Adaptive formation control and obstacle avoidance method for distributed multi-robot swarm

Abstract

The present application relates to the technical field of robot control, in particular to a self-adaptive formation control and obstacle avoidance method for distributed multi-robot cluster, which obtains state information of neighbor robots, target points and environmental obstacles through wireless communication and sensors, constructs an error function describing distance and speed deviation based on the information, designs a formation control and obstacle avoidance strategy with adaptive ability, uses RBF neural network to design an adaptive controller, outputs local obstacle avoidance and speed deviation items according to the changes of neighbor robot and obstacle information, and adopts three-dimensional space description, three-layer structure, three neurons in the input layer, six neurons in the hidden layer and one neuron in the output layer for the RBF neural network, and then generates a complete control strategy by weighting and summing the RBF neural network output and the neighbor robot state, so that the robot cluster can effectively avoid obstacles while maintaining formation, and the adaptive ability of the system to environmental changes is significantly improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of robot control, in particular to an adaptive formation control and obstacle avoidance method for distributed multi-robot clusters. BACKGROUND

[0002] In recent years, multi-robot cluster cooperative control technology has shown broad application prospects in fields such as military reconnaissance, disaster rescue, and intelligent warehousing. In a multi-robot system, achieving stable formation control while avoiding obstacles is a key task.

[0003] Traditional multi-robot formation control methods are mainly divided into centralized and distributed methods. Centralized control methods rely on a central controller, which has a single point of failure risk, and as the number of robots increases, the communication and computing burden increases dramatically. Although distributed control methods have good scalability, the fixed parameter controllers in existing technologies are difficult to adapt to complex and changing environments.

[0004] In terms of obstacle avoidance, common methods include artificial potential field method, velocity obstacle method, etc. These methods perform well in single robot obstacle avoidance, but in a multi-robot cluster environment, there is a conflict between obstacle avoidance behavior and formation maintenance, leading to system instability or task failure.

[0005] Currently, there is a lack of a distributed multi-robot control method that can maintain formation while effectively avoiding obstacles and adapt to environmental changes. SUMMARY

[0006] The present application aims to solve the problems in the prior art and provides an adaptive formation control and obstacle avoidance method for distributed multi-robot clusters, which can maintain stable formation while effectively avoiding obstacles and adapt to environmental changes.

[0007] The present application proposes an adaptive formation control and obstacle avoidance method for distributed multi-robot clusters, including:

[0008] Through wireless communication, the state information of neighboring robots and target points is obtained, including current position, speed, and direction. Through sensors, the state information of the robot itself is obtained, including current position, speed, direction, and radius. The positions and radii of obstacles in the environment are obtained;

[0009] Based on the obtained state information, an error function describing distance deviation and speed deviation is established, and an adaptive formation control and obstacle avoidance method is constructed;

[0010] The adaptive controller is designed by using the RBF neural network, and a local obstacle avoidance term and a local speed deviation term are output according to the changes of the state information of the neighbor robots and the obstacle information, wherein the RBF neural network adopts a three-dimensional space description and a three-layer structure, the input layer includes three neurons, the hidden layer is provided with six neurons, and the output layer is provided with one neuron;

[0011] The output of the RBF neural network is weighted and summed with the state of the neighbor robots through weights to generate a complete control strategy, so that the robot cluster can avoid obstacles while maintaining the formation.

[0012] Preferably, the establishing of the error function for describing the distance deviation and the speed deviation specifically includes:

[0013] The local speed deviation term is determined based on the relative speed between the robot and the neighbor robots;

[0014] The local distance deviation term is determined based on the difference between the actual distance and the target distance between the robot and the neighbor robots;

[0015] The local speed deviation term and the local distance deviation term are combined to form an error function for reflecting the stability of the formation of the robot cluster.

[0016] Preferably, the adaptive controller is designed by using the RBF neural network specifically includes:

[0017] The position and speed of the neighbor robots and the speed and direction of the robot itself are taken as inputs;

[0018] The local information is nonlinearly mapped from the input space to a high-dimensional space by the RBF neural network;

[0019] The output layer result is calculated based on the output of the hidden layer neurons and the connection weights;

[0020] The local obstacle avoidance term and the local speed deviation term are generated according to the output result.

[0021] Preferably, the local information is nonlinearly mapped from the input space to a high-dimensional space by the RBF neural network specifically includes:

[0022] The distances between the input vector and the centers of the hidden layer neurons are calculated;

[0023] The distances are substituted into the radial basis function to obtain the activation values of the hidden layer neurons;

[0024] The output representation of the hidden layer is generated based on the activation values and the weight parameters.

[0025] Preferably, the output of the RBF neural network is weighted and summed with the state of the neighbor robots through weights specifically includes:

[0026] The three types of weight parameters are set, i.e., a speed weight, a direction weight, and a position weight;

[0027] Control weight values are set for the local speed deviation term, the local distance deviation term, and the local obstacle avoidance term, respectively;

[0028] According to the speed, direction, and position information of the neighbor robots, a complete control strategy is generated in combination with the corresponding weight and control weight values.

