A multi-agent swarm obstacle avoidance method based on artificial potential field algorithm

Abstract

A multi-agent cluster obstacle avoidance method based on an artificial potential field algorithm belongs to the field of path planning technology for intelligent agents. A three-dimensional artificial potential field algorithm that simply applies a normal control force is proposed to realize the multi-agent cluster obstacle avoidance task, so that the intelligent agent cluster can avoid obstacles during the movement and successfully reach the target point. S1. Clarify the initial information, including map information and initial information of the intelligent agent; S2. Design an artificial potential field function; S3. Use coordinate transformation to design an artificial potential field algorithm that simply applies a normal control force; S4. Add a speed negative feedback. The method of virtual center gravitational potential field and intelligent agent repulsive potential field of the present invention realizes the distance constraint control of the multi-agent cluster; the artificial potential field algorithm that simply applies a normal control force realizes the solution to the obstacle avoidance problem of the intelligent agent that lacks the speed tangential direction control force; the method of adding an additional coefficient to the control force solves the problem of failure of the artificial potential field algorithm under special circumstances.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent agent path planning, and specifically relates to a multi-agent cluster obstacle avoidance method based on an artificial potential field algorithm. Background Art

[0002] Obstacle avoidance has always been an important problem that needs to be solved in the field of path planning. In order to achieve the goal of multi-agent collaborative pursuit, solving the clustering and obstacle avoidance problems during movement has become an important research direction. At present, the research on multi-agent clustering and obstacle avoidance problems mainly focuses on multi-UAV collaborative guidance and obstacle avoidance, and has achieved certain research results. However, there are few related studies on multi-agents. Some agents have certain special needs, that is, the control force applied to the agent can only be along the normal direction of its velocity, but there is no control force along the tangential direction of the velocity, which puts certain requirements on the obstacle avoidance algorithm.

[0003] Drones are small in size, flexible in flight, and easy to control, while the intelligent agent targeted by this patent is an intelligent agent with the above-mentioned special needs, which is subject to certain conditions and increases the difficulty of related research.

[0004] The artificial potential field method studied by this patent is a widely used obstacle avoidance method with a simple principle and easy implementation. However, the implementation of multi-agent cluster obstacle avoidance tasks is different from that of ordinary agents, mainly in the following aspects:

[0005] 1. Multi-agent collaboration. When multi-agents perform tasks, different agents do not fly as separate individuals, but in a cluster. This requires that multiple agents must always maintain a certain distance constraint during the flight, neither too far apart nor colliding with each other;

[0006] 2. Lack of control force. The intelligent agent targeted by the present invention cannot provide control force along the tangent direction of the intelligent agent's speed during the obstacle avoidance process. Therefore, the intelligent agent can only change the speed direction through the control force in the normal direction of the speed to avoid obstacles.

[0007] 3. The problem of failure of the artificial potential field method. Due to the lack of tangential control of speed, when the intelligent agent, the target point, and the obstacle are in the same straight line, the artificial potential field method will fail, causing the intelligent agent to collide with the obstacle.

[0008] Based on the above problems, the traditional artificial potential field algorithm cannot be directly applied to the implementation of multi-agent cluster obstacle avoidance and needs further improvement. Summary of the invention

[0009] The purpose of the present invention is to propose a three-dimensional artificial potential field algorithm that simply applies normal control force to realize the obstacle avoidance task of multi-agent clusters, so that the intelligent cluster can avoid obstacles during the movement and successfully reach the target point.

[0010] The technical solution adopted by the present invention is: a multi-agent cluster obstacle avoidance method based on an artificial potential field algorithm, comprising the following steps:

[0011] S1. Clarify the initial information, including map information and agent initial information;

[0012] S2. Design artificial potential field function;

[0013] S3. Using coordinate transformation, design an artificial potential field algorithm that simply applies normal control force;

[0014] S4. Add a speed negative feedback;

[0015] S5. Conduct simulation test.

