Formation obstacle avoidance method, system and device of multi-robot system and medium

Abstract

The invention discloses a multi-robot system formation obstacle avoidance method, system and device and a medium, and relates to the technical field of multi-mobile robot formation obstacle avoidance, the method comprises the following steps: the multi-robot system is divided into a first navigator, a second navigator and followers, and the first navigator obtains an obstacle avoidance path in an environment with obstacles by adopting an artificial force field method; the second navigator follows the obstacle avoidance path of the first navigator through trajectory tracking and keeps a determined distance; according to the obstacle avoidance path of the first navigator and the distance between the second navigator and the first navigator, the follower forms a formation with the first navigator and the second navigator through an azimuth angle information formation control method with speed estimation and follows the first navigator and the second navigator; the method is suitable for a multi-robot system of a navigator and a follower satisfying a corresponding quantitative relationship, and improves the formation stability when the multi-robot system encounters an obstacle.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-mobile robot formation obstacle avoidance, and particularly relates to a formation obstacle avoidance method, system, device and medium for a multi-robot system. Background Art

[0002] Compared with a single robot, a multi-robot system has advantages such as better parallelism, fault tolerance, and robustness, and can better complete tasks that a single robot cannot complete. Among them, mobile robots have the richest application scenarios and can be applied in scenarios such as intelligent inspection, warehousing logistics, and military activities. Therefore, the multi-mobile robot system has become a research hotspot in the current multi-robot system. On the one hand, multiple robots can achieve distributed control in space and time, with higher work efficiency and a wider working range. When the multi-robot system completes actual tasks, it is often required that the positions of multiple robots are relatively stable, so that the robots in the system can carry out information interaction and task assistance, thereby efficiently completing common tasks. Therefore, multi-mobile robot formation control is a basic research issue for application in actual scenarios, and subsequent related collaborations or other tasks need to be carried out on this basis. At the same time, when the multi-mobile robot system operates in a working environment, there will inevitably be obstacles. At this time, in order to enable the multi-mobile robot system to operate in a more complex working environment and expand the application scenarios of multi-mobile robots.

[0003] Currently, formation obstacle avoidance is achieved by switching between the formation strategy and the obstacle avoidance strategy in the multi-robot system. When there are no obstacles, a formation is formed under the formation strategy, and when obstacles are encountered, the obstacle avoidance strategy is switched. This method reduces the obstacle avoidance problem of the multi-robot system to the obstacle avoidance problem of a single robot. Combining the relatively mature research on single-robot obstacle avoidance has certain advantages, but it loses the relative stability of the overall formation during obstacle avoidance and cannot perform corresponding cooperation. Summary of the Invention

[0004] Aiming at the deficiency of the existing formation obstacle avoidance method that cannot maintain the stability of the formation when the multi-robot system encounters obstacles, the present invention proposes a formation obstacle avoidance method, system, device and medium for a multi-robot system. By dividing the multi-robot system into a first leader, a second leader and followers, where the first leader uses the artificial force field method to obtain a collision-free path in an environment with obstacles, the second leader realizes maintaining a certain distance from the first leader through trajectory tracking, and the followers form a formation with the first and second leaders and follow the movement through the azimuth angle information formation control method with speed estimation, thereby solving the problems existing in the prior art.

[0005] A formation obstacle avoidance method for a multi-robot system, the multi-robot system includes a first leader, a second leader and followers, and the formation obstacle avoidance method includes the following steps:

[0006] The first leader uses the artificial potential field method to obtain an obstacle avoidance path in an environment with obstacles;

[0007] The second leader follows the obstacle avoidance path of the first leader through trajectory tracking and maintains a certain distance from the first leader;

[0008] Within a set time, the follower estimates the speed of the first leader. Based on the estimated speed of the first leader and the certain distance between the second leader and the first leader, the azimuth angle information of the first leader and the azimuth angle information of the second leader following the first leader through trajectory tracking are obtained. According to the azimuth angle information of the first leader and the azimuth angle information of the second leader, the azimuth of the follower is determined using the minimum azimuth rigidity method, and then the formation of multiple robots is generated and obstacle avoidance is performed following the obstacle avoidance path.

