Multi-agent swarm obstacle avoidance method for complex obstacle fields

Abstract

The present application discloses a multi-agent cluster obstacle avoidance method suitable for complex obstacle fields. The method includes: determining the control factor of the action of the neighboring agent on the current agent; determining the control factor of the action of the obstacle on the current agent in the obstacle field; determining the control factor of the action of the target on the current agent; according to the control factor of the action of the neighboring agent on the current agent, the control factor of the action of the obstacle on the current agent, and the control factor of the action of the target on the current agent, obtaining the control parameters for the next moment of the current agent, and controlling the motion of the current agent according to the control parameters. The present application can realize the cluster obstacle avoidance control of multiple agents, and solves the problem of the agent being captured by the boundary of the polygonal obstacle.

Description

Technical Field

[0001] The present application relates to the field of collaborative control of multi-agent systems, and in particular to a multi-agent cluster obstacle avoidance method suitable for complex obstacle fields. Background Art

[0002] With the development of navigation technology, communication technology, control technology and artificial intelligence technology, more and more intelligent equipment such as drones, unmanned vehicles and unmanned boats will go to the battlefield in the future, taking on tasks such as reconnaissance, vigilance, nuclear, biological and chemical detection, ammunition supply, personnel rescue, equipment repair, and even becoming a member of the main combat equipment. A multi-agent system composed of multiple drones, unmanned vehicles or unmanned boats can replace soldiers to perform combat tasks and minimize casualties. For multi-agent systems put into the battlefield, it is necessary to give full play to the scale effect of the cluster and avoid too many individuals from wandering in the group. In addition, it is also necessary to be able to quickly cross complex obstacle fields while maintaining the cluster as much as possible. Especially on the ground battlefield, the multi-agent system not only faces traditional obstacles such as blocking walls, barbed wire, triangular cones, trenches, etc., but also needs to bypass the obstacles formed by bunkers, weapons and equipment on the path. Therefore, cluster obstacle avoidance technology is the key to improving the adaptability of multi-agent groups on the ground battlefield. Summary of the invention

[0003] The purpose of this application is to solve at least one of the above technical problems to a certain extent. To this end, one purpose of this application is to propose a multi-agent cluster obstacle avoidance method suitable for complex obstacle fields. The method can realize cluster obstacle avoidance control of multi-agents and solve the problem of agents being captured by the boundaries of polygonal obstacles.

[0004] To achieve the above objectives, an embodiment of the present application proposes a multi-agent cluster obstacle avoidance method suitable for complex obstacle fields, including:

[0005] Determine the current position and speed of each agent in the multi-agent cluster, and determine the neighboring agents of the current agent based on the position;

[0006] Based on the action function between the agents, the position and the speed, obtaining the action control factor of the neighboring agent on the current agent;

[0007] Obtaining the distance between the current intelligent agent and each obstacle in the obstacle field, and identifying a repelling obstacle relative to the current intelligent agent from the obstacles according to the distance;

[0008] Generate a virtual agent based on the repulsive obstacle, and determine the position and speed of the virtual agent; wherein the virtual agent is used to simulate the normal force of the repulsive obstacle on the current agent;

[0009] Based on the action function between the agent and the obstacle, the position and speed of the virtual agent, and the position and speed of the current agent at the current moment, obtaining the action control factor of the obstacle repelling agent on the current agent;

[0010] Determine the position and speed of the target, and obtain a control factor of the target's effect on the current agent based on the current position and speed of the current agent and the position and speed of the target;

[0011] According to the control factor of the neighboring agent on the current agent, the control factor of the repulsion obstacle on the current agent, and the control factor of the target on the current agent, the control parameters for the current agent at the next moment are obtained, and the motion of the current agent is controlled according to the control parameters.

[0012] In some embodiments of the present application, the obtaining of the control factor of the action of the neighboring agent on the current agent based on the action function between the agents, the position and the speed includes:

[0013] Based on the impact function and the current position of each agent, obtaining a spatial adjacency matrix between each agent;

[0014] Acquire the action function between the agents based on the impact function;

[0015] Based on the spatial adjacency matrix, the action functions between the agents, and the positions and velocities of the agents at the current moment, the action control factors of the neighboring agents on the current agent are obtained.

[0016] In some embodiments of the present application, the impact function is expressed as follows:

[0017]

[0018] The σ-norm of the vector is defined as

[0019] The spatial adjacency matrix between the agents is expressed by the following formula:

[0020] A(q)=[a ij (q)], where

[0021] Among them, q j is the position of the jth agent, q i is the current agent's position, r α =||r||α ;

[0022] The interaction function between the agents is expressed by the following formula:

[0023]

[0024] in, d α =||d|| σ ;

[0025] The control factor of the neighboring agent on the current agent is expressed by the following formula:

[0026]

[0027] in, is a fixed value, and the following relationship exists Vector i,j Solve by the following formula:

[0028] In some embodiments of the present application, obtaining the distance between the current agent and each obstacle in the obstacle field includes:

[0029] Constructing a polygonal geometric model of each obstacle body, and determining the center point and radius of the circumscribed circle of each polygonal obstacle body based on the polygonal geometric model;

[0030] Determine the center and radius of the circumscribed circle of the current agent;

[0031] Calculate the distance between the current intelligent body and the circumscribed circle boundary of each polygonal obstacle body according to the circumscribed circle center and circumscribed circle radius of each polygonal obstacle body and the circumscribed circle center and circumscribed circle radius of the current intelligent body;

[0032] The distance between the current intelligent body and the circumscribed circle boundary of each polygonal obstacle body is determined as the distance between the current intelligent body and each obstacle body in the obstacle field.

[0033] In some embodiments of the present application, the step of identifying a repulsive obstacle relative to the current intelligent body from among the obstacles according to the distance comprises:

[0034] Identify an obstacle whose distance is less than or equal to the activation distance from the obstacles, and determine the obstacle whose distance is less than or equal to the activation distance as an activated obstacle relative to the current agent;

[0035] Solve for a line connecting the center of the circumscribed circle of the current intelligent body and the center of the inscribed circle of the activated obstacle body, and obtain intersection points between the line and each side of the activated obstacle body;

[0036] According to the intersection point, identifying an activated edge from the edges of the activated obstacle body;

[0037] Calculate the length of the perpendicular line segment between the center of the circumscribed circle of the current intelligent body and the activated edge of the activated obstacle body;

[0038] If the length of the vertical line segment is less than or equal to the repulsion distance, the activated obstacle body is determined as a repulsion obstacle body relative to the current agent.