[0016] Compared with the prior art, the present invention has the following beneficial effects:

[0017] The present invention improves the traditional artificial potential field method. The method of designing the virtual center gravitational potential field and the agent repulsive potential field realizes the distance constraint control of the multi-agent cluster; the artificial potential field algorithm designed to simply apply the normal control force realizes the solution to the obstacle avoidance problem of the agent lacking the speed tangential direction control force; the method of adding an additional coefficient to the designed control force solves the problem of the failure of the artificial potential field algorithm under special circumstances. It realizes that the multi-agent cluster obstacle avoidance flight can be completed in the absence of the speed tangential control force, and solves the problem that the artificial potential field method may fail under special circumstances. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a flow chart of algorithm design of the obstacle avoidance method of the present invention;

[0019] Figure 2 It is a schematic diagram of the principle of artificial potential field method;

[0020] Figure 3 It is a schematic diagram of the force acting on the intelligent agent;

[0021] Figure 4 It is a schematic diagram of the forces acting on the intelligent agent cluster;

[0022] Figure 5 It is the relationship between the ground coordinate system and the ballistic coordinate system;

[0023] Figure 6 is the simulation result of the intelligent agent cluster;

[0024] Figure 7is the distance between agents;

[0025] Figure 8 is the distance between the virtual center and each agent;

[0026] Fig. 9 is the distance between the agent and the obstacle. DETAILED DESCRIPTION

[0027] In order to better understand the purpose, structure and function of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings.

[0028] The algorithm flow of the present invention is as follows: when no obstacles are encountered, multiple intelligent agents maintain a certain distance constraint between each other through the control force they are subjected to, and move toward a target point as a cluster; when encountering obstacles, due to the repulsive force of the obstacles, the intelligent agents each bypass the obstacles, and the cluster distance increases at this time; after avoiding the obstacles, the intelligent agents maintain the distance constraint again under the action of the virtual center gravity and continue to move toward the target point.

[0029] Specific reference Figure 1 As shown, a multi-agent cluster obstacle avoidance method based on an artificial potential field algorithm of the present invention comprises the following steps:

[0030] S1. Clarify the initial information. This includes map information and agent initial information, including: target point coordinates q g , the number of obstacles and their coordinates q r , the number of agents and their starting coordinates q, and the initial velocity V0 of each agent.

[0031] S2. Design artificial potential field function.

[0032] According to the principle of artificial potential field algorithm, the potential field function U of each part is designed, and according to the negative gradient of the potential field function, that is, Get the potential field force F corresponding to each part.

[0033] like Figure 2 As shown in the figure, the principle of the artificial potential field method is to artificially construct a virtual potential field in the motion space of the intelligent agent, which is composed of the gravitational potential field generated by the target point and the repulsive potential field generated by obstacles in the space.

[0034] In the present invention, the intelligent agent is an intelligent agent, which is subject to the gravitational force of the target point in space and thus moves toward the target point. At the same time, when encountering an obstacle, the intelligent agent bypasses the obstacle due to the repulsive force of the obstacle, thereby achieving obstacle avoidance.

[0035] The force diagram is as follows Figure 3 shown.

[0036] In order to realize the distance constraint control of multi-agents, in addition to designing the target point gravitational potential field and obstacle repulsive potential field of the traditional artificial potential field algorithm, a virtual center gravitational potential field and agent repulsive potential field are added.

[0037] The virtual center is the average coordinate of all intelligent agents. It is located at the center of the intelligent agent cluster and is a virtual point that is created. This point generates a gravitational potential field, so that all intelligent agents tend to move toward the virtual center.

[0038] At the same time, a repulsive potential field is set for each intelligent agent, so that each intelligent agent is a dynamic obstacle relative to other intelligent agents. When an intelligent agent approaches other intelligent agents, it will be repelled and moved away.

[0039] In this way, when only the intelligent agent cluster is considered, a single intelligent agent will not collide with other intelligent agents while moving toward the center of the cluster due to the repulsive force of other intelligent agents, thus realizing the distance constraint of the intelligent agent cluster.

[0040] The force diagram is as follows Figure 4 shown.

[0041] In summary, the artificial potential field that needs to be designed includes four parts: the target point gravitational potential field function U att , obstacle repulsion potential field function U rep , virtual central gravitational potential field function U attmid 、Agent repulsive potential field function U repi ;

[0042] The steps for designing the artificial potential field function in the artificial potential field algorithm are as follows:

[0043] S21. Target point gravitational potential field function U att :

[0044] The target point has a gravitational effect on the agent, and the greater the distance between the agent and the target point, the greater the corresponding gravitational potential energy, and the smaller the distance, the smaller the corresponding gravitational potential energy. When the agent is close enough to the target point, the gravitational potential energy is zero, and the agent is considered to have reached the target point. The gravitational potential field function of the target point designed in this way is:

[0045] U att =k att ×(qq g ) 2 / 2;

[0046] Among them: U att is the gravitational potential field of the target point; k att is the gravitational coefficient; q is the current position of the agent; q g is the location of the target point.