[0009] Furthermore, the first leader uses the artificial potential field method to obtain an obstacle avoidance path in an environment with obstacles, which specifically includes the following steps:

[0010] Set a repulsive potential field U for the obstacles in the environment att , and set an attractive potential field U for the target point rep , which is expressed as:

[0011]

[0012] Among them, k att represents the gain coefficient, p tar represents the position of the target point, p represents the position of the robot, k rep represents the gain coefficient of the repulsive field, p obs represents the position of the obstacle, d o represents the range within which the obstacle can affect the robot, d represents the distance between the robot and the obstacle, is the introduced distance exponential function;

[0013] Superimpose the repulsive force generated by the repulsive potential field in the environment and the attractive force obtained by taking the partial derivative of the attractive potential field as the resultant force F tot (p) of the controller, and add the resultant force to the controller for motion solution of the mobile robot. Assume that there is a unique target point and n obstacles in the environment, represents the resultant force of the repulsive forces generated by all obstacles, and an obstacle avoidance path is obtained, which is specifically expressed as:

[0014]

[0015] Further, the distance exponential function is used to increase the gravitational force from the target point when the robot reaches within the obstacle range, enabling the robot to smoothly reach the target point; by determining whether the robot reaches a local extreme point, when it does, a randomly generated boundary force is introduced to make the robot leave the local extreme point it is currently trapped in; the determination condition is:

[0016]

[0017] where ε represents a minimum value, |ε|→0 indicates that the resultant force magnitudes of the two are equal; δ represents the cosine value of the angle between the gravitational force and the repulsive force, and δ→-1 indicates that their directions are opposite.

[0018] Further, the second leader follows the obstacle avoidance path of the first leader through trajectory tracking and maintains a determined distance from the first leader. Specifically, by controlling the input control quantities of the second leader, the tracking error is made to tend to zero, thereby achieving trajectory tracking; the input control quantities of the second leader include the angular velocity and linear velocity of the robot.

[0019] Further, making the tracking error tend to zero by controlling the input control quantities of the second leader, thereby achieving trajectory tracking, specifically includes the following steps:

[0020] Define the robot model as a unicycle model:

[0021]

[0022] where p i =(x, y, θ)∈R 2 ×[-π, π) represents the pose of the robot, (x, y) represents the coordinates of the center point of the robot, θ represents the direction angle of the unicycle relative to the inertial coordinate axes in the inertial coordinate system, v represents the linear velocity of the robot, ω represents the angular velocity of the robot, is the derivative of x, y, θ, and R 2 represents in the two-dimensional space;

[0023] The leader reference model is:

[0024]

[0025] where, (x r , t r , θ r )∈R 2 ×[-π, π) represents the pose of the leader, (x r , y r ) represents the coordinates of the center point of the leader, θ r represents the direction angle of the unicycle relative to the inertial coordinate axes in the inertial coordinate system, v rThe linear velocity of the leader, ω r represents the angular velocity of the leader; is the derivative of x r , y r , θ r .

[0026] With x e , y e , θ e representing the tracking error, the error model in the coordinates of the second leader is expressed as:

[0027]

[0028] Derive the error model:

[0029]

[0030] Design the local control law first and then the overall control law through the backstepping method, and the trajectory tracking control is obtained as:

[0031]

[0032] where k 1 , k 2 , k 3 , k 4 are variable parameters.

[0033] Furthermore, within the set time, the follower estimates the speed of the first leader, and the estimation process is expressed as:

[0034]

[0035]

[0036] where represents the follower i's estimation of the leader's speed; v L (t) represents the known leader's speed; represents the leader's speed estimation k ij (t), q i (t) represent the adaptive weights, are the derivatives of k ij , q ij respectively; m, n represent positive control gains; h ij represents the communication relationship between robots in the multi-robot formation; b i represents the leader's speed v L (t) that the follower can obtain. At this time, b i = 1, otherwise b i = 0.

[0037] Furthermore, the formation shape generation process of the multi-robots is expressed as:

[0038]

[0039] wherein, g ij represents the azimuth angle information of the current formation, i and j represent the robots in the multi-robot formation, represents the derivative of the pose p i of robot i, describes the closed-loop dynamic equation of the robot, represents the transformation relationship of the robot attitude; g ij = p j - p i / || p j - p i ||, p j represents the pose of robot j, represents the desired pose of robot j, represents the desired pose of robot i, represents the azimuth angle information of the desired formation, represents the estimated speed of the leader, k p and k h are gain coefficients.