[0039] In some embodiments of the present application, generating a virtual agent based on the repulsive obstacle and determining the position and speed of the virtual agent includes:

[0040] Projecting the current agent onto the boundary of the repulsive obstacle to obtain a virtual agent;

[0041] Determine the projection of the current intelligent body on the boundary of the repulsive obstacle as the position of the virtual intelligent body;

[0042] According to the position of the current agent and the position of the virtual agent, a unit normal vector on the activation edge of the repulsive obstacle is obtained;

[0043] The speed of the virtual agent at the current moment is obtained according to the unit normal vector and the speed of the current agent at the current moment.

[0044] In some embodiments of the present application, the step of obtaining the control factor of the action of the repelling obstacle on the current agent based on the action function between the agent and the obstacle, the position and speed of the virtual agent, and the position and speed of the current agent includes:

[0045] Based on the impact function, the current position of the virtual agent, the current position of the current agent, and the expected distance between the agent and the obstacle, a spatial adjacency matrix between the current agent and the repulsive obstacle is obtained;

[0046] Based on the impact function and the expected distance, obtaining an action function between the current agent and the repulsive obstacle;

[0047] Based on the spatial adjacency matrix between the current agent and the repulsive obstacle, the action function between the current agent and the repulsive obstacle, the current position and speed of the virtual agent, and the current position and speed of the current agent, the control factor of the action of the repulsive obstacle on the current agent is obtained.

[0048] In some embodiments of the present application, the impact function is expressed as follows:

[0049]

[0050] The σ-norm of the vector is defined as

[0051] The spatial adjacency matrix between the current agent and the repulsive obstacle is expressed by the following formula:

[0052]

[0053] Among them, d β =||d'|| σ , d' is the expected distance between the current agent and the repulsive obstacle;

[0054] The interaction function between the current agent and the repulsive obstacle is expressed by the following formula:

[0055]

[0056] in,

[0057] The control factor of the effect of the repelling obstacle on the current agent is expressed by the following formula:

[0058]

[0059] in, is a fixed value, and the following relationship exists Among them, vector Solve by the following formula: in, are the current position and speed of the virtual agent, respectively, i 、p i are respectively the position and speed of the current agent at the current moment.

[0060] In some embodiments of the present application, obtaining the control factor of the target's effect on the current agent according to the current position and speed of the current agent and the position and speed of the target includes:

[0061] According to the current position and speed of the current agent and the position and speed of the target, a preset formula is used to obtain the control factor of the target's effect on the current agent; wherein the preset formula is expressed as follows:

[0062]

[0063] in, is the control factor of the effect of the target on the current agent, are fixed values ​​respectively, and the following relationship exists: q i 、p i are the position and speed of the current agent at the current moment respectively; q r 、p r are the position and velocity of the target respectively.

[0064] In some embodiments of the present application, the step of obtaining a control parameter for the current agent at the next moment according to the control factor of the neighboring agent on the current agent, the control factor of the repelling obstacle on the current agent, and the control factor of the target on the current agent includes:

[0065] Calculate the driving acceleration of the current agent at the current moment according to the control factor of the neighboring agent on the current agent, the control factor of the repelling obstacle on the current agent, and the control factor of the target on the current agent;

[0066] Determine whether the driving acceleration of the current agent at the current moment is greater than the maximum driving acceleration of the agent;

[0067] If yes, adjusting the driving acceleration of the current agent at the current moment according to the maximum driving acceleration of the agent;

[0068] Calculate the speed of the current agent at the next moment according to the adjusted driving acceleration and the speed of the current agent at the current moment;

[0069] Determine whether the speed at the next moment is greater than the maximum speed of the agent;

[0070] If yes, adjusting the speed at the next moment according to the maximum speed of the agent;

[0071] The next moment position of the current agent is calculated according to the adjusted next moment speed, the current moment speed of the current agent, and the current moment position of the current agent.

[0072] In summary, this application aims at the complex obstacle field existing on the ground battlefield, analyzes the shortcomings of the minimum circumscribed circle (sphere) in the traditional artificial potential field method to describe the obstacle body, and introduces the concept of polygon to describe the complex obstacle body, so as to reduce the probability of narrowing and blocking of the obstacle field channel; secondly, the interaction between the intelligent agent and the obstacle body in the cluster obstacle avoidance process of the multi-agent system is studied in detail, and whether the obstacle body is in an activated state is determined based on the distance between the outer center of the intelligent agent and the outer center of the obstacle body, and the activation edge of the activated obstacle body is determined based on the line between the outer center of the intelligent agent and the inner center of the obstacle body, and the expression of the force is given; thirdly, the capture phenomenon of the straight boundary and its cause are analyzed, and it is proposed to use a temporary target to bypass the capture edge to overcome the capture phenomenon, and the discretization solution method and the rules for selecting key parameters in the model are introduced; finally, the simulation analysis results are given, which verifies that regardless of whether the target is static or dynamic, the cluster obstacle avoidance control under the complex obstacle field can be realized, and the multi-agent cluster obstacle avoidance method proposed in this application is practical and effective.

[0073] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through the practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0075] Figure 1 This is an example diagram of a multi-agent system cluster facing a complex obstacle course.

[0076] Figure 2 It is a flowchart of a multi-agent cluster obstacle avoidance method suitable for complex obstacle fields according to an embodiment of the present application.

[0077] Figure 3 is an intelligent agent A according to an embodiment of the present application i An example diagram of the domain space of .

[0078] Figure 4 is the obstacle body O according to the embodiment of the present application k For Agent A i Schematic diagram of the interaction scenario.

[0079] Figure 5 It is a flow chart of obtaining the control factor of the obstacle body's effect on the current intelligent body according to an embodiment of the present application.

