Cooperative positioning adaptive motion control method and system based on PSO mixed output
By combining the GWO and PSO algorithms and using Tent mapping and nonlinear convergence factors to adjust particle positions, the problem of the PSO algorithm getting stuck in local extrema in high-dimensional complex scenes is solved, achieving a more efficient balance between global and local search, and improving the accuracy and robustness of the motion control system.
Patent Information
- Application Number
- CN202510663232.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-22
- Publication Date
- 2025-10-28
AI Technical Summary
In existing technologies, PSO algorithms are prone to getting stuck in local optima, especially in high-dimensional and complex scenarios. During collaborative localization, if multiple agents converge to the same local optimum too early, the system will lose diversity and will be unable to explore better solutions.
A collaborative positioning adaptive motion control method based on PSO hybrid output is adopted. Through the GWO and PSO collaborative optimization technology, combined with Tent mapping and nonlinear convergence factor, the particle position and velocity are adjusted to achieve a balance between global and local search, thereby improving the algorithm's search capability and convergence speed.
This effectively avoids the algorithm getting stuck in local optima in the early stages, improves the global search efficiency and convergence accuracy of the algorithm, and achieves accurate search and optimization in complex environments.
Smart Images
Figure CN120848168A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of motion control system technology, and particularly relates to a cooperative positioning adaptive motion control method and system based on PSO hybrid output. Background Technology
[0002] The PSO (Particle Swarm Optimization) hybrid output-based cooperative positioning adaptive motion control method is a motion control approach that combines particle swarm optimization (PSO) algorithms, cooperative positioning techniques, and adaptive control strategies. This method aims to optimize the parameters of the motion control system using PSO algorithms, achieve precise positioning and coordination among multiple moving bodies using cooperative positioning techniques, and combine adaptive control strategies to enable the system to adjust in real time to adapt to changes in the external environment. This method has significant advantages in improving the accuracy, robustness, and adaptability of motion control systems.
[0003] In existing technologies, PSO algorithms are prone to getting stuck in local optima, especially in high-dimensional and complex scenarios. During collaborative localization, if multiple agents converge to the same local optimum too early, the system will lose diversity and will be unable to explore better solutions.
[0004] Based on this, the present invention designs a cooperative positioning adaptive motion control method and system based on PSO hybrid output to solve the above problems. Summary of the Invention
[0005] The purpose of this invention is to address the problem that the existing PSO algorithm is prone to getting stuck in local optima, especially in high-dimensional complex scenarios. In cooperative localization, if multiple agents converge to the same local optimum too early, the system will lose diversity and be unable to explore better solutions. Therefore, this invention proposes a cooperative localization adaptive motion control method and system based on PSO hybrid output.
[0006] To achieve the above objectives, the present invention adopts the following technical solution: The cooperative positioning adaptive motion control method based on PSO hybrid output includes the following steps: S1: System modeling, establishing a mathematical model of the cluster motion control system; S2: Parameter initialization, randomly generate a certain number of particles, each particle represents a set of initial control parameters, and at the same time, initialize the parameters of the cooperative positioning system and the parameters of the adaptive control strategy; S3: Fitness assessment, based on GWO and PSO collaborative optimization technology, calculates the fitness value of each particle according to the system's performance indicators, including positioning accuracy, control stability and response speed; S4: Particle update. According to the update formula of the PSO algorithm, adjust the position and velocity of each particle, and at the same time, update the state of the cooperative behavior system and the parameters of the adaptive control strategy. S5: Iterative optimization, repeating the fitness evaluation and particle update steps until the stopping conditions are met, including reaching the maximum number of iterations and fitness value convergence; S6: Output the optimal solution, output the particle with the optimal fitness value, whose corresponding control parameters are the optimal parameters. At the same time, output the final state of the cooperative localization system and the parameters of the adaptive control strategy.