[0040] The present invention also proposes a formation obstacle avoidance system for a multi-robot system. The multi-robot system includes a first leader, a second leader and followers. The formation obstacle avoidance system includes:

[0041] An obstacle avoidance path generation module, which is used for the first leader to obtain an obstacle avoidance path in an environment with obstacles by using the artificial potential field method;

[0042] A following module, which is used for the second leader to track and follow the obstacle avoidance path of the first leader through trajectory tracking and maintain a determined distance from the first leader;

[0043] A formation module, which is used for the followers to estimate the speed of the first leader within a set time, obtain the azimuth angle information of the first leader and the azimuth angle information of the second leader following the first leader through trajectory tracking according to the estimated speed of the first leader and the determined distance between the second leader and the first leader, and determine the azimuth of the followers based on the azimuth angle information of the first leader and the azimuth angle information of the second leader, and then generate the formation shape of the multi-robots and follow the obstacle avoidance path to avoid obstacles.

[0044] The present invention also provides a formation and obstacle avoidance computer device for a multi-robot system, comprising: a memory, a processor, and a computer program stored in the memory. When the processor executes the computer program, the steps of the formation and obstacle avoidance method for the multi-robot system are implemented.

[0045] The present invention also provides a readable storage medium storing a computer program, the computer program including program instructions which, when executed by a processor, are used to execute the steps of the formation and obstacle avoidance method for the multi-robot system.

[0046] The present invention provides a formation and obstacle avoidance method, system, device and medium for a multi-robot system, having the following beneficial effects:

[0047] The present invention decomposes the formation and obstacle avoidance problem for a multi-mobile robot system, hierarchically divides the obstacle avoidance and formation problems. Among them, the first and second leaders are responsible for the obstacle avoidance function part of the system, the followers are responsible for formation formation and following. The first leader uses the artificial force field method to obtain a collision-free path in an environment with obstacles, the second leader maintains a certain distance from the first leader through trajectory tracking. The followers form a formation with the first and second leaders and follow the movement through the azimuth angle information formation control method with speed estimation; this method is applicable to multi-robot systems with leaders and followers satisfying corresponding quantitative relationships, and is scalable in both the multi-robot system and shape, and is also transferable to the formation and obstacle avoidance problems of heterogeneous multi-robot systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a schematic diagram showing the difference between overall formation and obstacle avoidance and single-robot obstacle avoidance in an embodiment of the present invention;

[0049] Figure 2 It is a schematic diagram of the system architecture of the overall formation and obstacle avoidance method in an embodiment of the present invention;

[0050] Figure 3 It is a schematic diagram of control based on azimuth angle information and speed estimation in a multi-robot system in an embodiment of the present invention;

[0051] Figure 4 It is a schematic diagram under the Webots simulation environment in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0052] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments.

[0053] The present invention provides a multi-mobile robot formation and obstacle avoidance method, as Figure 1The difference between overall formation obstacle avoidance and individual robot obstacle avoidance is shown. The formation problem and obstacle avoidance problem of the multi-robot system are implemented by different control layers. The path is obtained through the obstacle avoidance method of the leader, and the followers' following of the leader realizes the purpose of multi-mobile robot formation obstacle avoidance in the obstacle environment. The formation obstacle avoidance problem of the multi-mobile robot system is decomposed, and the obstacle avoidance and formation problems are layered. Among them, the first and second leaders are responsible for the obstacle avoidance function part of the system, and the followers are responsible for formation formation and following. The formation obstacle avoidance problem of the multi-mobile robot system is described based on graph theory. In a system with N robots, it is represented by graph G=(v,ε), where v represents all vertices in the graph, that is, the set of robots, ε represents the set of edges connecting each vertex in the graph, representing the information interaction situation among the robots in the system; specifically, it includes the following steps:

[0054] S1. Manually set the force fields for the obstacles and targets in the environment, and use the improved artificial potential field method to generate corresponding control laws for the first leader, so as to generate an obstacle avoidance path in this obstacle environment, as Figure 2 shown.

