Cluster adaptive obstacle avoidance method based on improved artificial potential field

Abstract

The invention provides a cluster adaptive obstacle avoidance method based on an improved artificial potential field, and belongs to the technical field of multi-agent cluster intelligent decision. According to the method, the intelligent body cluster formation force is designed to provide repulsive force / gravitational force compensation, closed-loop adjustment of a geometrical relationship is formed, and therefore relative pose disturbance induced by obstacles is limited within an acceptable range; according to the method, non-linear design is carried out on gravitation, the adaptability of the robot in different environments is improved, dynamic weight is introduced to carry out distance-related non-linear amplification on attraction, when a vehicle approaches a target, an attraction item is enhanced along with reduction of the distance, and therefore the relative advantage of repulsive force is counteracted in the target neighborhood; a target perimeter barrier and a local minimum trap are prevented from being formed, so that the resultant force direction keeps unimodality and continuity pointing to the target; according to the method, the disturbance potential field is designed, the movement performance of the cluster in the complex potential field is remarkably improved, and stable and continuous collaborative obstacle avoidance and target convergence can be achieved in the multi-obstacle environment.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent cluster intelligent decision-making technology, specifically relating to a cluster adaptive obstacle avoidance method based on an improved artificial potential field. Background Technology

[0002] With the rapid development of intelligent decision-making and unmanned systems technologies, multi-agent swarms have become an important means of achieving complex tasks. Compared with single-agent systems, multi-agent systems (MAS) have significant advantages in environmental perception, task coordination, and fault tolerance, and have been widely applied in fields such as intelligent transportation, emergency search and rescue, military reconnaissance, and environmental monitoring. Among these, swarm obstacle avoidance is a key issue in ensuring the safety and stability of task execution, aiming to achieve cooperative obstacle avoidance and formation maintenance among multiple robots in complex and dynamic environments. Currently, existing technologies include artificial potential field methods, model predictive control methods, and collaborative methods. The main shortcomings of theoretical and multi-agent reinforcement learning are mainly reflected in problems such as local minima, unreachable goals, path oscillations and unevenness, and multi-agent conflicts. Summary of the Invention

[0003] To address the aforementioned problems in existing technologies, this invention proposes a multi-agent cluster adaptive obstacle avoidance method that integrates cooperative potential fields and dynamic weighting mechanisms, comprising the following steps:

[0004] S1: Initialize the position, velocity, and trajectory information of each agent in the agent cluster;

[0005] S2: Based on the current position of each agent, calculate the distance between the center of the agent cluster and the target point, compare the distance with the set disbanding threshold, and calculate the formation force between each agent based on the actual relative position and the expected relative position between each agent and the other agents.

[0006] S3: The attractiveness of the target point to each agent is designed non-linearly, and the attractiveness of the target point to each agent is calculated based on the dynamic weighting mechanism.

[0007] S4: Calculate the repulsive force of the target point on each agent;

[0008] S5: Calculate the net force on each agent based on the attractive and repulsive forces of the target point on each agent and the formation force between each agent;

[0009] S6: Detect the potential field equilibrium point based on the consistency coefficient of the motion direction of each agent and the repulsive force of the obstacle; if the agent enters the potential field equilibrium point, a perturbation potential field is generated, and the perturbation potential field is added to the resultant force to obtain the total resultant force;

[0010] S7: Update the position, velocity, and trajectory information of each agent; repeat steps S2 to S6 until all agents reach the target point.

[0011] Furthermore, in step S2, formation force is a core concept in multi-agent cluster control, used to maintain the structural stability of the overall formation. By rationally designing the relative forces between each agent, the actual relative positions are made to approximate the relative layout of the desired formation, thereby achieving formation maintenance and coordinated movement. The formation force of each agent is designed as the vector sum of the elastic constraint forces exerted on each agent by the other agents. Its magnitude is proportional to the deviation between the current actual relative position and the desired relative position, and its direction is along the shortest path to restore the desired formation, as shown in the following formula:

[0012] (1)

[0013] in, Represents intelligent agents With intelligent agents Formation strength between them; , Representing intelligent agents respectively and intelligent agents The current location; , Representing intelligent agents respectively and intelligent agents The desired location; Indicates the location of the center of the intelligent agent cluster; Indicates the location of the target point; Indicates the formation force coefficient;

[0014] Analysis of equation (1) shows that when the distance between adjacent agents in the agent cluster is less than the expected distance, the formation force is a repulsive force to prevent collisions between agents; when the distance between adjacent agents is greater than the expected distance, the formation force is an attractive force to prevent agents from leaving the formation.

[0015] Furthermore, the desired position is defined as the position point where each agent maintains the ideal formation.

[0016] Furthermore, in step S2, the center position of the agent cluster is the average coordinate of the current position of each agent.