[0080] Figure 6 It is a schematic diagram of the phenomenon of capturing an intelligent body by a straight line boundary of an obstacle according to an embodiment of the present application.

[0081] Figure 7It is a flow chart of a multi-agent cluster obstacle avoidance method suitable for complex obstacle fields according to an embodiment of the present application.

[0082] Figure 8 (a)- Figure 8 (h) is a schematic diagram of the multi-agent cluster exercise process on a complex obstacle field according to an embodiment of the present application.

[0083] Fig. 9 (a)- Fig. 9 (h) is a schematic diagram of the multi-agent cluster exercise process on a complex obstacle field according to another embodiment of the present application. DETAILED DESCRIPTION

[0084] Embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0085] For the convenience of research, the ground battlefield is approximated as a two-dimensional plane. Then the problem of unmanned vehicle clusters avoiding multiple obstacles on the ground battlefield can be abstracted as the problem of multi-agent system clusters crossing a complex obstacle field in a two-dimensional space. Suppose a group of intelligent clusters set out from a certain place to perform a task at a destination. There is a complex obstacle field composed of several obstacles on the way, such as Figure 1 As shown, the red polygon represents the original shape of the obstacle, and the gray circle represents the minimum circumscribed circle of the obstacle. It can be seen that there are relatively large gaps between the obstacles, which can serve as channels for the intelligent cluster. However, the traditional artificial potential field method often uses the minimum circumscribed circle (sphere) of the obstacle as the boundary of the polygonal obstacle, so the original channel will become narrower or even disappear. In order to solve the above problems, the present application proposes a multi-agent cluster obstacle avoidance method suitable for complex obstacle fields. Specifically, the multi-agent cluster obstacle avoidance method suitable for complex obstacle fields of an embodiment of the present application is described below with reference to the accompanying drawings.

[0086] Figure 2 FIG. 1 is a flow chart of a multi-agent cluster obstacle avoidance method applicable to a complex obstacle field according to an embodiment of the present application. Figure 2 As shown, the multi-agent cluster obstacle avoidance method applicable to complex obstacle fields may include:

[0087] Step 201, determine the current position and speed of each agent in the multi-agent cluster, and determine the neighboring agents of the current agent based on the position.

[0088] For example, consider the multi-agent system as a set V consisting of M agents. For the convenience of representation, the circumscribed circle of the i-th agent is denoted by Ai =B(C a_i , R a_i ), where C a_i ,R a_i They represent the center of the circumscribed circle (abbreviated as the circumcenter) and the radius of the circumscribed circle (abbreviated as the outer diameter) of agent i respectively. When the multi-agent system performs cluster motion, the motion state of the i-th agent is expressed by the following formula:

[0089]

[0090] Among them, q i ,p i ,u i ∈R D Represent the position, velocity and acceleration of agent i respectively, and D represents the dimension. To simplify the analysis, we can use agent A i The position of the circumcenter C a_i As the position q of agent i i .

[0091] Since the intelligent agent must be a physical entity, it has a certain volume. Define the intelligent agent A i Boundary and Agent A j The distance to the boundary is:

[0092] d(A i ,A j )=||C a_i -C a_j ||-R a_i -R a_j (5)

[0093] Here, || || represents the Euclidean norm of multidimensional space.

[0094] When the distance between agents is too large, the mutual influence between agents is negligible. Define agent A i The set of neighbors is:

[0095]

[0096] Where r represents the interaction distance between agents, r=μd, d is the expected distance between agents, and μ≥1.

[0097] like Figure 3 As shown, given a certain moment agent A i Distribution of surrounding agents. The light shaded circle represents agent A. i The dark shaded circle represents the circumscribed circle of the agent. According to formula (6), it can be seen that agents 1, 2, and 5 are all members of agent A. i Neighbors of agent A, and agents 3 and 4 are not agents A.i Neighbors.

[0098] In other words, the center and radius of the circumscribed circle of each intelligent agent can be determined, and the current position of the center of the circumscribed circle of each intelligent agent is used as the current position of each intelligent agent. The distance between the intelligent agents is calculated using the center and radius of the circumscribed circle of each intelligent agent, and then the distance is used to find the neighboring intelligent agents of the current intelligent agent from among the intelligent agents.

[0099] Step 202, based on the action functions, positions and speeds between the agents, obtain the action control factor of the neighboring agent on the current agent.

[0100] In some embodiments of the present application, the spatial adjacency matrix between agents can be obtained based on the impact function and the current position of each agent; the action function between agents can be obtained based on the impact function; the action control factor of the neighboring agent on the current agent can be obtained based on the spatial adjacency matrix, the action function between agents, and the current position and speed of each agent. As an example, in order to construct a smooth potential function, the impact function that can be used in the present application can be expressed as the following formula (2):

[0101]

[0102] The σ-norm of the vector is defined as

[0103] For example, based on the impact function in formula (2), the spatial adjacency matrix between agents can be defined as A(q)=[a ij (q)], where the elements are:

[0104]

[0105] Among them, q j is the position of the jth agent, q i is the current agent's position, r α =||r|| α .

[0106] Based on the impact function in formula (2) above, the action function between agents is defined as:

[0107]

[0108] in, d α =||d|| σ .

[0109] In the embodiment of the present application, agent A i The equation of the neighboring agent (i.e. the current agent) acting on it is:

[0110]

[0111] in, is a fixed value, and the following relationship exists Vector i,j Solve by the following formula: That is to say, after obtaining the spatial adjacency matrix and action function between the agents, we can use the above formula (9) to obtain the neighboring agent's influence on the current agent A based on the spatial adjacency matrix, the action function between the agents, and the current position and speed of each agent. i The controlling factor

[0112] Step 203, obtaining the distance between the current intelligent agent and each obstacle in the obstacle field, and identifying the repulsive obstacle relative to the current intelligent agent from each obstacle according to the distance.

[0113] In some embodiments of the present application, polygons can be used to geometrically model each obstacle in the obstacle field to obtain a polygonal geometric model of each obstacle. Then, according to the center and radius of the circumscribed circle of each polygonal obstacle, the center and radius of the circumscribed circle of the current agent, the distance between the current agent and the circumscribed circle boundary of each polygonal obstacle is calculated, and this distance can be understood as the distance between the current agent and each obstacle in the obstacle field.

