial optimal path and removing redundant inflection points, the resulting path becomes smoother and shorter, improving the quality and feasibility of the path. BRIEF DESCRIPTION OF THE DRAWINGS
[0015] Figure 1 It is a schematic diagram of the process of the present invention.
[0016] Figure 2 The convergence factor curves before and after improvement when the maximum number of iterations is 100.
[0017] Figure 3 The fitness and iteration number curves of the whale optimization algorithm before improvement, the algorithm of this application after improvement, the PSO algorithm and the genetic algorithm. DETAILED DESCRIPTION
[0018] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0019] This paper proposes a robot path planning method, analyzes the problems of low convergence accuracy of the whale optimization algorithm and falling into local optimality, and proposes corresponding solutions. In practical application, such as Figure 1 As shown, it specifically includes the following steps:
[0020] S1: Initialize the whale optimization algorithm, set the algorithm parameters, use the Logistic Chaos Map to initialize the population, use the fitness function to obtain the fitness value of the whale at all positions, and determine the initial individual optimal position of the whale population and the global optimal position.
[0021] The method for determining the initial individual optimal position and the global optimal position of the whale population in step S1 is as follows: the position of each whale in the first iteration is set as the initial individual optimal position; and the fitness values of all whale individuals are compared, and the position of the whale individual with the minimum fitness value is taken as the global optimal position.
[0022] In step S1, the algorithm parameters are set, the population is initialized using the Logistic Chaotic Map, and the initial individuals are randomly generated. The mathematical model is: y t+1 =μy t (1-yt ) Among them, μ is the control parameter, y t is the state variable of the system at the tth iteration;
[0023] The algorithm fitness function is: Where X=[X1,X2,...,X d ] is the position of a whale, d is the dimension of the vector, X i is the value of the vector in the i-th dimension.
[0024] S2: Construct the convergence factor a and calculate the coefficient vector A.
[0025] In step S2, the calculation formula of the convergence factor a is: Among them, t is the current iteration number, t max is the maximum number of iterations; The calculation formula of the coefficient vector A is: A=2a×r1-a, where r1 is a random vector on [0, 1].
[0026] S3: Update the individual position of the whale according to the whale's individual position update formula, use the two-dimensional grid map model to obtain the parameters of the feasible path from the starting point to the target point of the mobile robot, and obtain all feasible initial paths for each whale.
[0027] In step S3, the updating methods of individual whale positions include shrinking encirclement, spiral predation and random search.
[0028] Furthermore, let p be a random number in [0, 1]; When p<0.5 and |A|>1, the update method of the whale's individual position is random search, and the whale's individual position update formula is: X(t+1)=X rand (t)-A×|C×X rand (t)-X(t)|, where t is the current iteration number, X rand (t) represents the position vector of an individual randomly selected from the current group, and the coefficient vector C is defined as: C = 2×r2; where r2 is a random number in [0,1]. When p < 0.5 and |A| ≤ 1, the update method of the whale's individual position is shrinkage and encirclement, and the update formula of the whale's individual position is: X(t+1) = X best (t)-A×|C×X best (t)-X(t)|, where X best Represents the current global optimal individual position vector; When p≥0.5, the update method of the whale's individual position is spiral predation, and the whale's position update formula is: X(t+1)=|X best (t)-X(t)|×e bl ×cos(2πl)+X best (t); where X best represents the current global optimal individual position vector, b is a constant used to limit the logarithmic spiral shape, and l is a random number between [-1, 1].
[0029] Furthermore, b is calculated using the following formula: Among them, b max is 2, b min is 0.1, t is the current iteration number, t max is the maximum number of iterations.
[0030] S4: Calculate the fitness of the individual whale at the new position and compare it with the fitness of the original position. If the fitness of the new position is better than the fitness of the original position, update the individual optimal position of the whale population and update the global optimal position.
[0031] S5: Randomly select several individuals from all whale populations as partners of a single whale, calculate the average position of the surrounding partners, and combine it with the individual's own position to obtain the new individual position.
[0032] Step S5 includes the following steps: Let the position of a random whale be z r , randomly select n individuals from all individuals as companions of this whale individual, and the position of the companion is z j ,j=(1,2...n), calculate the average position Z of all peers j . The weighted coefficient w is used to adjust the influence of the average position of the companions on the individual whale and update the individual whale position. The specific formula is as follows: z j =(1-w)z j +w×Z j Wherein, w is a constant between [0, 1].