[0007] As a further description of the above technical solution: The moving body includes a host computer, which is a Raspberry Pi running the ROSRobot Operating System (Ubuntu). The moving body is composed of multiple built-in mechanical moving parts, each driven by a DC motor. A microcontroller sends different PWM waves to multiple motor drive control chips to drive the DC motors. The magnitude of the PWM waves controls the running speed of the multiple built-in mechanical moving parts, enabling the moving body to move straight, backward, turn left, and turn right according to a set schedule. Multiple collision detection switches are installed at the front of the moving body to detect collision information in front, to the left, and to the right of the moving body. A collision detection sensor system is installed at the bottom of the moving body to detect the distance between the moving body and the ground.
[0008] As a further description of the above technical solution: The main controller of the moving body is used to control the motor drive downwards, and to receive and collect data from the encoder and gyroscope, providing a control interface for the host computer ROSRobot Operating System and sending positioning information.
[0009] As a further description of the above technical solution: The main controller needs to receive speed information from the ROSRobot Operating System to control the movement speed of multiple mechanical moving parts of the differential motion body. The positioning information data obtained by the encoder and gyroscope built into the motion body after data fusion is fed back to the ROS host computer through the serial port. At the same time, the data from the collision detection sensing system, the bottom-touching and suspension sensor and the cliff sensor are also transmitted to the ROS host computer through this interface.
[0010] As a further description of the above technical solution: Establishing a mathematical model for the cluster motion control system includes the following steps: A moving part cluster consists of multiple individual moving parts, and the quantization expression of a moving part cluster is:
[0011] in, This represents the number of individual moving parts in a group of moving bodies. The moving bodies that make up the group are either heterogeneous or homogeneous, and multiple moving bodies maintain communication and interaction. The pose relationship between any two moving bodies at any given time is represented as:
[0012] In the formula, , and Representing moving bodies Current position and attitude angle, The distance between two moving bodies. For the movement body The deflection angle; To ensure the system can accurately control all moving bodies in the cluster, each moving body in the cluster needs to be matched before straight-line control. Based on the Euler-Lagrange principle, the dynamic model of a single moving body is established as follows:
[0013] In the formula, and These correspond to the inertia matrix and input matrix of the moving body, respectively. and These are the Coriolis matrix and center vector of a single moving body, respectively. and These represent the Lagrange multiplier and the input torque, respectively. Finally, multiple moving bodies are integrated to form a mathematical model of the moving body cluster by fusing the structural, motion characteristics and dynamic models.
[0014] As a further description of the above technical solution: The PSO algorithm is as follows: The essence of the PSO algorithm is that particles continuously change speed in a specific direction within a space volume, and find their next position through their own memory function and cluster communication, thereby obtaining the optimal solution. The update formulas for velocity and position are as follows:
[0015] .
[0016] As a further description of the above technical solution: The GWO algorithm optimization includes population initialization and nonlinear convergence factor based on the Tent chaotic mapping method; The population initialization content based on the Tent chaotic mapping method includes: The Tent mapping, through a simple mathematical iterative formula, can generate seemingly random but actually uniformly distributed sequences within a given interval. Introducing the Tent mapping into the GWO algorithm as a random number generation mechanism, the Tent formula is as follows:
[0017]
[0018] Pick , Then it means the first The second iteration The object in the first Information data on the dimension.
[0019] As a further description of the above technical solution: The nonlinear convergence factor includes: Global search capability is crucial for an algorithm to find its target, while local search capability determines its convergence speed. Therefore, the GWO algorithm needs to balance global and local search capabilities to achieve better optimization results and convergence factor. The size of determines the convergence ability of the algorithm. When the value is greater than 1, the gray wolf will try to find a more advantageous position to avoid prey, while when... When the value is less than 1, it will launch an attack in the hope of capturing its prey, according to... The value characteristic increases the time it takes for the gray wolf to converge to the target, thereby increasing the algorithm's ability to search local areas and improving its convergence ability, as shown in the following equation:
[0020] In the formula, and They represent the convergence factors, respectively. The starting point and the ending point, This represents the factor that adjusts the local search capability. Represents the number of iterations. Represents the maximum number of iterations; Improved The rate decreases non-linearly and reaches 0 after half the iterations. At this point, the wolves begin attacking their prey, performing a local search. In simple maps, the wolf pack can easily perform a global search, so a local search needs to be performed earlier. In complex maps, appropriate adjustments are necessary. The value of is increased, and the number of iterations is increased. By combining the overall performance of the algorithm with the properties of local search, the over-concentration on a specific target is prevented, thereby achieving the goal of precise search.