[0114] Optionally, after obtaining the distance between the current agent and each obstacle in the obstacle field, the activated obstacle relative to the current agent can be identified from each obstacle according to the distance. Then, the line connecting the center of the circumscribed circle of the current agent and the center of the inscribed circle of the activated obstacle is solved, and the intersection point between the line and each side of the activated obstacle is obtained. The activated side is identified from each side of the activated obstacle according to the intersection point, and then the length of the perpendicular line segment between the center of the circumscribed circle of the current agent and the activated side of the activated obstacle is solved, and whether the activated obstacle is the repulsive obstacle of the current agent is identified according to the length of the perpendicular line segment.

[0115] For example, consider the complex obstacle field as a set F consisting of N polygonal obstacles, with the kth obstacle denoted as O k =B(P1, P2, ... P w ), where w represents the number of edges of the polygonal obstacle, P i represents the position coordinates of the ith vertex of the polygonal obstacle. Obviously, if Figure 4 As shown, according to the obstacle O k The vertex coordinates are used to solve the center and radius of the circumscribed circle, which are recorded as and At the same time, the center (referred to as the inner center) and radius of the inscribed circle can be solved and recorded as and Then, according to the circumscribed circle center and circumscribed circle radius of each polygonal obstacle, and the circumscribed circle center and circumscribed circle radius of the current intelligent body, the distance between the current intelligent body and the circumscribed circle boundary of each polygonal obstacle is calculated. Then, the obstacle body whose distance is less than or equal to the activation distance is identified from each obstacle body, and the obstacle body whose distance is less than or equal to the activation distance is determined as the activated obstacle body relative to the current intelligent body; the line connecting the circumscribed circle center of the current intelligent body and the inscribed circle center of the activated obstacle body is solved, and the intersection point between the line and each side of the activated obstacle body is obtained; according to the intersection point, the activated edge is identified from each side of the activated obstacle body; the length of the perpendicular line segment between the circumscribed circle center of the current intelligent body and the activated edge of the activated obstacle body is solved; if the perpendicular line segment length is less than or equal to the repulsion distance, the activated obstacle body is determined as the repulsion obstacle body relative to the current intelligent body.

[0116] Step 204, generating a virtual intelligent body based on the repulsive obstacle body, and determining the position and speed of the virtual intelligent body; wherein the virtual intelligent body is used to simulate the normal force of the repulsive obstacle body on the current intelligent body.

[0117] In some embodiments of the present application, the current agent can be projected onto the boundary of the repulsive obstacle to obtain a virtual agent; the projection of the current agent on the boundary of the repulsive obstacle is determined as the position of the virtual agent; based on the position of the current agent and the position of the virtual agent, the unit normal vector on the activated edge of the repulsive obstacle is obtained; based on the unit normal vector and the speed of the current agent at the current moment, the speed of the virtual agent at the current moment is obtained.

[0118] Step 205, based on the action function between the agent and the obstacle, the position and speed of the virtual agent, and the position and speed of the current agent at the current moment, obtain the action control factor of the obstacle repelling agent on the current agent.

[0119] Optionally, based on the impact function, the position of the virtual agent at the current moment, the position of the current agent at the current moment, and the expected distance between the agent and the obstacle, the spatial adjacency matrix between the current agent and the repulsive obstacle is obtained; based on the impact function and the expected distance, the action function between the current agent and the repulsive obstacle is obtained; based on the spatial adjacency matrix between the current agent and the repulsive obstacle, the action function between the current agent and the repulsive obstacle, the current position and speed of the virtual agent, and the current position and speed of the current agent, the action control factor of the repulsive obstacle on the current agent is obtained.

[0120] For example, Figure 4 Take the interaction scene between the intelligent agent and the obstacle as an example. Figure 5 As shown, the computational agent A will be given i (i.e. the current agent) and the polygonal obstacle O k General steps of interaction:

[0121] Step 51, solve the agent A by the following equation (11): i The circumscribed circle boundary and the polygonal obstacle O k Distance between circumcircle boundaries:

[0122]

[0123] Step 52: polygonal obstacle O k Relative to Agent A i Whether to activate, for example, define agent A i The set of all nearby activated obstacles is:

[0124]

[0125] Among them, r a is the activation distance. It can be seen that agent A i With polygonal obstacle O k Is the distance between them less than or equal to the activation distance? If so, it can be determined that the polygonal obstacle O k Relative to Agent A i To activate the barrier.

[0126] Step 53, if the polygonal obstacle O k Relative to Agent A i To activate the obstacle, solve the problem of agent A i Circumcenter and polygonal obstacle O k Inner connection Determine the connection The intersection points between the edges of the polygonal obstacle. k Take the line P1P2 corresponding to the first and second vertices as an example. The intersection point C with the line P1P2 p The coordinates of can be obtained by formula (13):

[0127]

[0128] Among them, λ is the line C a_i C p With connection The ratio of the length can be calculated by the following formula (14):

[0129]

[0130] Step 54, get the intersection point C p After obtaining the coordinates of p Are they both on the same line? Between the connection P1P2. To determine C p Taking whether it is between line segments P1P2 as an example, the following formula (15) is used to explain:

[0131]

[0132] If the above formula (15) holds, then C p is between line segments P1P2; similarly, determine C p Is it in a line segment? If the intersection point C p Also located on the line Between the line P1P2, P1P2 is considered to be a polygonal obstacle O k Otherwise, continue to determine other edges, at least one edge is an active edge. Although the probability is small, when the intersection point is a polygonal obstacle O k If a vertex is located on a node, any edge where the vertex is located is considered an active edge.

[0133] Step 55, assuming that the activation edge is P1P2, further solve the problem of agent A i Circumcenter C a_i With polygonal obstacle O k The perpendicular line of the active edge P1P2, with foot K, line segment C a_i K is calculated by the following formula (16):

[0134]

[0135] Among them, P1A is the intersection of obstacle vertex P1 and agent A. i The line between them, Δ is C a_i The cosine value of the angle θ between the line P1 and the line P1P2 can be calculated by the following formula (17):

[0136]

[0137] Step 56: polygonal obstacle O k Relative to Agent A i Whether it is excluded is determined by the following formula (18):

[0138] ||C a_i K||≤r' (18)

[0139] Where r' is the repulsion distance, r'≤r a Usually, if the above formula (18) is satisfied, then the polygonal obstacle O is called k Relative to Agent Ai To exclude obstacles.