[0047] From the formula, we can see that the gravitational potential field U att The distance between the agent and the target point (qq g ) is in a square relationship, and the gravitational potential field increases monotonically as the distance between the agent and the target point increases, and the direction is that the line connecting the agent and the target point points to the target point. Gravitational coefficient k att The proportional gain that determines the gravitational potential field can be changed through artificial adjustment to change the strength of the gravitational potential field.

[0048] The corresponding attraction F att is the gravitational potential field U att The negative gradient of is the gravitational potential field U att The derivative of the distance between the agent and the target point is:

[0049]

[0050] From the above formula, we can see that the gravitational function F att It increases monotonically as the distance between the agent and the target point increases, and the direction is that the line connecting the agent and the target point points to the target point.

[0051] S22. Obstacle repulsive potential field

[0052] The repulsive force from obstacles during the movement of the agent is also related to the distance: the closer the agent is to the obstacle, the greater the repulsive force it receives, and the farther the distance, the smaller the repulsive force, so as to ensure that it will not collide with the obstacle. The obstacle repulsive force potential field function designed in this way is:

[0053]

[0054] Among them, k rep is the repulsion coefficient; q r is the position of the obstacle; d r is the distance of the repulsive force of the obstacle. When the agent enters the repulsive force range of the obstacle during movement, it will be affected by a relatively large repulsive force. When the agent leaves the repulsive force range of the obstacle, the repulsive force of the obstacle on it is zero, thus avoiding the influence of obstacles far away from the agent on its movement.

[0055] The corresponding repulsive force is the repulsive potential field U rep The negative gradient of . That is:

[0056]

[0057] From the above formula, we can see that the repulsive force function F rep It increases monotonically as the distance between the agent and the obstacle decreases, and the direction is that the line connecting the agent and the target point points to the agent.

[0058] S23. Virtual central gravitational potential field function

[0059] Just like the gravitational potential field of the target point, the closer the agent is to the virtual center, the smaller the gravitational force it receives, and the farther away it is, the greater the gravitational force it receives. The gravitational potential field function of the virtual center is:

[0060] U attmid =k att ×(qq mid ) 2 / 2;

[0061] Among them: U attmid is the gravitational field of the virtual center; k att is the gravitational coefficient; q is the current position of the agent; q mid The location of the virtual center.

[0062] The virtual center is taken as the center point of all agents, that is:

[0063]

[0064] The corresponding gravitational force from the virtual center is:

[0065]

[0066] S24. Agent repulsive potential field function

[0067] Just like the repulsive potential field of obstacles, the closer the agent is to other agents, the greater the repulsive force it receives, and the smaller the distance, the smaller the repulsive force it receives. Thus, the repulsive potential field function of the agent is obtained:

[0068]

[0069] U repi is the agent repulsive potential field, q i is the position of the agent that exerts repulsive force; d0 is the influence distance of the agent.

[0070] Repulsion F repi From the negative gradient of the repulsive potential field function, we can get:

[0071]

[0072] S25. Improvements to Prioritize Distance Constraint Tasks

[0073] The gravitational force of the target point on which multi-agents are subject during their movement is the same as that in the design of the single-agent artificial potential field method, but the movement of multi-agents adds distance constraints. Therefore, the priority of the task of multi-agents moving toward the virtual center should be higher than that of moving toward the target. That is, when the distance between an agent and the virtual center is greater than a certain value during the movement of multi-agents, it is necessary to reduce the gravitational force of the target point on the agent so that the agent can satisfy the distance constraint first.

[0074] That is, the gravitational force exerted on the target point by the agent is:

[0075]

[0076] Where d is the distance that is set to prioritize distance constraints.

[0077] S3. Design of an artificial potential field method for simply applying normal control force (using coordinate transformation to convert the control force obtained according to the S2 artificial potential field algorithm into an artificial potential field algorithm for simply applying normal control force).

[0078] In order to facilitate the design of the three-dimensional artificial potential field method, coordinate transformation is required. The final design requirement is to change the control force along the speed direction of the intelligent agent to 0 and only apply the normal control force. Therefore, the ground coordinate system and the ballistic coordinate system are introduced, and the definitions are given below:

[0079] 1. Ground coordinate system Axyz

[0080] The ground coordinate system Axyz is a coordinate system fixed to the surface of the earth. The origin A of the coordinate system is usually selected at the starting point of the intelligent body's movement (i.e., the center of mass of the intelligent body at the moment of movement starting); the direction of the Ax axis can be arbitrary; the Ay axis is upward along the vertical line, and the Az axis is perpendicular to the other two axes and forms a right-handed coordinate system.