[0021] As a further description of the above technical solution: The hybrid strategy includes: A single swarm intelligence algorithm is limited by its own search capabilities, and when dealing with complex problems, it may suffer from low solution accuracy and be prone to getting trapped in local optima. Based on the individual memory characteristics of particle swarms, particle position updates are used instead of individual wolf position updates, making the gray wolf algorithm memorizable in optimization. Inertial weights are introduced. To adjust the parameters dynamically for global and local optimization in the GWO model. Then the velocity formula in the PSO algorithm becomes:
[0022] Inertia weight As a dynamically adjustable parameter, it can adaptively adjust the wolf pack's transition between global and local optimization based on the search needs at different stages. When the algorithm is in the initial exploration phase, a larger... The value prompts the wolf pack to traverse the solution space more extensively, enhancing their global search capabilities. However, as the search process deepens, the value gradually decreases. The value helps the wolf pack focus on potential optimal areas and improves local search accuracy. In this way, the GWO algorithm achieves the optimal balance between global search and local search.
[0023] A cooperative positioning adaptive motion control system based on PSO hybrid output includes: The system modeling module is used to establish the mathematical model of the cluster motion control system; The parameter initialization module is used to randomly generate a certain number of particles, each particle representing a set of initial control parameters. At the same time, it initializes the parameters of the cooperative positioning system and the parameters of the adaptive control strategy. The fitness evaluation module, based on GWO and PSO collaborative optimization technology, is used to calculate the fitness value of each particle according to the system's performance indicators, including positioning accuracy, control stability, and response speed. The particle update module is used to adjust the position and velocity of each particle according to the update formula of the PSO algorithm, and at the same time, update the state of the cooperative behavior system and the parameters of the adaptive control strategy. The iterative optimization module is used to repeatedly perform fitness evaluation and particle update steps until the stopping conditions are met. The stopping conditions include reaching the maximum number of iterations and fitness value convergence. The optimal solution output module is used to output the particle with the optimal fitness value, whose corresponding control parameters are the optimal parameters. At the same time, it outputs the final state of the cooperative localization system and the parameters of the adaptive control strategy.
[0024] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: 1. In this invention, the Tent mapping, through a simple mathematical iterative formula, can generate seemingly random but actually uniformly distributed sequences within a given interval. This characteristic allows the initial population generated based on the Tent mapping to cover a wider solution space, effectively avoiding the trap of falling into local optima in the early stages of the algorithm. Furthermore, the pseudo-randomness of the Tent mapping also means that the generated sequences have a certain degree of unpredictability, which helps the algorithm maintain sufficient exploration capabilities during the search process, thereby further improving the global search efficiency and convergence accuracy of the algorithm. Introducing the Tent mapping into the GWO algorithm as a random number generation mechanism is an effective means to improve algorithm performance and enhance population diversity.
[0025] 2. In this invention, the improved version The rate decreases non-linearly and reaches 0 after half the iterations. At this point, the wolves begin attacking their prey, performing a local search. In simple maps, the wolf pack can easily perform a global search, so a local search needs to be performed earlier. In complex maps, appropriate adjustments are necessary. The value of is increased, and the number of iterations is increased. By combining the overall performance of the algorithm with the properties of local search, the over-concentration on a specific target is prevented, thereby achieving the goal of precise search.
[0026] 3. In this invention, the accuracy of local search is improved. In this way, the optimal balance between global search and local search is achieved in the GWO algorithm, thereby improving the overall search capability and convergence speed of the algorithm, and finally achieving the best effect in solving complex optimization problems. Attached Figure Description
[0027] Figure 1 This is a flowchart illustrating the cooperative positioning adaptive motion control method and system based on PSO hybrid output proposed in this invention. Figure 2 This is a diagram showing the overall hardware framework of the motion control system of the cooperative positioning adaptive motion control method and system based on PSO hybrid output proposed in this invention. Detailed Implementation
[0028] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.