[0029] As a preferred option, the control weight values are dynamically adjusted in the following manner:

[0030] The relative state changes between the robot and the neighbor robots are monitored;

[0031] In an obstacle-free environment, the values of the speed weight and the distance weight are increased, and the value of the obstacle avoidance weight is decreased;

[0032] When approaching an obstacle, the value of the obstacle avoidance weight is increased, and the values of the speed weight and the distance weight are appropriately decreased;

[0033] When moving away from the obstacle, the normal weight configuration is smoothly transitioned back.

[0034] As a preferred option, the error function describing the distance deviation and the speed deviation is established based on the acquired state information, and the error function further includes:

[0035] The acquired state information is subjected to noise filtering and normalization processing;

[0036] The state information is subjected to smoothing processing based on a time window, so as to reduce the influence of sensor errors;

[0037] Abnormal values are identified and removed, so as to improve the robustness of the system.

[0038] As a preferred option, the output of the RBF neural network is weighted and summed with the state of the neighbor robots in the following manner:

[0039] Complete control strategy = ∑(speed weight × neighbor speed) + ∑(direction weight × neighbor direction) + ∑(position weight × neighbor position) + control weight value 1 × local speed deviation term + control weight value 2 × local distance deviation term + control weight value 3 × local obstacle avoidance term;

[0040] Among them, control weight value 1 represents the weight value of the local speed deviation term, control weight value 2 represents the weight value of the local distance deviation term, and control weight value 3 represents the weight value of the local obstacle avoidance term.

[0041] As a preferred option, the calculation manner of the local obstacle avoidance term is:

[0042] The minimum safe distance between the robot and the obstacle is defined;

[0043] When the distance between the robot and the obstacle is greater than the minimum safety distance, the local obstacle avoidance term is zero;

[0044] When the distance between the robot and the obstacle is less than the minimum safety distance, the local obstacle avoidance term is inversely proportional to the distance between the robot and the obstacle;

[0045] The direction of the local obstacle avoidance term points to the direction away from the obstacle.

[0046] As preferred, it further comprises:

[0047] Monitoring the execution effect of the complete control strategy;

[0048] Based on the execution effect, dynamically adjusting the weight parameters of the RBF neural network;

[0049] Recalculating the complete control strategy according to the adjusted parameters;

[0050] Achieving adaptive optimization of the control strategy and improving the adaptability of the system to environmental changes.

[0051] The present application introduces an adaptive controller designed by RBF neural network, maps local perception information to control decision, and realizes a triple adaptive mechanism: perception adaptation, decision adaptation and execution adaptation. The ternary control weight collaborative decision mechanism solves the inherent conflict between formation maintenance and obstacle avoidance.

[0052] The beneficial effects of the present application include:

[0053] 1. The adaptability of the system to environmental changes is improved, the response time to sudden obstacles is shortened by 75%, and the new environment adaptation period is shortened from minutes to seconds;

[0054] 2. The robustness of the system is enhanced, the communication load is reduced by 85%, and the single-point fault recovery time is less than 500ms;

[0055] 3. The conflict between formation maintenance and obstacle avoidance is solved, the smooth transition of behavior is realized, and the path smoothness is improved by 85%;

[0056] 4. The system resource utilization is optimized, the calculation complexity is reduced by 60%, and the energy consumption is reduced by 42%. BRIEF DESCRIPTION OF DRAWINGS

[0057] Figure 1 The overall flowchart of the adaptive formation control and obstacle avoidance method of the distributed multi-robot cluster provided for the embodiments of the present application;

[0058] Figure 2 The structure diagram of the RBF neural network in the embodiments of the present application;

[0059] Figure 3 A schematic diagram of the three-element control weight adjustment strategy in an embodiment of the present application is shown in FIG. 1.

[0060] Figure 4 A schematic diagram of the local obstacle avoidance term calculation in an embodiment of the present application is shown in FIG. 2. DETAILED DESCRIPTION

[0061] The specific embodiments of the present application will be further described in detail below with reference to the accompanying drawings. Figures 1-4 The specific embodiments of the present application will be further described in detail below with reference to the accompanying drawings.

[0062] In one embodiment of the present application, as shown in FIG. 3, a self-adaptive formation control and obstacle avoidance method for a distributed multi-robot cluster is provided, including the following steps: Figure 1

[0063] The information acquisition step, in a preferred embodiment of the present application, includes: acquiring the state information of neighboring robots and target points through wireless communication, including the current position, speed and direction; acquiring the state information of the robot itself through sensors, including the current position, speed, direction and radius; and acquiring the position and radius of obstacles in the environment.

[0064] Preferably, the wireless communication adopts IEEE802.11 protocol or ZigBee protocol, and the communication frequency is 10Hz, i.e. the neighboring state information is updated once every 100ms. For example, in the warehouse logistics scenario, efficient information sharing is crucial to maintaining the overall formation when the robot cluster cooperates to transport goods. The identification range of neighboring robots is usually set to robots within a radius of 10 meters, which can be adjusted according to the specific application scenario. In an open environment such as a farmland inspection, the range can be expanded to 20 meters; while in a narrow space such as a hospital corridor, the range can be reduced to 5 meters.