[0140] Step 57, when agent A i In the polygonal obstacle O k A virtual agent is introduced to simulate the normal force of the obstacle on the agent within the repulsive distance, and this virtual agent is recorded as β-agent. The position of β-agent is the position of agent A. i In the polygonal obstacle O k Projected on the boundary, the position and velocity of the β-agent can be obtained by the following equation (19):

[0141]

[0142] in, a k is the unit normal vector on the activated edge of the obstacle, which can be solved by the following formula (20):

[0143]

[0144] Step 58: Based on the impact function of formula (2), define agent A i With polygonal obstacle O k The spatial adjacency matrix B(q) between , where the elements are:

[0145]

[0146] Among them, d β =||d'|| σ , d' is the expected distance between the current agent and the repulsive obstacle, usually d'≤r'.

[0147] Step 59, Agent A i With polygonal obstacle O k The interaction function between them is:

[0148]

[0149] in,

[0150] Step 510, Agent A i The obstacle to the agent A i The action equation is:

[0151]

[0152] in, is a fixed value, and the following relationship exists Among them, vector Solve by the following formula (24):

[0153]

[0154] in, are the current position and speed of the virtual agent, q i 、p i are the current agent A i The current position and velocity.

[0155] Thus, through the above steps 51 to 510, the control factor of the obstacle on the current intelligent body can be calculated:

[0156] Step 206, determine the position and speed of the target, and obtain the control factor of the target's effect on the current agent based on the current position and speed of the current agent and the position and speed of the target.

[0157] It should be noted that the target of the agent can be static or dynamic. In the embodiment of the present application, the target G can be given as r is defined as:

[0158] G r =(q r , p r ) (25)

[0159] Among them, q r 、p r Represent the position and velocity of the target respectively. When p r =0, the target is stationary.

[0160] Based on the artificial potential function, the guiding role of the target on the agent can be directly given by the following formula (26):

[0161]

[0162] in, is a fixed value, and the following relationship exists It can be seen that the control factor of the target's effect on the current agent can be calculated by the above formula (26):

[0163] It should be noted that in the embodiment of the present application, by using polygons to represent obstacles, the problem of channel narrowing and blockage caused by the traditional artificial potential field method using the minimum circumscribed circle (sphere) to represent obstacles can be solved. However, the straight edges of the polygon may cause capture. Therefore, the present application determines the capture edge of the polygonal obstacle and the temporary target of the agent based on the relationship between the outer center of the agent, the boundary of the polygonal obstacle and the target, and uses the position and speed of the temporary target to calculate the control factor of the temporary target on the agent, which can solve the problem of the agent being captured by the boundary of the polygonal obstacle.

[0164] For example, Figure 6 As shown in Figure 1, it is an example of the phenomenon of the obstacle's straight line boundary capturing the intelligent agent. The target and the obstacle's repulsive edge P1P2 are perpendicular, refer to the above formula (16). When the foot of the perpendicular is above the repulsive edge P1P2, the intelligent agent is easily captured by the obstacle, such as Figure 6 As shown. It can be seen that due to the repulsive force of the obstacle on the intelligent body Traction with the goal The resultant force points between P1 and P2, so agents A1 and A2 cannot bypass the vertex to reach the target. Similar situations are called repulsive edges. P1 and P2 are capture edges. Specific situations of capture edges include the following:

[0165] (1) Solve the problem of agent A i Circumcenter C a_i With target G r Connection C a_i G r With obstacle O k The intersection point C of the repelling edge g , refer to the above formula (13). If the intersection point is also located on line segment C a_i G r and obstacle O k On the repulsive edge, the repulsive edge is a capturing edge;

[0166] (2) Solve the problem of agent A i Circumcenter C a_i With obstacle O k The distance between the endpoints of the repulsive edge, taking the repulsive edge P1P2 as an example, is determined by the following formula (27):

[0167] C a_i P1≤r'||C a_i P2≤r' (27)

[0168] If the above formula (27) holds true, then the repelling edge is a capturing edge.

[0169] If the repelling edge is a capturing edge, the target is set to a temporary target. The temporary target is determined by the agent A. i, capture edge endpoints P1P2, target G r The positions of the three are determined by drawing a perpendicular line from the position of the agent to the repulsive edge. When the foot of the perpendicular K is within the repulsive edge, the position of the temporary target point is obtained by the following formula (28):

[0170]

[0171] When the foot of the perpendicular K is outside the exclusion edge, the position of the temporary target point is obtained by the following formula (29):

[0172]

[0173] Among them, L n is the normal vector of line segment P1P2, P n =P1P2 / ||P1P2||, Δ=(C a_i P1+P1G)-(C a_i P2+P2G).

[0174] In the embodiment of the present application, if only the obstacle is stationary, the speed of the temporary target point is expressed by the following formula (30):

[0175] p r_temp =0 (30)

[0176] That is to say, when the repelling edge of the obstacle is the capturing edge of the agent, the target can be set as a temporary target, and the position of the temporary target point can be calculated using the above formula (28) or (29), and the speed of the temporary target point can be obtained using the above formula (30). After obtaining the position and speed of the temporary target point, the above formula (26) can be used to calculate the control factor of the target's effect on the current agent: When the target is perpendicular to the repulsive edge of the obstacle, and the foot of the perpendicular is outside the repulsive edge, it can be considered that the intelligent agent will not be captured by the obstacle. At this time, the target is set to the original target formula (25). Then, using the position and speed of the original target, the control factor of the target on the current intelligent agent is calculated through the above formula (26):

[0177] Step 207, based on the control factors of the neighboring agents on the current agent, the control factors of the repelling obstacle on the current agent, and the control factors of the target on the current agent, obtain the control parameters for the current agent at the next moment, and control the motion of the current agent according to the control parameters.