[0029] Please see the appendix Figure 1 -Appendix Figure 2This invention provides a technical solution: a cooperative positioning adaptive motion control method based on PSO hybrid output, comprising the following steps: S1: System modeling, establishing a mathematical model of the cluster motion control system; S2: Parameter initialization, randomly generate a certain number of particles, each particle represents a set of initial control parameters, and at the same time, initialize the parameters of the cooperative positioning system and the parameters of the adaptive control strategy; S3: Fitness assessment, based on GWO and PSO collaborative optimization technology, calculates the fitness value of each particle according to the system's performance indicators, including positioning accuracy, control stability and response speed; S4: Particle update. According to the update formula of the PSO algorithm, adjust the position and velocity of each particle, and at the same time, update the state of the cooperative behavior system and the parameters of the adaptive control strategy. S5: Iterative optimization, repeating the fitness evaluation and particle update steps until the stopping conditions are met, including reaching the maximum number of iterations and fitness value convergence; S6: Output the optimal solution, output the particle with the optimal fitness value, whose corresponding control parameters are the optimal parameters. At the same time, output the final state of the cooperative localization system and the parameters of the adaptive control strategy.
[0030] Specifically, the moving body includes a host computer, which is a Raspberry Pi running the ROSRobot Operating System (Ubuntu). The moving body is composed of multiple built-in mechanical moving parts, each driven by a DC motor. A microcontroller sends different PWM waves to multiple motor drive control chips to drive the DC motors. The magnitude of the PWM waves controls the running speed of the multiple built-in mechanical moving parts, enabling the moving body to move straight, backward, turn left, and turn right according to a set schedule. Multiple collision detection switches are installed at the front of the moving body to detect collision information in front, to the left, and to the right of the moving body. A collision detection sensor system is installed at the bottom of the moving body to detect the distance between the moving body and the ground.
[0031] Specifically, the main controller of the moving body is used to control the motor drive downwards, and to receive and collect data from the encoder and gyroscope, providing a control interface for the host computer ROSRobot Operating System and sending positioning information.
[0032] Specifically, the main controller needs to receive speed information from the ROSRobot Operating System and control the movement speed of multiple mechanical moving parts of the differential motion body. The positioning information data obtained by the encoder and gyroscope built into the motion body after data fusion is fed back to the ROS host computer through the serial port. At the same time, the data from the collision detection sensing system, the bottom-touching and suspension sensor and the cliff sensor are also transmitted to the ROS host computer through this interface.
[0033] Preferably, establishing a mathematical model for the cluster motion control system includes the following steps: A moving part cluster consists of multiple individual moving parts, and the quantization expression of a moving part cluster is:
[0034] in, This represents the number of individual moving parts in a group of moving bodies. The moving bodies that make up the group are either heterogeneous or homogeneous, and multiple moving bodies maintain communication and interaction. The pose relationship between any two moving bodies at any given time is represented as:
[0035] In the formula, , and Representing moving bodies Current position and attitude angle, The distance between two moving bodies. For the movement body The deflection angle; To ensure the system can accurately control all moving bodies in the cluster, each moving body in the cluster needs to be matched before straight-line control. Based on the Euler-Lagrange principle, the dynamic model of a single moving body is established as follows:
[0036] In the formula, and These correspond to the inertia matrix and input matrix of the moving body, respectively. and These are the Coriolis matrix and center vector of a single moving body, respectively. and These represent the Lagrange multiplier and the input torque, respectively. Finally, multiple moving bodies are integrated to form a mathematical model of the moving body cluster by fusing the structural, motion characteristics and dynamic models.
[0037] Preferably, the PSO algorithm is as follows: The essence of the PSO algorithm is that particles continuously change speed in a specific direction within a space volume, and find their next position through their own memory function and cluster communication, thereby obtaining the optimal solution. The update formulas for velocity and position are as follows:
[0038] .