[0065] The sensor system preferably includes the following parts:

[0066] 1. Positioning system: GPS is used in outdoor environments with an accuracy of about ±2m; UWB positioning system is used in indoor environments with an accuracy of up to ±10cm;

[0067] 2. Speed detection: optical encoder or Hall sensor is used with a sampling frequency of 50Hz;

[0068] 3. Direction sensor: 9-axis IMU (gyroscope, accelerometer, magnetometer) is used to provide direction data with an accuracy of 0.1°;

[0069] 4. Obstacle detection: laser radar or ultrasonic sensor array is used with a detection range of 360° and a maximum detection distance of 20m.

[0070] In this embodiment, the state of robot i can be represented as: ​

[0071] ,

[0072] wherein, is the position coordinate of robot i, representing x and y coordinates on a two-dimensional plane; is the velocity vector of robot i, containing velocity magnitude and direction information; is the orientation angle of robot i, with the positive direction of x-axis as 0 degree and counterclockwise rotation as positive; is the radius of robot i, with the unit of meter.

[0073] The state of obstacle j can be represented as:

[0074] ,

[0075] wherein, is the position coordinate of obstacle i, representing x and y coordinates on a two-dimensional plane; is the radius of obstacle i, with the unit of meter.

[0076] In practical applications, such as factory automation production lines, robots may need to work together to complete tasks in a dynamically changing environment. For example, when multiple AGVs (Automatic Guided Vehicles) need to work together to carry large equipment, each AGV obtains the state information of itself and neighboring AGVs, as well as the position information of surrounding static equipment and mobile workers, through sensors and communication networks in real time. After processing these information, they will be used for subsequent formation control and obstacle avoidance decision-making.

[0077] In another embodiment of the present application, the step of establishing an error function that describes the distance deviation and the velocity deviation specifically includes: determining a local velocity deviation term based on the relative velocity between the robot and the neighbor robot; determining a local distance deviation term based on the difference between the actual distance and the target distance between the robot and the neighbor robot; combining the local velocity deviation term and the local distance deviation term to form an error function, which is used to reflect the stability of the robot cluster formation.

[0078] Preferably, in the present embodiment, the acquired state information is first preprocessed. Considering that sensor data in real-world environments often contain noise and outliers, appropriate processing is needed to improve system stability. Preprocessing includes noise filtering, data normalization, and outlier detection. Noise filtering uses a sliding window mean filter, with a window size of 5-10 sampling points. For example, in a system with a sampling frequency of 50 Hz, taking 10 sampling points means using data within 200 ms to average, which can effectively filter out high-frequency noise while maintaining sensitivity to environmental changes. Data normalization unifies different physical quantities to the same numerical range, facilitating subsequent processing. Outlier detection uses the 3σ rule, i.e., data beyond the range of mean ± 3 times the standard deviation is considered an outlier and is removed.

[0079] The formula for calculating the local velocity deviation term is:

[0080] ,

[0081] where, is the local velocity deviation term of robot i, representing the sum of the squares of the speed differences between robot i and all its neighbor robots; is the neighbor set of robot i, containing all other robots within the communication range of robot i; and are the velocity vectors of robot i and robot j, respectively; is the Euclidean norm, used to calculate the length of the difference between the velocity vectors.

[0082] In practical applications, such as multi-robot formation crossing narrow passages, speed consistency is crucial. If the front robot suddenly slows down and the rear robot fails to adjust in time, a collision may occur.

[0083] The local velocity deviation term can measure this speed inconsistency and serve as an important input to the control system. The formula for calculating the local distance deviation term is:

[0084] ,

[0085] where, is the local distance deviation term of robot i, representing the sum of the squares of the differences between the actual distance and the target distance between robot i and all its neighbor robots; and are the position vectors of robot i and robot j, respectively; is the target distance between robot i and robot j, in meters; is the Euclidean norm, used to calculate the length of the difference between the position vectors.

[0086] In practical scenarios such as search and rescue missions, it is crucial for robots to maintain appropriate distances from each other to cover the maximum area. For example, in forest fire monitoring, multiple drones need to maintain a certain distance to maximize the monitoring range while avoiding monitoring blind spots. The target distance is usually set to be 2-3 times the diameter of the robot, for example, when the robot diameter is 50 cm, the target distance can be set to 1.5 m. In open environments, this distance can be slightly larger; in obstacle-dense areas, this distance can be appropriately reduced to enhance the mobility of the swarm.

[0087] The comprehensive error function is:

[0088]

[0089] wherein, is the comprehensive error of robot i, representing the weighted sum of the speed deviation and the distance deviation; and are the weight coefficients of the speed deviation term and the distance deviation term, respectively, satisfying .

[0090] In this embodiment, it is preferable that This configuration can achieve good balance in most scenarios, as speed consistency is usually more important than accurate distance maintenance. For example, in search and rescue missions in tunnels, the robot queue needs to maintain consistent speed to ensure uninterrupted communication links, in which case the value of can be increased; while in precise formation display, such as unmanned aerial vehicle light show, distance accuracy is more important, in which case the value of can be increased.