[0055] Considering the obstacle avoidance path of the first leader under the improved artificial potential field method, the traditional artificial potential field method artificially adds a gravitational potential field and a repulsive potential field to the targets and obstacles in the environment. The distance between the robot and the target point in the traditional force field determines the magnitude of the gravitational potential field. As the distance between the robot and the target increases, the gravitational potential field increases. Conversely, as the distance decreases, the gravitational potential field weakens. Similarly, the distance between the robot and the obstacle determines the magnitude of the repulsive potential field. The closer the robot is to the obstacle, the greater the repulsive force. In the potential field environment, the robot is subject to the resultant force of the gravitational force from the target and the repulsive force from the obstacle, and a corresponding path is generated under the action of this resultant force. This path is a path that avoids obstacles and tends to the target. However, due to two inherent problems in the traditional artificial potential field method, one is the problem of target unreachability, that is, when there is an obstacle near the target point, when approaching the target point, the repulsive force from the obstacle is greater than the gravitational force from the target point, and the target point cannot be reached; the other is the local minimum problem. In the potential field movement, when the repulsive force and the gravitational force received are exactly equal in magnitude and opposite in direction, and the resultant force is 0, the robot falls into a local minimum and stops moving. In view of the above situation, the present invention adopts an improved artificial potential field to improve the problems of the above traditional artificial potential field method:

[0056]

[0057] where k att represents the gain coefficient, p tar represents the position of the target point, p represents the position of the robot, k rep represents the gain coefficient of the repulsive force field, p obsIndicates the position of the obstacle, d o Indicates the range within which the obstacle can affect the robot. d represents the distance between the robot and the obstacle. Is the introduced distance exponential function.

[0058] The repulsive force generated by the repulsive potential field in the environment is superimposed with the gravitational force obtained by taking the partial derivative of the gravitational potential field as the resultant force F of the controller tot (p), and the resultant force is added to the controller for motion resolution of the mobile robot. Assume that there is a single target point and n obstacles in the environment. Represents the resultant force of the repulsive forces generated by all obstacles, obtaining an obstacle avoidance path, specifically expressed as:

[0059]

[0060] By introducing the distance exponential function, when the robot reaches within the range of the obstacle, the gravitational force from the target point increases, enabling the robot to reach the target point more smoothly. In solving the problem of the target being unreachable, first judge whether it reaches the local extreme situation (in the artificial potential field method, it is easy to have a situation where the gravitational force and the repulsive force are exactly equal in magnitude and opposite in direction, but the target point has not been reached, and at this time, it falls into the local extreme situation). The judgment condition is:

[0061] F att +∑F rep =0

[0062]

[0063] cos(∠F att -∑F rep )=δ, δ→-1

[0064] Among them, ε represents a minimum value, |ε|→0 indicates that the magnitudes of the two resultant forces are equal; δ represents the cosine value of the angle between the gravitational force and the repulsive force, and δ→-1 indicates that they are opposite in direction.

[0065] The present invention judges whether the local extreme situation occurs by judging the above conditions, and introduces a randomly generated boundary force to enable the robot to leave the local extreme point it is currently trapped in, thus avoiding the problem that the robot cannot move forward when the resultant force is 0.

[0066] S2. According to the obstacle avoidance path of the first leader obtained in S1, perform trajectory tracking on the second leader, so that the second leader maintains a certain distance between the first and second leaders under the movement path of the first leader to control the size of the entire formation. The robot model adopted in the present invention is a unicycle model:

[0067]

[0068] Among them, p i =(x, y, θ) ∈ R 2 ×[-π, π) represents the pose of the robot, (x, y) represents the coordinates of the center point of the robot, θ represents the direction angle of the unicycle relative to the inertial coordinate axes in the inertial coordinate system, v represents the linear velocity of the robot, and ω represents the angular velocity of the robot. is the derivative with respect to x, y, and θ, and R 2 represents in the two-dimensional space;

[0069] The leader reference model is:

[0070]

[0071] Among them, (x r , y r , θ r ) ∈ R 2 ×[-π, π) represents the pose of the leader, (x r , y r ) represents the coordinates of the center point of the leader, θ r represents the direction angle of the unicycle relative to the inertial coordinate axes in the inertial coordinate system, v r represents the linear velocity of the leader, and ω r represents the angular velocity of the leader; is the derivative with respect to x r , y r , θ r ;

[0072] Taking x e , y e , θ e to represent the tracking error, the error model in the coordinates of the second leader is expressed as:

[0073]

[0074] Taking the derivative of the error model:

[0075]

[0076] By using the backstepping method to first design the local control law and then design the overall control law, the trajectory tracking control is obtained as:

[0077]

[0078]

[0079] Among them, k 1 , k 2 , k 3 , k 4 are variable parameters.