[0039] Preferably, the GWO algorithm optimization includes population initialization and nonlinear convergence factor based on the Tent chaotic mapping method; The population initialization content based on the Tent chaotic mapping method includes: The Tent mapping, through a simple mathematical iterative formula, can generate seemingly random but actually uniformly distributed sequences within a given interval. Introducing the Tent mapping into the GWO algorithm as a random number generation mechanism, the Tent formula is as follows:
[0040]
[0041] Pick , Then it means the first The second iteration The object in the first Information data on the dimension; This characteristic allows the initial population generated based on the Tent mapping to cover a wider solution space, effectively avoiding the trap of falling into local optima in the early stages of the algorithm. Furthermore, the pseudo-randomness of the Tent mapping means that the generated sequence has a certain degree of unpredictability, which helps the algorithm maintain sufficient exploration ability during the search process, thereby further improving the global search efficiency and convergence accuracy of the algorithm. It is an effective means to improve algorithm performance and enhance population diversity.
[0042] Preferably, the nonlinear convergence factor includes: Global search capability is crucial for an algorithm to find its target, while local search capability determines its convergence speed. Therefore, the GWO algorithm needs to balance global and local search capabilities to achieve better optimization results and convergence factor. The size of determines the convergence ability of the algorithm. When the value is greater than 1, the gray wolf will try to find a more advantageous position to avoid prey, while when... When the value is less than 1, it will launch an attack in the hope of capturing its prey, according to... The value characteristic increases the time it takes for the gray wolf to converge to the target, thereby increasing the algorithm's ability to search local areas and improving its convergence ability, as shown in the following equation:
[0043] In the formula, and They represent the convergence factors, respectively. The starting point and the ending point, This represents the factor that adjusts the local search capability. Represents the number of iterations. Represents the maximum number of iterations; Improved The rate decreases non-linearly and reaches 0 after half the iterations. At this point, the wolves begin attacking their prey, performing a local search. In simple maps, the wolf pack can easily perform a global search, so a local search needs to be performed earlier. In complex maps, appropriate adjustments are necessary. The value of is increased, and the number of iterations is increased. By combining the overall performance of the algorithm with the properties of local search, the over-concentration on a specific target is prevented, thereby achieving the goal of precise search.
[0044] Preferably, the hybrid strategy includes: A single swarm intelligence algorithm is limited by its own search capabilities, and when dealing with complex problems, it may suffer from low solution accuracy and be prone to getting trapped in local optima. Based on the individual memory characteristics of particle swarms, particle position updates are used instead of individual wolf position updates, making the gray wolf algorithm memorizable in optimization. Inertial weights are introduced. To adjust the parameters dynamically for global and local optimization in the GWO model. Then the velocity formula in the PSO algorithm becomes:
[0045] Inertia weight As a dynamically adjustable parameter, it can adaptively adjust the wolf pack's transition between global and local optimization based on the search needs at different stages. When the algorithm is in the initial exploration phase, a larger... The value prompts the wolf pack to traverse the solution space more extensively, enhancing their global search capabilities. However, as the search process deepens, the value gradually decreases. The value helps the wolf pack focus on potential optimal areas and improves local search accuracy. In this way, the GWO algorithm achieves the optimal balance between global search and local search. By improving the accuracy of local search, the GWO algorithm achieves an optimal balance between global and local search, thereby enhancing its overall search capability and convergence speed, and ultimately achieving the best results in solving complex optimization problems.
[0046] A cooperative positioning adaptive motion control system based on PSO hybrid output includes: The system modeling module is used to establish the mathematical model of the cluster motion control system; The parameter initialization module is used to randomly generate a certain number of particles, each particle representing a set of initial control parameters. At the same time, it initializes the parameters of the cooperative positioning system and the parameters of the adaptive control strategy. The fitness evaluation module, based on GWO and PSO collaborative optimization technology, is used to calculate the fitness value of each particle according to the system's performance indicators, including positioning accuracy, control stability, and response speed. The particle update module is used to adjust the position and velocity of each particle according to the update formula of the PSO algorithm, and at the same time, update the state of the cooperative behavior system and the parameters of the adaptive control strategy. The iterative optimization module is used to repeatedly perform fitness evaluation and particle update steps until the stopping conditions are met. The stopping conditions include reaching the maximum number of iterations and fitness value convergence. The optimal solution output module is used to output the particle with the optimal fitness value, whose corresponding control parameters are the optimal parameters. At the same time, it outputs the final state of the cooperative localization system and the parameters of the adaptive control strategy.
[0047] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.