[0178] Optionally, when obtaining the control factors of the neighboring agents on the current agent, the control factors of the repulsive obstacle on the current agent, and the control factors of the target on the current agent, all the control factors can be combined to discretize the acceleration, velocity and displacement of the current agent.

[0179] In some embodiments of the present application, the driving acceleration of the current agent at the current moment can be calculated based on the control factor of the action of the neighboring agent on the current agent, the control factor of the action of the repelling obstacle on the current agent, and the control factor of the action of the target on the current agent. As an example, the driving acceleration of the current agent at the current moment can be calculated by the following formula (3):

[0180]

[0181] Among them, u i is the driving acceleration of the current agent at the current moment, For the neighboring agent to the current agent A i The controlling factor of To control the effect of obstacles on the current agent, is the control factor of the target on the current agent.

[0182] In an embodiment of the present application, when the driving acceleration of the current intelligent agent at the current moment is obtained, it can be determined whether the driving acceleration of the current intelligent agent at the current moment is greater than the maximum driving acceleration of the intelligent agent; if so, the driving acceleration of the current intelligent agent at the current moment is adjusted according to the maximum driving acceleration of the intelligent agent; the speed of the current intelligent agent at the next moment is calculated according to the adjusted driving acceleration and the speed of the current intelligent agent at the current moment; it is determined whether the speed at the next moment is greater than the maximum speed of the intelligent agent; if so, the speed at the next moment is adjusted according to the maximum speed of the intelligent agent; the position of the current intelligent agent at the next moment is calculated according to the adjusted speed at the next moment, the speed of the current intelligent agent at the current moment, and the position of the current intelligent agent at the current moment.

[0183] It should be noted that the above formula (4) is the mathematical relationship between position, velocity and acceleration, which is given in the form of continuous derivatives. In actual simulation, a discrete form is often required. Therefore, it is necessary to modify the form of formula (4), and the specific method is as follows:

[0184] (1) Through the above formula (3), we can get agent A i Acceleration u i In fact, the acceleration ability of the intelligent agent cannot be infinite. Suppose the maximum value of the intelligent agent driving acceleration u max Then, the following judgment should be made:

[0185] ||ui ||>u max (31)

[0186] When the above formula (31) holds true, it means that the calculated acceleration is greater than the maximum acceleration of the agent, then let:

[0187] u i =u max u i / ||u i || (32)

[0188] Otherwise, no changes are made;

[0189] (2) Calculate the agent A by the following formula (33): i Next moment speed:

[0190] p i+1 =p i +u i δ t (33)

[0191] Among them, δ t is the discrete time step.

[0192] Similarly, the speed of the agent cannot be infinite. Let the maximum speed of the agent be p max , then first make the following judgment:

[0193] ||p i+1 ||>p max (34)

[0194] When the above formula (34) holds true, it means that the calculated speed is greater than the maximum speed of the agent, so let:

[0195] p i+1 =p max p i+1 / ||p i+1 || (35)

[0196] Otherwise, no processing is done.

[0197] (3) Calculate the agent A through the following formula (36): i Next moment position:

[0198]

[0199] It should be noted that the following are several key parameter selection rules:

[0200] (1) If the attraction of the target to the agent is too great, it may exceed the attraction or repulsion between the agents, making the ability of the agent to maintain the configuration relatively weak, and the configuration is easily destroyed during the cluster movement; on the contrary, if the attraction of the target to the agent is too small, it is easy to make the cluster movement less targeted, which is equivalent to weakening the role of the target in order to maintain a complete configuration. Parameters The selection of roughly satisfies the following formula (37):

[0201]

[0202] in, represents the number of neighbors of the agent, and D is the spatial dimension.

[0203] (2) When an agent has a large number of neighbors, the repulsive force of all neighbors on the agent and the attractive force of the target on the agent may be greater than the repulsive force of the obstacle on the agent. In order to avoid collision between the agent and the obstacle, the parameter The selection of roughly satisfies the following formula:

[0204]

[0205] In engineering applications, it is preferred to determine The value of is then determined by the above formulas (37) and (38): and The value range of and Under the guidance of this rule, the cluster obstacle avoidance model proposed in this application can meet the cluster obstacle avoidance requirements, but due to the discretization solution method and the strong repulsive effect of obstacles on the intelligent body, the configuration will inevitably be temporarily destroyed. Therefore, the above rules can only ensure the largest possible configuration retention rate.

[0206] (3)(3) The expected distance d between agents is based on the maximum speed u of the agents. max , maximum speed p max , discrete time step δ t 、Agent diameter D α The following factors are set to satisfy the following formula:

[0207]

[0208] (4) The expected distance d' between the agent and the obstacle can also be calculated based on the agent's maximum speed u max , maximum speed p max , discrete time step δ t 、Agent diameter D α The following factors are set to satisfy the following formula:

[0209]

[0210] In engineering applications, if the minimum distance d between two polygonal obstacles is min With the diameter D of the intelligent body a , there is the following relationship between the expected distance d' α ≤d min <2d', a local minimum may be formed between the two obstacles. It can be seen that the present application can further reduce the value of the expected distance d' by reducing the speed of the intelligent agent and shortening the discrete time step, so that d min ≥2d', thus eliminating the influence of local minima.

[0211] The following is a simulation verification of the multi-agent cluster obstacle avoidance method of the present application. i For the object, the multi-agent cluster obstacle avoidance method of the embodiment of the present application can be as follows Figure 7 First, the parameters are initialized according to the geometric properties of the agent and the obstacle, as shown in the top dashed box; secondly, the effects of other agents, obstacles and target points on agent A are calculated respectively. i The middle layer is shown in the dotted box from left to right. Finally, all the forces are integrated to discretize the acceleration, velocity and displacement of the intelligent agent, as shown in the dotted box at the bottom layer.

[0212] Below is the simulation result of 20 agents crossing the obstacle course and reaching the goal. At the initial moment, the radius of the circumscribed circle of the group of agents is 1.0m, starting at [25,0], in a 4×5 formation with a 2m interval, along the positive direction of the X-axis and symmetrically distributed about the X-axis, and the initial speed of all agents is [0, 0].