[0080] With this design, the second leader can follow the obstacle avoidance path of the first leader and maintain a certain distance, achieving the control of the overall formation.

[0081] S3. According to the path of the first leader obtained in S1 and the distance of the second leader in S2, design a formation following control algorithm for the follower based on azimuth information, so that the follower forms a definite formation under the constraints of the first and second leaders and follows the leaders to move. Finally, the control objective of the follower layer is to form a relevant formation under the relevant information of the first and second leaders and follow the obstacle avoidance path of the leaders and the determined size to move, as Figure 3 shown. Therefore, the control objective of the present invention for the follower is further split into two parts: one is to form a formation using azimuth information; the other is to follow the movement of the leader. When designing, first rewrite the unicycle model as:

[0082]

[0083] The present invention proposes the following follower formation control algorithm:

[0084]

[0085] After the follower forms a formation, it needs to move with the leader. Therefore, the algorithm includes an estimation of the leader's speed by the follower in a multi-robot system under finite time. Robots can estimate the leader's speed through information interaction. Therefore, only some follower robots need to obtain the information of the leader in the system. After estimating the speed in finite time, when forming a formation, when the desired formation is formed under azimuth information, we can get:

[0086]

[0087] That is to say, after forming the desired formation, it will move at the estimated leader's speed, realize forming the desired formation on the obstacle avoidance path of the first and second leaders and carry out the overall movement of the formation, and finally achieve the overall formation obstacle avoidance effect.

[0088] The present invention also provides a multi-mobile robot formation obstacle avoidance simulation verification system based on hierarchical control. The method includes the following steps (as Figure 4 shown):

[0089] S1. Generate an obstacle avoidance path for the first leader using an improved artificial potential field method based on a hierarchical control framework.

[0090] S2. Obtain relevant information of neighbor robots through the Supervisor node in the webots simulation platform for speed estimation.

[0091] S3. Design the formation control algorithm for the follower robots based on the azimuth information.

[0092] S4. Resolve the above control law into the speeds of the two wheels of the mobile robot to control the robot to implement the formation obstacle avoidance scheme.

[0093] Example: Manually set the potential fields for the obstacles and targets in the environment.

[0094] To obtain a path in the obstacle environment, the first leader needs to set a repulsive potential field for the obstacles in the environment to avoid collisions with the obstacles, and set an attractive potential field for the target point. The resultant force obtained by superimposing the repulsive force generated by the repulsive potential field and the attractive force generated by the attractive potential field is used as the design of the controller for the first leader to obtain an obstacle avoidance path. The manually designed potential fields are as follows:

[0095]

[0096] Superimpose the forces in the environment as the resultant force of the controller. Superimpose the repulsive forces generated by all the obstacles in the environment and the attractive force of the target point:

[0097]

[0098] Add the resultant force to the controller to perform the motion resolution of the mobile robot:

[0099]

[0100] Perform trajectory tracking according to the motion trajectory of the first leader and maintain a certain distance. Convert the global coordinate system to the tracking error model in the local coordinate system of the second leader. By controlling the input control quantities of the mobile robot such as the linear velocity and angular velocity, make the tracking error tend to zero to achieve trajectory tracking while maintaining a certain distance. Use the backstepping method to design the stability of the local system for the tracking in the y direction to obtain the conditions for the stability of the local subsystem, and then design the global tracking error system; among them, to maintain stability, the required control law can be obtained as follows:

[0101]

[0102] The followers estimate the speed of the first leader. Information can be exchanged among the followers. Therefore, only some followers can directly obtain the speed information of the leader to estimate the accurate speed information. Design the speed estimation algorithm for each mobile robot among the followers as follows:

[0103]

[0104] The follower layer uses azimuth information to determine a unique formation and uses the azimuth information control quantity to enable the follower to generate an expected formation of a determined size at the distances determined by the first and second leaders.

[0105]

[0106] A hierarchical control scheme is adopted. Verification is carried out under Webots simulation. The designed control law algorithm is converted into a discrete control law under discrete-time control and written into the corresponding controller as the control law for motion control. In the Webots environment, information about other robots can be obtained through the Supervisor node, and then distributed to each robot in the simulation platform through the message passing mode of Emitter / Receiver. Here, Emitter and Receiver are message channels encapsulated in the simulation environment. Each mobile robot has a separate controller such as Figure 4 , each robot conducts information interaction in the multi-robot system and has its own controller, so this simulation environment fully simulates the environment of distributed multi-mobile robot formation obstacle avoidance. Based on the above communication framework, the formation obstacle avoidance simulation of multi-mobile robots is carried out.