Claims
1. A cooperative positioning adaptive motion control method based on PSO hybrid output, characterized in that, Includes the following steps: S1: System modeling, establishing a mathematical model of the cluster motion control system; S2: Parameter initialization, randomly generate a certain number of particles, each particle represents a set of initial control parameters, and at the same time, initialize the parameters of the cooperative positioning system and the parameters of the adaptive control strategy; S3: Fitness assessment, based on GWO and PSO collaborative optimization technology, calculates the fitness value of each particle according to the system's performance indicators, including positioning accuracy, control stability and response speed; S4: Particle update. According to the update formula of the PSO algorithm, adjust the position and velocity of each particle, and at the same time, update the state of the cooperative behavior system and the parameters of the adaptive control strategy. S5: Iterative optimization, repeating the fitness evaluation and particle update steps until the stopping conditions are met, including reaching the maximum number of iterations and fitness value convergence; S6: Output the optimal solution, output the particle with the optimal fitness value, whose corresponding control parameters are the optimal parameters. At the same time, output the final state of the cooperative localization system and the parameters of the adaptive control strategy.
2. The cooperative positioning adaptive motion control method based on PSO hybrid output according to claim 1, characterized in that, The moving body includes a host computer, which is a Raspberry Pi running the ROSRobot Operating System (Ubuntu). The moving body is composed of multiple built-in mechanical moving parts, each driven by a DC motor. A microcontroller sends different PWM waves to multiple motor drive control chips to drive the DC motors. The magnitude of the PWM waves controls the running speed of the multiple built-in mechanical moving parts, enabling the moving body to move straight, backward, turn left, and turn right according to a set schedule. Multiple collision detection switches are installed at the front of the moving body to detect collision information in front, to the left, and to the right of the moving body. A collision detection sensor system is installed at the bottom of the moving body to detect the distance between the moving body and the ground.
3. The cooperative positioning adaptive motion control method based on PSO hybrid output according to claim 2, characterized in that, The main controller of the moving body is used to control the motor drive downwards, and to receive and collect data from the encoder and gyroscope, providing a control interface for the host computer ROSRobot Operating System and sending positioning information.
4. The cooperative positioning adaptive motion control method based on PSO hybrid output according to claim 3, characterized in that, The main controller needs to receive speed information from the ROSRobot Operating System to control the movement speed of multiple mechanical moving parts of the differential motion body. The positioning information data obtained by the encoder and gyroscope built into the motion body after data fusion is fed back to the ROS host computer through the serial port. At the same time, the data from the collision detection sensing system, the bottom-touching and suspension sensor and the cliff sensor are also transmitted to the ROS host computer through this interface.
5. The cooperative positioning adaptive motion control method based on PSO hybrid output according to claim 1, characterized in that, Establishing a mathematical model for the cluster motion control system includes the following steps: A moving part cluster consists of multiple individual moving parts, and the quantization expression of a moving part cluster is: ； in, This represents the number of individual moving parts in a group of moving bodies. The moving bodies that make up the group are either heterogeneous or homogeneous, and multiple moving bodies maintain communication and interaction. The pose relationship between any two moving bodies at any given time is represented as: ； in, , and Representing moving bodies Current position and attitude angle, The distance between two moving bodies. For the movement body The deflection angle; To ensure the system can accurately control all moving bodies in the cluster, each moving body in the cluster needs to be matched before straight-line control. Based on the Euler-Lagrange principle, the dynamic model of a single moving body is established as follows: ； in, and These correspond to the inertia matrix and input matrix of the moving body, respectively. and These are the Coriolis matrix and center vector of a single moving body, respectively. and These represent the Lagrange multiplier and the input torque, respectively. Finally, multiple moving bodies are integrated to form a structure, and the motion characteristics and dynamic models are fused to obtain a mathematical model of the moving body cluster.