[0081] As an inertial reference system, the ground coordinate system is mainly used to determine the coordinate position of the center of mass of the intelligent body in space and the reference benchmark such as the posture of the intelligent body in space.

[0082] 2. Ballistic coordinate system Ox2y2z2

[0083] The origin O of the ballistic coordinate system is taken at the instantaneous center of mass of the intelligent body; the Ox2 axis coincides with the velocity vector V of the intelligent body; the Oy2 axis is located in the plumb plane containing the velocity vector V and is perpendicular to the Ox2 axis, pointing upward; the Oz2 axis is perpendicular to the other two axes and forms a right-handed coordinate system. The ballistic coordinate system is fixed to the velocity vector V of the intelligent body and is a moving coordinate system.

[0084] The design idea is to convert the coordinate representation of the control force vector in the ground coordinate system to the coordinate representation of the ballistic coordinate system, set the component on the Ox2 axis (i.e., along the direction of the velocity vector V) to 0, and then convert the new coordinates to the ground coordinate system. To do this, the coordinate conversion between the ground coordinate system and the ballistic coordinate system is required (such as Figure 5 As shown), two angles are introduced:

[0085] 1. Ballistic inclination angle θ:

[0086] The angle between the agent's velocity vector V (i.e., the Ox2 axis) and the horizontal plane. If the velocity vector points upwards, the angle θ is positive; otherwise, it is negative.

[0087] 2. Ballistic deviation

[0088] The projection of the agent's velocity vector V in the horizontal plane (i.e. Figure 5 The angle between the Ax' axis of the ground coordinate system and the Ax axis of the ground coordinate system. Observe from the angular plane (i.e. looking down towards the Ay axis), if the rotation from the Ax axis to the Ax' axis is counterclockwise, then The angle is positive; the opposite is negative.

[0089] The matrix form of the transformation from the ground coordinate system to the ballistic coordinate system is expressed as:

[0090]

[0091] in

[0092] L(θ) and L(φ V ) are the rotation matrices for the two-step rotation from the ground coordinate system to the ballistic coordinate system.

[0093] The control force of the artificial potential field method is expressed as follows in the ballistic coordinate system:

[0094]

[0095] in, is the coordinate expression of the control force in the ground coordinate system, It is the coordinate representation of the control force in the ballistic coordinate system.

[0096] The control force component F along the velocity vector direction x2 Set to 0 to get the coordinate representation of the new ballistic coordinate system

[0097] Thus, the control force of the improved artificial potential field method is obtained:

[0098]

[0099] In some special cases, the control force may coincide with the direction of the velocity vector. In this case, the artificial potential field method using a simple normal control force will cause the artificial potential field method to fail. Therefore, an additional coefficient k is added to update the improved artificial potential field method to:

[0100]

[0101] S4. To increase the stability of the intelligent agent, a velocity negative feedback is added to the control force part. Finally, the resultant force of the intelligent agent during the movement is:

[0102] F=F att +F rep +F attmid +F repi -k v *V;

[0103] Where V is the agent speed, k v is the speed feedback coefficient.

[0104] S5. Conduct simulation experiments. Run the simulation program to obtain the results of the intelligent agent cluster movement.

[0105] Example:

[0106] The following introduces a representative embodiment to further illustrate the relevant design of the technical solution of the present invention.

[0107] S1. Clarify the initial information.

[0108] The target point coordinates are q g =(10 10 10)(km);

[0109] There are 5 obstacles with coordinates q r1 =(4.0 3.3 4.0)(km),q r2 =(4.0 4.0 3.0)(km),q r3 =(4.4 4.2 3.4)(km),q r4 =(3.6 4.6 4)(km),q r1 =(2.5 3.0 3.5)(km);

[0110] There are 3 agents, and their starting coordinates are q1 = (0 0 1.0) (km), q2 = (0 1.0 0) (km), and q3 = (1.0 0 0) (km);

[0111] The initial velocity of each agent is the same, V0 = (1 1 1) (km / s);

[0112] S2. Design artificial potential field function.