[0107] Based on the same inventive concept, the present invention also proposes a formation obstacle avoidance system for a multi-robot system, including:

[0108] An obstacle avoidance path generation module, which is used for the first leader to obtain an obstacle avoidance path in an environment with obstacles by using the artificial potential field method.

[0109] A following module, which is used for the second leader to follow the obstacle avoidance path of the first leader through trajectory tracking and maintain a determined distance from the first leader.

[0110] A formation module, which is used for the follower to estimate the speed of the first leader within a set time. According to the estimated speed of the first leader and the determined distance between the second leader and the first leader, the azimuth information of the first leader and the azimuth information of the second leader following the first leader through trajectory tracking are obtained. Based on the azimuth information of the first leader and the azimuth information of the second leader, the azimuth of the follower is determined by using the minimum azimuth rigidity method, and then the formation of the multi-robot is generated and obstacle avoidance is carried out following the obstacle avoidance path.

[0111] The present invention also proposes a formation obstacle avoidance computer device for a multi-robot system, including: a memory, a processor, and a computer program stored in the memory. When the processor executes the computer program, the steps of the formation obstacle avoidance method for the multi-robot system are implemented.

[0112] The present invention also provides a readable storage medium storing a computer program, the computer program including program instructions which, when executed by a processor, are used to perform the steps of the formation obstacle avoidance method for a multi-robot system.

[0113] The above are only the preferred specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention should cover the equivalent replacement or change made according to the technical solution and inventive concept of the present invention within the protection scope of the present invention.

Claims

1. A formation obstacle avoidance method for a multi-robot system, the multi-robot system comprising a first navigator, a second navigator and a follower, characterized in that: The formation obstacle avoidance method comprises the following steps: The first navigator uses the artificial force field method to obtain an obstacle avoidance path in an environment with obstacles; The second navigator follows the obstacle avoidance path of the first navigator through trajectory tracking and maintains a certain distance from the first navigator; Within the set time, the follower estimates the speed of the first navigator, and obtains the azimuth information of the first navigator and the azimuth information of the second navigator following the first navigator through trajectory tracking according to the estimated speed of the first navigator and the determined distance between the second navigator and the first navigator. According to the azimuth information of the first navigator and the azimuth information of the second navigator, the minimum azimuth rigidity method is used to determine the follower's orientation, and then a formation of multiple robots is generated and the follower follows the obstacle avoidance path to avoid obstacles.

2. The formation obstacle avoidance method of a multi-robot system according to claim 1, characterized in that: The first navigator uses an artificial force field method to obtain an obstacle avoidance path in an environment with obstacles, which specifically includes the following steps: Set a repulsive potential field U for obstacles in the environment att , set the gravitational potential field U for the target point rep , which is expressed as: Among them, k att represents the gain coefficient, p tar represents the position of the target point, p represents the position of the robot, k rep represents the gain coefficient of the repulsive field, p obs represents the location of the obstacle, d o represents the range in which the obstacle can affect the robot, d represents the distance between the robot and the obstacle, is the distance exponential function introduced; The repulsive force generated by the repulsive potential field in the environment and the gravitational force obtained by partial derivative of the gravitational potential field are superimposed as the resultant force F of the controller. tot (p), the resultant force is added to the controller to solve the motion of the mobile robot. Assuming that there is a unique target point and n obstacles in the environment, Represents the resultant repulsive force on all obstacles, and obtains an obstacle avoidance path, which is specifically expressed as:

3. The formation obstacle avoidance method of a multi-robot system according to claim 2, characterized in that: The distance exponential function is used to increase the gravitational force from the target point when the robot reaches the obstacle range, so that the robot can smoothly reach the target point; by judging whether the robot has reached the local extreme point, when reaching the local extreme point, the robot is allowed to leave the local extreme point where it is currently trapped by introducing randomly generated boundary forces; the judgment condition is: Among them, ε represents a minimum value, |ε|→0 means that the magnitude of the two forces is equal; δ represents the cosine value of the angle between attraction and repulsion, and δ→-1 means that the two forces are in opposite directions.