6. The cooperative positioning adaptive motion control method based on PSO hybrid output according to claim 1, characterized in that, The PSO algorithm is as follows: The essence of the PSO algorithm is that particles continuously change speed in a specific direction within a space volume, and find their next position through their own memory function and cluster communication, thereby obtaining the optimal solution. The update formulas for velocity and position are as follows: ； 。 7. The cooperative positioning adaptive motion control method based on PSO hybrid output according to claim 6, characterized in that, The GWO algorithm optimization includes population initialization and nonlinear convergence factor based on the Tent chaotic mapping method; The population initialization content based on the Tent chaotic mapping method includes: The Tent mapping, through a simple mathematical iterative formula, can generate seemingly random but actually uniformly distributed sequences within a given interval. Introducing the Tent mapping into the GWO algorithm as a random number generation mechanism, the Tent formula is as follows: ； ； Pick , Then it means the first The second iteration The object in the first Information data on the dimension.
8. The cooperative positioning adaptive motion control method based on PSO hybrid output according to claim 7, characterized in that, The nonlinear convergence factor includes: Global search capability is crucial for an algorithm to find its target, while local search capability determines its convergence speed. Therefore, the GWO algorithm needs to balance global and local search capabilities to achieve better optimization results and convergence factor. The size of determines the convergence ability of the algorithm. When the value is greater than 1, the gray wolf will try to find a more advantageous position to avoid prey, while when... When the value is less than 1, it will launch an attack in the hope of capturing its prey, according to... The value characteristic increases the time it takes for the gray wolf to converge to the target, thereby increasing the algorithm's ability to search local areas and improving its convergence ability, as shown in the following equation: ； in, and They represent the convergence factors, respectively. The starting point and the ending point, This represents the factor that adjusts the local search capability. Represents the number of iterations. Represents the maximum number of iterations; Improved The rate decreases non-linearly and reaches 0 after half the iterations. At this point, the wolves begin attacking their prey, performing a local search. In simple maps, the wolf pack can easily perform a global search, so a local search needs to be performed earlier. In complex maps, appropriate adjustments are necessary. The value of is increased, and the number of iterations is increased. By combining the overall performance of the algorithm with the properties of local search, the over-concentration on a specific target is prevented, thereby achieving the goal of precise search.
9. The cooperative positioning adaptive motion control method based on PSO hybrid output according to claim 8, characterized in that, The hybrid strategy includes: A single swarm intelligence algorithm is limited by its own search capabilities, and when dealing with complex problems, it may suffer from low solution accuracy and be prone to getting trapped in local optima. Based on the individual memory characteristics of particle swarms, particle position updates are used instead of individual wolf position updates, making the gray wolf algorithm memorizable in optimization. Inertial weights are introduced. To adjust the parameters dynamically for global and local optimization in the GWO model. Then the velocity formula in the PSO algorithm becomes: ； Inertia weight As a dynamically adjustable parameter, it can adaptively adjust the wolf pack's transition between global and local optimization based on the search needs at different stages. When the algorithm is in the initial exploration phase, a larger... The value prompts the wolf pack to traverse the solution space more extensively, enhancing their global search capabilities. However, as the search process deepens, the value gradually decreases. The value helps the wolf pack focus on potential optimal areas and improves local search accuracy. In this way, the GWO algorithm achieves the optimal balance between global search and local search.
10. A cooperative positioning adaptive motion control system based on PSO hybrid output, wherein the cooperative positioning adaptive motion control method based on PSO hybrid output according to any one of claims 1-9 is characterized in that, include: The system modeling module is used to establish the mathematical model of the cluster motion control system; The parameter initialization module is used to randomly generate a certain number of particles, each particle representing a set of initial control parameters. At the same time, it initializes the parameters of the cooperative positioning system and the parameters of the adaptive control strategy. The fitness evaluation module, based on GWO and PSO collaborative optimization technology, is used to calculate the fitness value of each particle according to the system's performance indicators, including positioning accuracy, control stability, and response speed. The particle update module is used to adjust the position and velocity of each particle according to the update formula of the PSO algorithm, and at the same time, update the state of the cooperative behavior system and the parameters of the adaptive control strategy. The iterative optimization module is used to repeatedly perform fitness evaluation and particle update steps until the stopping conditions are met. The stopping conditions include reaching the maximum number of iterations and fitness value convergence. The optimal solution output module is used to output the particle with the optimal fitness value, whose corresponding control parameters are the optimal parameters. At the same time, it outputs the final state of the cooperative localization system and the parameters of the adaptive control strategy.