[0213] The complex obstacle field is composed of 2 triangles, 2 quadrilaterals and 1 pentagonal obstacle bodies, and the positions of their vertices are expressed as follows:

[0214]

[0215] Each row represents the vertex coordinates (X, Y) of an obstacle, and each vertex is separated by a semicolon. Each obstacle is stationary. The parameters involved in the simulation process are shown in Table 1.

[0216] Table 1 Parameters involved in the simulation process

[0217]

[0218] The first task is to traverse the obstacle course and reach the perimeter of a static target. The target state is represented by G r =(q r ,pr ) is determined, where q r =[220,0],p r =[0,0]. The cluster motion process corresponding to the first task is as follows Figure 8 In order to better demonstrate the separation / aggregation behavior of the agent cluster when encountering obstacles, the coordinate range is artificially set. It can be seen that: initially, the agents are relatively densely concentrated at the starting point. Figure 8 (a); then, the agents maintain the desired distance and arrive near the bar obstacle. Figure 8 (b) When the agent enters the exclusion distance of the bar obstacle, due to the effect of formula (24), the agent selects two different temporary goals and begins to split into two groups of clusters. Figure 8 (c); Next, the next group of agent clusters continues to split into two groups of agent clusters through the quadrilateral obstacle, as shown in Figure 8 As shown in (d); when most agents pass through the rear triangle and quadrilateral obstacle, due to the narrow passage, there is a very obvious squeezing behavior, and the agents can only file out, as shown in Figure 8 (e) As shown. Figure 8 (a)-8(e) also show that when avoiding obstacles, a few agents are not connected to the cluster composed of the majority of agents. However, after passing the obstacle, the agents all move towards the target direction at the same speed and quickly form a cluster. Figure 8 (f) Figure 8 (g) and Figure 8 (h) shown.

[0219] The second task is to traverse an obstacle course. The agent cluster is divided into two groups to track or attack two dynamic targets. The states of the two targets can be expressed as follows:

[0220] q r_1 =[220 Asin(ωt)] p r_1 =[0 Aωcos(ωt)]

[0221] q r_2 =[220+Asin(ωt)0] p r_2 =[Aωcos(ωt)0]

[0222] Among them, A=20, ω=0.01π.

[0223] The first group of agents corresponds to the first goal, and the second group of agents corresponds to the second goal. Under the condition that other parameters remain unchanged, the cluster movement process corresponding to the second task is as follows: Fig. 9As shown in the figure, the black circle and black star represent the first group of agents and their corresponding goals respectively; the white circle and white star represent the second group of agents and their corresponding goals respectively. It can be seen that at the beginning, all agents arrive near the obstacle field in a cluster with a specific configuration, such as Fig. 9 (a); then, due to the repulsive effect of the obstacle, the cluster begins to separate and the configuration is destroyed, as shown in Fig. 9 As shown in (b), due to the traction of the target, after most of the agents have crossed the obstacle field, they begin to gradually form new clusters and move towards their respective target clusters, as shown in Fig. 9 (c) and Fig. 9 (d) When the two targets intersect, the two groups of agents come together, as shown in Fig. 9 As shown in (e); when the two targets are separated again, the two groups of agents diverge towards their respective targets, as shown in Fig. 9 (f); however, when the two targets approach and separate again, the two groups of agents gather again and then disperse towards their respective targets. At this time, some (black) agents are forced to join another group (white) of agents, as shown in Fig. 9 (g) and Fig. 9 (h). It is not difficult to conclude that the model can still play a good dominant role in the presence of two dynamic targets. However, the "coercion" phenomenon that exists when the two groups of agents are discrete still needs to be eliminated by designing other rules, such as there is only repulsion but no attraction between agents corresponding to different targets.

[0224] In summary, this application aims at the complex obstacle field existing on the ground battlefield, analyzes the shortcomings of the minimum circumscribed circle (sphere) in the traditional artificial potential field method to describe the obstacle body, and introduces the concept of polygon to describe the complex obstacle body, so as to reduce the probability of narrowing and blocking of the obstacle field channel; secondly, the interaction between the intelligent agent and the obstacle body in the cluster obstacle avoidance process of the multi-agent system is studied in detail, and whether the obstacle body is in an activated state is determined based on the distance between the outer center of the intelligent agent and the outer center of the obstacle body, and the activation edge of the activated obstacle body is determined based on the line between the outer center of the intelligent agent and the inner center of the obstacle body, and the expression of the force is given; thirdly, the capture phenomenon of the straight boundary and its cause are analyzed, and it is proposed to use a temporary target to bypass the capture edge to overcome the capture phenomenon, and the discretization solution method and the rules for selecting key parameters in the model are introduced; finally, the simulation analysis results are given, which verifies that regardless of whether the target is static or dynamic, the cluster obstacle avoidance control under the complex obstacle field can be realized, and the multi-agent cluster obstacle avoidance method proposed in this application is practical and effective.

[0225] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0226] Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limitations on the present application. Ordinary technicians in the field can change, modify, replace and modify the above embodiments within the scope of the present application.