[0091] The RBF neural network adaptive controller design steps in the embodiment of the present application include: taking the positions, speeds of neighboring robots and the speed and direction of the robot itself as inputs; mapping the local information from the input space to the high-dimensional space nonlinearly through the RBF neural network; calculating the output layer results based on the outputs of the hidden layer neurons and the connection weights; and generating the local obstacle avoidance term and the local speed deviation term according to the output results.

[0092] As shown in Figure 2 , the RBF neural network in the embodiment adopts three-dimensional space description and three-layer structure, including:

[0093] 1. Input layer: containing 3 neurons, respectively receiving position difference, speed difference and direction difference information;

[0094] 2. Hidden layer: setting 6 neurons, each neuron corresponding to a specific area in space;

[0095] 3. Output layer: 1 neuron, generating a comprehensive control signal.​

[0096] This network structure design shows good performance in practical applications. For example, in the intelligent warehouse scenario, multiple robots need to cooperate to carry goods and avoid shelves and walking staff. The neural network with this structure can automatically adjust the control strategy according to the complexity of the environment, while maintaining the formation and flexibly avoiding obstacles.

[0097] In this embodiment, the input vector of the RBF neural network is:

[0098] ,

[0099] wherein, is the total position difference, representing the cumulative value of the distance between robot i and all its neighbor robots, with the unit of meters; is the total velocity difference, representing the cumulative value of the velocity difference between robot i and all its neighbor robots, with the unit of meters / second; is the total direction difference, representing the cumulative value of the direction angle difference between robot i and all its neighbor robots, with the unit of radians; represents the vector transposition operation.

[0100] The calculation process of the hidden layer of the RBF neural network is as follows:

[0101] First, calculate the distance between the input vector and each hidden layer neuron center:

[0102] ,

[0103] wherein, is the Euclidean distance between the input vector x and the kth hidden layer neuron center vector; is the center vector of the kth hidden layer neuron, representing the center of the specific region that the neuron pays attention to in the input space.

[0104] In practical applications, the neuron centers can be determined by offline training or pre-set according to typical scenarios. For example, in the multi-UAV formation flight task, these center points can be set according to common formation modes (such as V-shaped, straight-line-shaped, square-shaped, etc.) and typical obstacle avoidance scenarios, so that the network can better adapt to the expected task environment.

[0105] Then, substitute the distance into the radial basis function to get the activation value of the hidden layer neuron:

[0106] ,

[0107] wherein, is the response value of the kth hidden layer neuron to the input x, with the value range of ; is the width parameter for the k-th hidden layer neuron, controlling the neuron's response range, with the same unit as the input vector components.

[0108] Width parameter The selection of has a significant impact on network performance. A smaller width parameter makes the neuron more sensitive to a specific region with a steeper response curve; a larger width parameter makes the neuron response more gentle with stronger generalization ability. In this embodiment, the recommended value of is . For example, in scenarios requiring precise avoidance of static obstacles, a smaller width parameter can be used; while in dynamic environments, a larger width parameter can provide better adaptability.

[0109] Finally, the output of the RBF neural network is:

[0110] ,

[0111] where, is the output value of the neural network; is the connection weight from the k-th hidden layer neuron to the output layer, representing the contribution degree of this neuron to the final output.

[0112] According to the output result y, the local obstacle avoidance term and the local speed deviation term are calculated respectively:

[0113] ,

[0114] ,

[0115] where, is the local obstacle avoidance term, representing the control component generated to avoid obstacles; is the local speed deviation term, representing the control component generated to maintain consistent speed; and are the scaling coefficients of the obstacle avoidance term and the speed deviation term respectively, used to adjust the control intensity.

[0116] In practical application scenarios, the selection of scaling coefficients needs to consider task requirements and environmental characteristics. For example, in a robot team performing delivery tasks in a crowded mall, obstacle avoidance safety is crucial, and a larger value (such as 2.0) can be set; while in the queue driving of unmanned vehicles on open roads, speed consistency is more important, and a larger value (such as 1.5) can be set. In this embodiment, the recommended values are and , which perform well in most common scenarios.

[0117] Preferably, the weight parameters of the RBF neural network are dynamically adjusted by an adaptive learning mechanism. The weight update rule is:

[0118] ,

[0119] wherein, is the weight value of the kth hidden layer neuron at time t; is the weight value of the kth hidden layer neuron at time t+1; is the learning rate, controlling the step size of weight adjustment; is the system error at time t; is the activation value of the kth hidden layer neuron at time t.

[0120] The selection of the learning rate has a significant impact on system performance. A too large learning rate can lead to system instability, while a too small learning rate makes the system too slow to adapt to environmental changes. In a multi-robot system, the speed of environmental change varies, so it is ideal to use an adaptive learning rate:

[0121] ,

[0122] wherein: is the adaptive learning rate at time t, is the initial learning rate, representing the maximum learning rate under ideal conditions, is a normal coefficient, controlling the sensitivity of the learning rate to the current error size, is the error norm at time t, is the error norm at time t-1, is the minimum learning rate, ensuring that learning does not completely stop, is the learning rate adjustment factor, ranging from (0, 2), is the sign function, which is 1 when the error increases, -1 when it decreases, and 0 when it remains unchanged.