[0113] S21. Target point gravitational potential field function U att :

[0114] Assume that the gravitational coefficient k att =2;

[0115] Then the gravitational potential field function of the target point is:

[0116] U att =(qq g ) 2 ;

[0117] The target point gravity is:

[0118] F att =-2(qq g );

[0119] S22. Obstacle repulsion potential field:

[0120] Let the repulsion coefficient be k rep =0.5, the distance affected by the obstacle repulsion is d r =2(km);

[0121] Then the obstacle repulsive force potential field function is:

[0122]

[0123] The obstacle repulsion force is:

[0124]

[0125] S23. Virtual center gravitational potential field function:

[0126] The gravitational coefficient remains unchanged and is k att =2;

[0127] The virtual center gravitational potential field function is:

[0128] U attmid =(qq mid ) 2 ;

[0129] The virtual center gravity is:

[0130] F attmid =-2(qq mid );

[0131] S24. Agent repulsive potential field function:

[0132] The repulsion coefficient remains unchanged and is k rep =0.5, the distance of the agent's repulsive influence is d0=2 (km);

[0133] Then the agent repulsive potential field function is:

[0134]

[0135] The agent repulsion is:

[0136]

[0137] S25. Improvements to Prioritize Distance Constraint Tasks:

[0138] Assume that the distance of the distance-constrained task is prioritized d = 0.5 (km);

[0139] Then the gravitational force exerted on the target point by the agent is:

[0140]

[0141] S3. Design of artificial potential field method that simply applies normal control force.

[0142] Assume additional coefficient k = 0.001;

[0143] The updated control force is:

[0144]

[0145] S4. In order to increase the stability of the intelligent body's operation, a speed negative feedback is added to the control force part.

[0146] Assume the speed feedback coefficient k v =5;

[0147] Then the final resultant force on the intelligent body during movement is:

[0148] F=F att +F rep +F attmid +F repi -5*V

[0149] According to the above algorithm design, run the simulation program to obtain the results of the intelligent cluster movement as follows Figure 6 , Figure 7 , Figure 8 , Fig. 9 shown.

[0150] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A multi-agent cluster obstacle avoidance method based on artificial potential field algorithm, characterized by: The following steps are involved: S1. Clarify the initial information, including map information and agent initial information; S2. Design artificial potential field function; S3. Using coordinate transformation, design an artificial potential field algorithm that simply applies normal control force; S4. Add a speed negative feedback; S5. Conduct simulation test; The initial information of S1 specifically includes: target point coordinates q g , the number of obstacles and their coordinates q r , the number of agents and their starting coordinates q, the initial velocity V0 of each agent; S2. Designing an artificial potential field function, according to the principle of artificial potential field algorithm, designing the potential field function U of each part, and according to the negative gradient of the potential field function, that is, Obtaining the potential field force F corresponding to each part specifically includes the following steps: S21. Target point gravitational potential field function U att 、Target point gravity F att : U att =k att ×(q-q g ) 2 / 2; Among them, U att is the gravitational field of the target point, k att is the gravitational coefficient, q is the current position of the agent, q g is the target point position; S22. Obstacle repulsion potential field function U rep , obstacle repulsion F rep : Among them, k rep is the repulsion coefficient, q r is the obstacle position, d r The distance affected by the repulsive force of the obstacle; S23. Virtual central gravitational potential field function U attmid , virtual center gravity F attmid : U attmid =k att ×(q-q mid ) 2 / 2; Among them, U attmid is the gravitational field of the virtual center, k att is the gravitational coefficient, q is the current position of the agent, q mid is the location of the virtual center; The virtual center is taken as the center point of all agents: S24. Agent repulsive potential field function U repi 、Agent repulsion F repi : Among them, U repi is the agent repulsive potential field, q i is the position of the agent exerting repulsive force, d0 is the influence distance of the agent; The S2 also includes S25. Improvements to the priority distance constraint task: When the distance between an agent and the virtual center is greater than a certain value during the multi-agent movement, it is necessary to reduce the gravitational force of the target point on the agent so that the agent can satisfy the distance constraint first. That is, the gravitational force exerted on the target point by the agent is: Where d is the distance set to prioritize distance constraints; Specifically, S3 uses coordinate transformation to transform the control force obtained according to the artificial potential field algorithm of S2 into an artificial potential field algorithm that simply applies normal control force; the transformation method is: in, is the coordinate expression of the control force in the ground coordinate system, is the coordinate representation of the control force in the ballistic coordinate system, It is the control force of the updated method of simply applying normal control force; At the same time, in order to avoid the problem of failure of the artificial potential field algorithm in special cases, an additional coefficient k is added to the control force, and the final updated control force is: The S4 is specifically as follows: in order to increase the running stability of the intelligent body, a speed negative feedback is added to the control force part, and finally the resultant force received by the intelligent body during the movement is: F=F att +F rep +F attmid +F repi -k v *V; Where V is the agent speed, k v is the speed feedback coefficient.

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