Claims

1. A multi-agent cluster obstacle avoidance method suitable for complex obstacle fields, characterized in that: include: Determine the current position and speed of each agent in the multi-agent cluster, and determine the neighboring agents of the current agent based on the position; Based on the action function between the agents, the position and the speed, obtaining the action control factor of the neighboring agent on the current agent; Obtaining the distance between the current intelligent agent and each obstacle in the obstacle field, and identifying a repelling obstacle relative to the current intelligent agent from the obstacles according to the distance; Generate a virtual agent based on the repulsive obstacle, and determine the position and speed of the virtual agent; wherein the virtual agent is used to simulate the normal force of the repulsive obstacle on the current agent; Based on the action function between the agent and the obstacle, the position and speed of the virtual agent, and the position and speed of the current agent at the current moment, obtaining the action control factor of the obstacle repelling agent on the current agent; Determine the position and speed of the target, and obtain a control factor of the target's effect on the current agent based on the current position and speed of the current agent and the position and speed of the target; According to the control factor of the neighboring agent on the current agent, the control factor of the repelling obstacle on the current agent, and the control factor of the target on the current agent, a control parameter for the current agent at the next moment is obtained, and the motion of the current agent is controlled according to the control parameter; Wherein, obtaining the distance between the current intelligent agent and each obstacle in the obstacle field includes: Constructing a polygonal geometric model of each obstacle body, and determining the center point and radius of the circumscribed circle of each polygonal obstacle body based on the polygonal geometric model; Determine the center and radius of the circumscribed circle of the current agent; Calculate the distance between the current intelligent body and the circumscribed circle boundary of each polygonal obstacle body according to the circumscribed circle center and circumscribed circle radius of each polygonal obstacle body and the circumscribed circle center and circumscribed circle radius of the current intelligent body; Determine the distance between the current intelligent body and the circumscribed circle boundary of each polygonal obstacle as the distance between the current intelligent body and each obstacle in the obstacle field; The step of identifying a repelling obstacle body relative to the current intelligent body from among the obstacles according to the distance comprises: Identify obstacles whose distances between the current agent and each obstacle in the obstacle field are less than or equal to the activation distance from the obstacles, and determine obstacles whose distances are less than or equal to the activation distance as activated obstacles relative to the current agent; Solve for a line connecting the center of the circumscribed circle of the current intelligent body and the center of the inscribed circle of the activated obstacle body, and obtain intersection points between the line and each side of the activated obstacle body; According to the intersection point, identifying an activated edge from the edges of the activated obstacle body; Calculate the length of the perpendicular line segment between the center of the circumscribed circle of the current intelligent body and the activated edge of the activated obstacle body; If the length of the vertical line segment is less than or equal to the repulsion distance, the activated obstacle body is determined as a repulsion obstacle body relative to the current agent.

2. The method according to claim 1, characterized in that The step of obtaining the control factor of the action of the neighboring agent on the current agent based on the action function between the agents, the position and the speed includes: Based on the impact function and the current position of each agent, obtaining a spatial adjacency matrix between each agent; Acquire the action function between the agents based on the impact function; Based on the spatial adjacency matrix, the action functions between the agents, and the positions and velocities of the agents at the current moment, the action control factors of the neighboring agents on the current agent are obtained.

3. The method according to claim 2, characterized in that The impulse function is expressed as follows: The σ-norm of the vector is defined as , ; ; The spatial adjacency matrix between the agents is expressed by the following formula: in, is the position of the jth agent, is the position of the current agent, represents the interaction distance between agents, ; The interaction function between the agents is expressed by the following formula: in, , , , , d is the expected distance between agents; The control factor of the neighboring agent on the current agent is expressed by the following formula: in, , is a fixed value, and the following relationship exists ; Vector Solve by the following formula: .

4. The method according to claim 1, characterized in that The generating of a virtual intelligent body based on the repelling obstacle body and determining the position and speed of the virtual intelligent body comprises: Projecting the current agent onto the boundary of the repulsive obstacle to obtain a virtual agent; Determine the projection of the current intelligent body on the boundary of the repulsive obstacle as the position of the virtual intelligent body; According to the position of the current agent and the position of the virtual agent, a unit normal vector on the activation edge of the repulsive obstacle is obtained; The speed of the virtual agent at the current moment is obtained according to the unit normal vector and the speed of the current agent at the current moment.

5. The method according to claim 1, characterized in that: The step of obtaining the control factor of the obstacle repelling body on the current agent based on the action function between the agent and the obstacle, the position and speed of the virtual agent, and the position and speed of the current agent includes: Based on the impact function, the current position of the virtual agent, the current position of the current agent, and the expected distance between the agent and the obstacle, a spatial adjacency matrix between the current agent and the repulsive obstacle is obtained; Based on the impact function and the expected distance, obtaining an action function between the current agent and the repulsive obstacle; Based on the spatial adjacency matrix between the current agent and the repulsive obstacle, the action function between the current agent and the repulsive obstacle, the current position and speed of the virtual agent, and the current position and speed of the current agent, the control factor of the action of the repulsive obstacle on the current agent is obtained.

6. The method according to claim 5, characterized in that The impulse function is expressed as follows: The σ-norm of the vector is defined as , ; ; The spatial adjacency matrix between the current agent and the repulsive obstacle is expressed by the following formula: in, , is the expected distance between the current agent and the repulsive obstacle; The interaction function between the current agent and the repulsive obstacle is expressed by the following formula: in, ; The control factor of the effect of the repelling obstacle on the current agent is expressed by the following formula: in, , is a fixed value, and the following relationship exists ; Among them, the vector Solve by the following formula: ,in, , are the current position and speed of the virtual agent, , are respectively the position and speed of the current agent at the current moment.

7. The method according to claim 1, characterized in that The step of obtaining the control factor of the target's effect on the current agent according to the current position and speed of the current agent and the position and speed of the target includes: According to the current position and speed of the current agent and the position and speed of the target, a preset formula is used to obtain the control factor of the target's effect on the current agent; wherein the preset formula is expressed as follows: in, is the control factor of the effect of the target on the current agent, , are fixed values ​​respectively, and the following relationship exists: ; , are the current position and speed of the current agent at the current moment respectively; , are the position and velocity of the target respectively.

8. The method according to any one of claims 1 to 6, characterized in that The step of obtaining a control parameter for the current agent at the next moment according to the control factor of the neighboring agent on the current agent, the control factor of the repelling obstacle on the current agent, and the control factor of the target on the current agent comprises: Calculate the driving acceleration of the current agent at the current moment according to the control factor of the neighboring agent on the current agent, the control factor of the repelling obstacle on the current agent, and the control factor of the target on the current agent; Determine whether the driving acceleration of the current agent at the current moment is greater than the maximum driving acceleration of the agent; If yes, adjusting the driving acceleration of the current agent at the current moment according to the maximum driving acceleration of the agent; Calculate the speed of the current agent at the next moment according to the adjusted driving acceleration and the speed of the current agent at the current moment; Determine whether the speed at the next moment is greater than the maximum speed of the agent; If yes, adjusting the speed at the next moment according to the maximum speed of the agent; The next moment position of the current agent is calculated according to the adjusted next moment speed, the current moment speed of the current agent, and the current moment position of the current agent.

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