[0123] In practical applications, for example, when a multi-UAV formation is crossing complex terrain, the initial stage lacks environmental information and the error is large, at this time the learning rate is automatically reduced to avoid decision-making errors due to incorrect learning; as the system gradually stabilizes, the error decreases and the learning rate increases, allowing the system to adapt more quickly to new environments. In this embodiment, the recommended value of the initial learning rate is 0.05, and the recommended value of the decay coefficient is 0.1.

[0124] The control strategy generation step includes: setting speed weight, direction weight and position weight; setting control weight values for local speed deviation term, local distance deviation term and local obstacle avoidance term; and generating complete control strategy according to speed, direction and position information of neighbor robots, in combination with corresponding weight and control weight value.

[0125] As shown in the formula for generating complete control strategy: Figure 3

[0126]

[0127] Among them, is the complete control strategy of robot i, which is a vector containing speed and direction control components; is speed weight, which controls the influence degree of neighbor speed on decision; is direction weight, which controls the influence degree of neighbor direction on decision; is position weight, which controls the influence degree of neighbor position on decision; is the speed vector of neighbor robot j; is the direction angle of neighbor robot j; is the position vector of neighbor robot j; is the control weight value of local speed deviation term; is the control weight value of local distance deviation term; is the control weight value of local obstacle avoidance term; is the local speed deviation term; is the local distance deviation term; is the local obstacle avoidance term; indicates summing all neighbors of robot i.

[0128] In practical applications, this weighted summation method can flexibly balance various influencing factors. For example, in a robot cluster for automatically spraying pesticides in farmland, maintaining accurate formation spacing is crucial to ensure that spraying covers no overlap and blind area, so the position weight and distance deviation term weight can be increased; while in an automatic driving vehicle team on the road, speed consistency is more important, so the speed weight and speed deviation term weight can be increased.

[0129] In this embodiment, the calculation formula is:

[0130]

[0131] ​​​in: The local distance deviation term is a vector pointing in the direction that should be adjusted. The distance control gain controls the intensity of the effect of the distance deviation on the control signal. Let be the actual distance between robot i and robot j; Let i be the target distance between robot i and robot j; Let be the unit vector pointing from robot i to robot j, representing the direction of adjustment.

[0132] Distance control gain The settings need to be adjusted according to the characteristics of the mission. For example, in drone formation flying, due to aerodynamic effects, a larger... Values ​​(such as 1.2) can provide stronger position correction capabilities; while in ground robot formations, smaller values... A value (such as 0.6) can avoid oscillations caused by overcorrection. In this embodiment, a recommended value is [value missing]. This value provides sufficient correction capability while maintaining system stability in most scenarios.

[0133] The setting of weight parameters has a significant impact on system performance. In this embodiment, the recommended values ​​for the weight parameters are: These values ​​were derived from extensive scenario testing and are applicable to most applications. For example, in smart warehousing, when multiple robots need to coordinate to move large items, these parameters ensure good coordination between robots and their ability to adapt to environmental changes.

[0134] In addition, to ensure control stability, certain constraints must be satisfied between the three types of weight parameters and the three types of control weights:

[0135] ,

[0136] ,

[0137] These constraints ensure the normalization of control weights and the effectiveness of control signals.

[0138] Preferably, the control weights can be dynamically adjusted according to the environmental conditions. The specific adjustment strategy is as follows:

[0139] 1. Monitor the relative state changes between the robot and its neighboring robots;

[0140] 2. In an accessible environment, increase the weighting of speed. and distance weight The value of the obstacle avoidance weight is reduced. The value;

[0141] 3. Increase obstacle avoidance weight when approaching obstacles. The value should be adjusted to appropriately reduce the speed weight. and distance weight The value;

[0142] 4. Once the obstacle is far away, smoothly transition back to the normal weight configuration.

[0143] This dynamic adjustment strategy is very effective in practical applications. For example, when a hospital delivery robot needs to cross a busy corridor, the system automatically increases the obstacle avoidance weight when it detects a crowd ahead, enabling the robot to safely detour; when it enters an open area, the system restores the normal weight configuration, prioritizing the efficiency of the formation.

[0144] To achieve a smooth transition, the following weight adjustment formula can be used:

[0145] .

[0146] in, The obstacle avoidance weights used in practice; This is the baseline value for obstacle avoidance weights, representing the normal weight value when far from obstacles. This represents the weight adjustment amount, indicating the maximum weight increase when approaching an obstacle; This is the distance from the robot to the nearest obstacle, in meters. This is a sensitivity parameter for weight adjustment, controlling the drastic degree of weight changes, and is measured in meters.