4. The formation obstacle avoidance method of a multi-robot system according to claim 1, characterized in that: The second navigator follows the obstacle avoidance path of the first navigator through trajectory tracking and maintains a certain distance from the first navigator, specifically by controlling the input control amount of the second navigator to make the tracking error approach zero, thereby achieving trajectory tracking; wherein the input control amount of the second navigator includes the angular velocity and linear velocity of the robot.

5. The formation obstacle avoidance method of a multi-robot system according to claim 4, characterized in that: The step of controlling the input control amount of the second navigator to make the tracking error approach zero, thereby achieving trajectory tracking, specifically includes the following steps: Define the robot model as a unicycle model: Among them, p i =(x,y,θ)∈R 2 ×[-π,π) represents the position of the robot, (x,y) represents the coordinates of the center point of the robot, θ represents the direction angle of the unicycle relative to the inertial coordinate axis in the inertial coordinate system, v represents the linear velocity of the robot, and ω represents the angular velocity of the robot. is the derivative of x, y, and θ, R 2 Represented in two-dimensional space; The navigator reference model is: Among them, (x r ,t r ,θ r )∈R 2 ×[-π,π) represents the position of the navigator, (x r ,y r ) represents the coordinates of the center point of the navigator, θ r represents the direction angle of the unicycle relative to the inertial coordinate axis in the inertial coordinate system, v r represents the linear velocity of the navigator, ω r represents the angular velocity of the leader; is x r ,y r ,θ r The derivation of x e ,y e ,θ e represents the tracking error, and the error model in the second navigator coordinates is expressed as: Derivative the error model: By backstepping, the local control law is designed first and then the overall control law is designed, and the trajectory tracking control is obtained as follows: Among them, k1, k2, k3, and k4 are changing parameters.

6. The formation obstacle avoidance method of a multi-robot system according to claim 1, characterized in that: The follower estimates the speed of the first leader within the set time, and the estimation process is expressed as: in, represents the follower i’s estimate of the leader’s speed; v L (t) represents the known pilot speed; Indicates the estimated speed of the pilot k ij (t), q i (t) represents the adaptive weight, are k ij ,q ij The derivative of; m, n represent positive control gains; h ij represents the communication relationship between robots in a multi-robot formation; b i Indicates the speed v of the leader that the follower can obtain L (t), at this time b i =1, otherwise b i =0.

7. The formation obstacle avoidance method of a multi-robot system according to claim 6, characterized in that: The multi-robot formation generation process is expressed as: in, g ij represents the azimuth information of the current formation, i and j represent the robots in the multi-robot formation, represents the position p of robot i i The derivation of The closed-loop dynamic equations of the robot are described. Indicates the transformation relationship of the robot posture; g ij =p j -p i / ||p j -p i ||, p j represents the position and posture of robot j, represents the desired posture of robot j, represents the desired posture of robot i, Indicates the azimuth information of the desired formation, represents the estimated leader speed, k p , k h is the gain factor.

8. A formation obstacle avoidance system for a multi-robot system, the multi-robot system comprising a first navigator, a second navigator and a follower, characterized in that: The formation obstacle avoidance system includes: The obstacle avoidance path generation module is used by the first navigator to obtain an obstacle avoidance path in an environment with obstacles using an artificial force field method; A following module, used for the second navigator to follow the obstacle avoidance path of the first navigator through trajectory tracking and maintain a certain distance from the first navigator; The formation module is used for the follower to estimate the speed of the first navigator within a set time, obtain the azimuth information of the first navigator and the azimuth information of the second navigator following the first navigator through trajectory tracking according to the estimated speed of the first navigator and the determined distance between the second navigator and the first navigator, determine the orientation of the follower according to the azimuth information of the first navigator and the azimuth information of the second navigator using the minimum orientation rigidity method, and then generate a formation of multiple robots and follow the obstacle avoidance path to avoid obstacles.

9. A computer device for formation obstacle avoidance of a multi-robot system, characterized in that: include: A memory, a processor, and a computer program stored in the memory, wherein when the processor executes the computer program, the steps of the formation obstacle avoidance method for a multi-robot system according to any one of claims 1 to 7 are implemented.

10. A readable storage medium, characterized in that: The readable storage medium stores a computer program, which includes program instructions. When the program instructions are executed by a processor, they are used to execute the steps of the formation obstacle avoidance method for a multi-robot system according to any one of claims 1 to 7.

Images