[0033] S6: Determine whether the algorithm has reached the maximum number of iterations. If so, execute step S7; otherwise, return to execute steps S2-S5;
[0034] S7: Based on the global optimal position obtained by the whale optimization algorithm, a whale path with the minimum fitness value is selected as the preliminary optimal path for the mobile robot path planning.
[0035] S8: Prune the preliminary optimal path to reduce the number of bends and obtain the optimal path for mobile robot path planning.
[0036] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with the present profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical content disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are still within the scope of the technical solution of the present invention.
Claims
1. A mobile robot path planning method, characterized in that: The following steps are involved: S1: Initialize the whale optimization algorithm, set the algorithm parameters, use the Logistic Chaos Map to initialize the population, use the fitness function to obtain the fitness value of the whale at all positions, and determine the initial individual optimal position of the whale population and the global optimal position; S2: Construct the convergence factor a and calculate the coefficient vector A; S3: Update the individual whale positions according to the whale position update formula, use the two-dimensional grid map model to obtain the parameters of the feasible path from the starting point to the target point of the mobile robot, and obtain all feasible initial paths for each whale; S4: Calculate the fitness of the individual whale at the new position and compare it with the fitness of the original position. If the fitness of the new position is better than the fitness of the original position, update the individual optimal position of the whale population and update the global optimal position. S5: Randomly select several individuals from all whale populations as partners of a single whale, calculate the average position of the surrounding partners, and combine it with the individual's own position to obtain the new individual position; S6: Determine whether the algorithm has reached the maximum number of iterations. If so, execute step S7; otherwise, return to execute steps S2-S5; S7: Based on the global optimal position obtained by the whale optimization algorithm, a whale path with the minimum fitness value is selected as the preliminary optimal path for the mobile robot path planning; S8: Prune the preliminary optimal path to obtain the optimal path for mobile robot path planning.
2. The mobile robot path planning method according to claim 1, wherein: In step S2, the calculation formula of the convergence factor a is: Among them, t is the current iteration number, t max is the maximum number of iterations; The calculation formula of the coefficient vector A is: A=2a×r1-a, where r1 is a random vector on [0, 1].
3. The mobile robot path planning method according to claim 1, wherein: The method for determining the initial individual optimal position and the global optimal position of the whale population in step S1 is as follows: the position of each whale in the first iteration is set as the initial individual optimal position; and the fitness values of all whale individuals are compared, and the position of the whale individual with the minimum fitness value is taken as the global optimal position.
4. The mobile robot path planning method according to claim 2, wherein: In step S3, the updating methods of individual whale positions include shrinking encirclement, spiral predation and random search.
5. The mobile robot path planning method according to claim 4, characterized in that: Let p be a random number in [0, 1]; When p<0.5 and |A|>1, the update method of the whale's individual position is random search, and the whale's individual position update formula is: X(t+1)=X rand (t)-A×|C×X rand (t)-X(t)|, where t is the current iteration number, X rand (t) represents the position vector of an individual randomly selected from the current population, and the coefficient vector C is defined as: C = 2 × r2; where r2 is a random number in [0, 1]; When p < 0.5 and |A| ≤ 1, the update method of the whale's individual position is shrinkage and encirclement, and the update formula of the whale's individual position is: X(t+1)=X best (t)-A×|C×X best (t)-X(t)|, where X best Represents the current global optimal individual position vector; When p≥0.5, the update method of the whale's individual position is spiral predation, and the whale's position update formula is: X(t+1)=|X best (t)-X(t)|×e bl ×cos(2πl)+X best (t); where X best represents the current global optimal individual position vector, b is a constant used to limit the logarithmic spiral shape, and l is a random number between [-1, 1].
6. The mobile robot path planning method according to claim 5, characterized in that: b is calculated using the following formula: Among them, b max is 2, b min is 0.1, t is the current iteration number, t max is the maximum number of iterations.
7. The mobile robot path planning method according to claim 1, wherein: In the step S5, The following steps are involved: Let the position of a random whale be z r , randomly select n individuals from all individuals as companions of this whale individual, and the position of the companion is z j ,j=(1,2...n), calculate the average position Z of all peers j . The weighted coefficient w is used to adjust the influence of the average position of the companions on the individual whale and update the individual whale position. The specific formula is as follows: With j =(1-in)with j +w×Z j Wherein, w is a constant between [0, 1].