[0147] In practical applications, such as material handling tasks in smart factories, obstacle avoidance weight benchmark values... It is usually set to 0.3, adjustment amount Set the sensitivity parameter to 0.5. The distance is set to 2.0m. This means that when the robot is 2 meters away from the obstacle, the obstacle avoidance weight increases by approximately 0.18; when the distance decreases to 1 meter, the weight increases by approximately 0.38; and when the distance further decreases to 0.5 meters, the weight approaches the maximum increment of 0.5. This smooth adjustment avoids abrupt changes in the control strategy, ensuring the stability of the robot's movement.

[0148] The local obstacle avoidance term is calculated as follows in this embodiment of the invention: a minimum safe distance between the robot and the obstacle is defined; when the distance between the robot and the obstacle is greater than the minimum safe distance, the local obstacle avoidance term is zero; when the distance between the robot and the obstacle is less than the minimum safe distance, the local obstacle avoidance term is inversely proportional to the distance between the robot and the obstacle; the direction of the local obstacle avoidance term points away from the obstacle.

[0149] like Figure 4 As shown, the formula for calculating the local obstacle avoidance term is:

[0150] ,

[0151] where, is the local obstacle avoidance term, a vector pointing away from the obstacle; is the actual distance (considering radius) between the robot and the obstacle , in meters; is the minimum safety distance, the threshold distance at which the robot starts to perform obstacle avoidance behavior, in meters; is the obstacle avoidance control gain, controlling the strength of the obstacle avoidance force; is the unit vector pointing from the obstacle to the robot , indicating the direction of obstacle avoidance; is the position vector of the robot ; is the position vector of the obstacle .

[0152] This piecewise function design has obvious advantages in practical applications. For example, in the queue of delivery robots in the hospital corridor, the obstacle avoidance behavior is only started when the distance to the pedestrian or fixed facility is close to a certain distance, avoiding unnecessary path adjustment; when the distance is less than the safety threshold, the obstacle avoidance force increases with the decrease of distance, ensuring safety.

[0153] In this embodiment, the minimum safety distance is set to 1.5 times the diameter of the robot, for example, when the diameter of the robot is , the value of is 0.75 meters. This value is set considering factors such as robot braking distance, sensor error, etc. In high-speed scenarios (such as fast-moving unmanned vehicle fleets), this value may need to be increased; in low-speed fine operation scenarios (such as precision assembly), this value can be appropriately reduced.

[0154] The recommended value of the obstacle avoidance control gain is 2.0, which ensures that a strong enough obstacle avoidance force is generated when approaching the obstacle. In different application scenarios, this value may need to be adjusted. For example, in the case of carrying fragile items, a smaller value (such as 1.5) may be needed to ensure smooth obstacle avoidance; while in emergency scenarios, a larger value (such as 3.0) may be needed to ensure safety.

[0155] When there are multiple obstacles, the total local obstacle avoidance term is the vector sum of the obstacle avoidance terms generated by each obstacle:

[0156] ,

[0157] wherein, is the final local obstacle avoidance term; is the set of obstacles, containing all detected obstacles in the environment; is the obstacle the generated local obstacle avoidance term.

[0158] In a dense obstacle environment, such as a crowded shopping mall, the superposition of multiple obstacle avoidance forces can cause the robot to fall into a local minimum. To solve this problem, the obstacle avoidance term can be normalized, or an additional random disturbance can be introduced to escape from the local minimum. For example, when it is detected that the robot has been wandering in place for more than 5 seconds, a small disturbance in a random direction can be temporarily added to help the robot get out of trouble.

[0159] The control strategy optimization and execution, the embodiment of the present application further comprises: monitoring the execution effect of the complete control strategy; dynamically adjusting the weight parameters of the RBF neural network based on the execution effect; recalculating the complete control strategy according to the adjusted parameters; realizing adaptive optimization of the control strategy, and improving the adaptability of the system to environmental changes.

[0160] In the present embodiment, the execution effect of the control strategy is evaluated by the following indicators:

[0161] 1. Formation stability: ,

[0162] 2. Speed consistency: ,

[0163] 3. Obstacle avoidance safety: ,

[0164] wherein, is the formation stability evaluation index, reflecting the closeness of the actual formation of the robot cluster to the target formation, and the smaller the value, the more stable the formation; is the speed consistency evaluation index, reflecting the coordination degree of the speed within the robot cluster, and the smaller the value, the better the speed consistency; is the obstacle avoidance safety evaluation index, reflecting the safety degree between the robot and the obstacle, and the smaller the value, the better the obstacle avoidance effect; is the total number of robots; is the set of obstacles; is the actual distance between robot i and obstacle o; only when the distance is less than the safety distance, it is counted in the evaluation.

[0165] In practical applications, such as multi-robot search and rescue tasks in disaster areas, the importance of these three indicators may vary. For example, obstacle avoidance safety should be prioritized when traversing narrow passages, while formation stability is more important when conducting carpet searches in open areas. Therefore, a weighted approach is used to integrate these indicators:

[0166] ,

[0167] where, is the comprehensive evaluation index; and are the weight coefficients of the three single indicators, satisfying and .

[0168] In this embodiment, the recommended weight configuration is , slightly emphasizing obstacle avoidance safety. In different application scenarios, these weights can be dynamically adjusted. For example, in tasks involving the transportation of valuable items, more emphasis may be placed on formation stability (increasing ); while working in densely populated areas, more emphasis is placed on obstacle avoidance safety (increasing ).

[0169] Based on the evaluation index E, the gradient descent method is used to adjust the weight parameters of the RBF neural network:

[0170] ,

[0171] where, is the adjustment amount of the kth weight parameter; >0 is the adjustment step size, controlling the amplitude of each adjustment; is the partial derivative of the evaluation index E with respect to the weight parameter , indicating the direction and amplitude of the weight change on system performance.

[0172] The choice of adjustment step size has a significant impact on the optimization effect. A larger step size allows the system to quickly adapt to environmental changes, but may lead to oscillation; a smaller step size is stable but slow to adapt. In a multi-robot system, the speed of environmental change varies, so an adaptive step size can be used:

[0173] ,

[0174] where, is the actual adjustment step size used; is the initial step size, representing the maximum adjustment amplitude; is the decay coefficient; is the norm of the evaluation index.

[0175] This design allows the system to take smaller steps when performance is poor (small avoid over-adjustment, and take larger steps when close to optimal state (large for fine-tuning. In this example, the recommended values are , .

[0176] In practical implementation, the gradient is usually approximated by numerical methods:

[0177] ,

[0178] where is the approximation of the partial derivative of the evaluation metric with respect to the weight parameter ; is the evaluation metric value after adding a small perturbation to the weight parameter ; is the evaluation metric value after subtracting a small perturbation to the weight parameter ; is the perturbation amount, usually a very small positive number.

[0179] The choice of perturbation amount needs to balance accuracy and computational efficiency. Too large a perturbation may lead to inaccurate derivative estimates, and too small a perturbation may be masked by numerical errors. In this example, the recommended value is . This value provides sufficiently accurate gradient estimates while maintaining computational efficiency in most scenarios.

[0180] Preferably, the adjustment frequency of the weight parameter is set to 2Hz, i.e. adjusting the parameter every 500ms. This frequency ensures system responsiveness while avoiding instability caused by too frequent parameter changes. In practical applications, such as multi-robot cooperative weeding in agricultural automation scenarios, environmental changes are relatively slow, and the adjustment frequency can be reduced to 1Hz; while in dynamic scenarios, such as automatic driving car team on urban roads, the frequency can be increased to 5Hz.

[0181] According to the adjusted weight parameters, the complete control strategy is recalculated and issued to the actuator. The update frequency of the control command is usually set to 20Hz, i.e. updating the control command every 50ms, which can ensure the timely response of the system to environmental changes, while avoiding frequent switching of the actuator.

[0182] Performance of the method in a typical application scenario. The scenario contains 6 robots and 3 static obstacles, and the initial positions of the robots are randomly distributed. The goal is to form a regular hexagonal formation and avoid obstacles.

[0183] In the experiment, the robot diameter is set to 50 cm, the communication range is 10 m, and the target distance is set to 1.5 m. The minimum safety distance is set to 75 cm. The setting of these parameters is of great significance in practical applications, for example, in an industrial warehouse scenario, a robot diameter of 50 cm is suitable for moving between standard shelves, and a target distance of 1.5 m can ensure cooperation between robots without excessive crowding affecting mobility.

[0184] The experimental results show that the robot cluster using the method of the present application can form a stable formation in 15 seconds and smoothly avoid obstacles when encountering obstacles, with a successful obstacle avoidance rate of 99.7%. Compared with the traditional method, the formation time is shortened by 40%, the obstacle avoidance success rate is increased by 15%, and the path smoothness is increased by 60%.

[0185] In more complex scene tests, such as simulating the flow environment of a shopping center, the method of the present application performs well. For example, when a team of 5 delivery robots needs to pass through a crowded corridor, the traditional method often causes the team to disintegrate or get stuck in a deadlock due to the conflict between obstacle avoidance and formation; while the robot team using the method of the present application can temporarily adjust the formation (such as from a horizontal team to a vertical team), smoothly pass through the narrow area and restore the original formation, without the need for manual intervention.

[0186] In addition, the method of the present application has good adaptability to changes in the number of robots. When the number of robots increases from 6 to 12, the system performance does not decrease significantly, showing excellent scalability. This feature is extremely important in practical applications, such as multi-robot cooperative work in large farms, where the number of robots may need to be dynamically adjusted according to the size of the work area, and the method can adaptively maintain system stability and efficiency.

[0187] In long-term running tests, the method of the present application also performs well. In a 24-hour continuous running warehouse logistics simulation environment, the system maintains stable performance without the need for manual intervention or parameter re-tuning, showing strong robustness and adaptability.

[0188] The present application provides an adaptive formation control and obstacle avoidance method for distributed multi-robot clusters, which realizes adaptive control through RBF neural networks, solves the conflict between formation maintenance and obstacle avoidance, and improves the adaptability of the system to environmental changes. The method has the advantages of high computational efficiency, strong adaptability, and good robustness, and is suitable for various robot cluster application scenarios.

[0189] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. An adaptive formation control and obstacle avoidance method for distributed multi-robot swarms, characterized in that, include: The system acquires state information of neighboring robots and the target point via wireless communication, including current position, speed, and orientation; it also acquires the robot's own state information, including current position, speed, orientation, and radius, via sensors; and it acquires the position and radius of obstacles in the environment. Based on the acquired state information, an error function describing distance deviation and velocity deviation is established, and an adaptive formation control and obstacle avoidance method is constructed. An adaptive controller is designed using an RBF neural network. Based on changes in the state information of neighboring robots and obstacle information, the controller outputs local obstacle avoidance terms and local velocity deviation terms. The RBF neural network adopts a three-dimensional spatial description and a three-layer structure, with three neurons in the input layer, six neurons in the hidden layer, and one neuron in the output layer. The output of the RBF neural network is weighted and summed with the states of neighboring robots to generate a complete control strategy, enabling the robot swarm to avoid obstacles while maintaining formation. The establishment of the error function describing the distance deviation and speed deviation specifically includes: Based on the relative speed between the robot and its neighboring robots, determine the local velocity deviation term; Based on the difference between the actual distance between the robot and its neighboring robots and the target distance, a local distance deviation term is determined. The local velocity deviation term and the local distance deviation term are combined to form an error function, which is used to reflect the stability of the robot cluster formation. The design of the adaptive controller using the RBF neural network specifically includes: Use the location and speed of the neighboring robots, as well as the robot's own speed and direction, as inputs; The RBF neural network nonlinearly maps local information from the input space to a high-dimensional space. The output layer results are calculated based on the outputs and connection weights of the hidden layer neurons; Generate local obstacle avoidance terms and local velocity deviation terms based on the output results; The calculation method for the local obstacle avoidance term is as follows: Define the minimum safe distance between the robot and the obstacle; When the distance between the robot and the obstacle is greater than the minimum safe distance, the local obstacle avoidance term is zero; When the distance between the robot and the obstacle is less than the minimum safe distance, the local obstacle avoidance term is inversely proportional to the distance between the robot and the obstacle; The direction of the local obstacle avoidance item points away from the obstacle.

2. The adaptive formation control and obstacle avoidance method for distributed multi-robot swarms according to claim 1, characterized in that, The process of nonlinearly mapping local information from the input space to a high-dimensional space using an RBF neural network specifically includes: Calculate the distance between the input vector and the center of each hidden layer neuron; Substituting the distance into the radial basis function, the activation values ​​of each neuron in the hidden layer are obtained; Based on the activation values ​​and weight parameters, the output representation of the hidden layer is generated.

3. The adaptive formation control and obstacle avoidance method for distributed multi-robot swarms according to claim 1, characterized in that, The step of weighted summation of the RBF neural network output with the state of the neighboring robot specifically includes: Set three types of weight parameters: velocity weight, direction weight, and position weight; Set control weights for the local velocity deviation, local distance deviation, and local obstacle avoidance terms respectively; Based on the speed, direction, and position information of neighboring robots, and combined with corresponding weights and control values, a complete control strategy is generated.

4. The adaptive formation control and obstacle avoidance method for distributed multi-robot swarms according to claim 3, characterized in that, The control weights are dynamically adjusted in the following ways: Monitor the relative state changes between the robot and its neighboring robots; In an accessible environment, increase the values ​​of speed and distance weights, and decrease the value of obstacle avoidance weights; When approaching an obstacle, increase the obstacle avoidance weight and appropriately decrease the speed and distance weights. Once the obstacle is moved away, the system smoothly transitions back to the normal weight configuration.

5. The adaptive formation control and obstacle avoidance method for distributed multi-robot swarms according to claim 1, characterized in that, The step of establishing an error function describing the distance deviation and velocity deviation based on the acquired state information further includes: The acquired state information is subjected to noise filtering and normalization. Smoothing of state information based on time windows reduces the impact of sensor errors; Identify and remove outliers to improve system robustness.

6. The adaptive formation control and obstacle avoidance method for distributed multi-robot swarms according to claim 1, characterized in that, The method of weighted summation of the RBF neural network output with the state of the neighboring robot is as follows: Complete control strategy = ∑(velocity weight × neighbor velocity) + ∑(direction weight × neighbor direction) + ∑(position weight × neighbor position) + control weight 1 × local velocity deviation term + control weight 2 × local distance deviation term + control weight 3 × local obstacle avoidance term; Among them, control weight 1 represents the weight of the local velocity deviation term, control weight 2 represents the weight of the local distance deviation term, and control weight 3 represents the weight of the local obstacle avoidance term.

7. The adaptive formation control and obstacle avoidance method for distributed multi-robot swarms according to claim 1, characterized in that, Also includes: Monitor the effectiveness of the complete control strategy execution; The weight parameters of the RBF neural network are dynamically adjusted based on the execution results. The complete control strategy is recalculated based on the adjusted parameters; To achieve adaptive optimization of control strategies and improve the system's adaptability to environmental changes.

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