[0017] Furthermore, in step S3, the attractiveness of the target point to each agent is calculated based on a dynamic weighting mechanism, as follows:

[0018] The gravitational potential field function is defined as:

[0019] (2)

[0020] In the formula, This is the gain coefficient; It is a vector, and its size is the agent's position. and target point location The Euclidean distance, with the direction from the agent to the target point;

[0021] The negative gradient of the gravitational potential field function yields the attraction of the target point to the agent. :

[0022] (3)

[0023] Considering that the presence of obstacles near the target can easily cause the agent to vibrate and fail to reach the target, a nonlinear design is implemented for gravity to improve the agent's adaptability in different environments; specifically as follows:

[0024] The revised definition of attractiveness:

[0025] (4)

[0026] In the formula, Represents intelligent agents Distance to the target point; The gain coefficient controls the degree to which the attraction increases when the agent approaches the target: when the agent is far from the target, Approximately equal to 0, attractiveness close to When the agent approaches the target, Increase the gravitational pull, thereby amplifying the gravitational pull and causing the agent to converge to the target quickly.

[0027] Furthermore, in step S4, the method for calculating the repulsive force of the target point on each agent is as follows:

[0028] The repulsive potential field function is defined as:

[0029] (5)

[0030] In the formula, It is the proportionality coefficient; It is a vector, and its size is the agent's position. and obstacle location The Euclidean distance, with the direction from the obstacle to the agent; is a constant representing the maximum distance at which the obstacle affects the agent;

[0031] The negative gradient of the repulsive potential function yields the repulsive force of the target point on the agent. :

[0032] (6)

[0033] Furthermore, in step S5, the resultant force acting on each agent... for:

[0034] (7)

[0035] The motion update equation of the agent is:

[0036] (8)

[0037] in, For intelligent agents in The equation of motion at time t.

[0038] Furthermore, in step S6, the potential field equilibrium point detection mainly monitors the geometric relationship between the motion direction of each agent in the cluster and the repulsive force it receives in real time, identifies the state of the potential field equilibrium point that may lead to local minima or unreachable target, and uses it as the basis for decision-making on the generation of perturbation potential field.

[0039] Potential field equilibrium point detection determines whether a potential field equilibrium point has occurred by calculating the consistency coefficient between the motion directions of each agent in the cluster and the repulsive force of obstacles. The formula is as follows:

[0040] (9)

[0041] in, Let be the unit vector representing the agent's current direction of motion. The unit vector representing the direction of the repulsive force from the obstacle; Let be the consistency coefficient between the agent's direction of motion and the repulsive force of the obstacle, when hour, The threshold parameter is used to determine the potential field equilibrium point. When the agent enters the potential field equilibrium point, a perturbation potential field is generated.

[0042] Furthermore, in step S6, the method for generating the perturbation potential field is as follows:

[0043] If standard basis vectors are used Generate perturbation direction; when the movement direction of agents within the cluster is in the same direction as the reference axis, perform the cross product operation. If the value is approximately 0, an effective perturbation potential field cannot be generated, and the agent will be trapped at the potential field equilibrium point. To address this issue, an adaptive reference axis design method based on the motion direction is adopted to generate perturbation components that are strictly orthogonal to the motion velocity direction, ensuring the generation of an effective perturbation potential field, as detailed below:

[0044] Initially, the X-axis (horizontal direction) is chosen as the reference axis, and the perturbation direction vector is calculated. If equation (10) is satisfied, then determine Trapped direction:

[0045] (10)

[0046] in, This represents the degradation threshold, used to determine... If the object is in a state of geometric degradation, switch the Y-axis (vertical direction) as the reference axis; otherwise, use the X-axis as the reference axis.

[0047] At this point, using the Y-axis as the reference axis, the disturbance direction vector is obtained. ; through normalization processing This allows for the acquisition of a perturbation basis orthogonal to the velocity direction, ensuring that agents within the cluster can effectively generate an effective perturbation potential field regardless of their direction of motion.

[0048] Finally, the generated perturbation potential field is added to the attraction, repulsion, and formation forces of the agent entering the potential field equilibrium point to form a total resultant force, causing it to leave the equilibrium point.

[0049] Compared with the prior art, the advantages of this invention are mainly reflected in the following three aspects:

[0050] First, we designed an intelligent agent swarm formation force. When the positions of intelligent agents within the swarm are "too close" or "too far" together, the formation force can provide repulsion / attraction compensation, forming a closed-loop adjustment of geometric relationships, thereby limiting the relative pose disturbances induced by obstacles to an acceptable range. The release disbanding threshold mechanism avoids unnecessary pulling and oscillations in the terminal stage, achieving a smooth ending of "near target disbanding - rapid convergence".

[0051] Secondly, nonlinear design of gravity is adopted to improve the robot's adaptability in different environments. After introducing a dynamic weighting mechanism, the dynamic weights amplify the attractive force nonlinearly with distance: when the vehicle approaches the target, the attractive term is enhanced as the distance decreases, thereby offsetting the relative advantage of the repulsive force in the target's neighborhood, avoiding the formation of a "target perimeter barrier" and local minimum traps, and ensuring that the resultant force direction maintains the unimodality and continuity pointing towards the target.

[0052] Third, a perturbation potential field was designed, which significantly improved the swarm's motion performance in complex potential fields, enabling it to achieve stable and continuous cooperative obstacle avoidance and target convergence in multi-obstacle environments. This result verifies the effectiveness of the proposed dynamic perturbation potential field design based on orthogonal compensation of motion direction in enhancing the global convergence and environmental adaptability of the swarm system. Attached Figure Description

[0053] Figure 1 This is a flowchart illustrating the method of the present invention.

[0054] Figure 2 This refers to the trajectory of the agent cluster near the equilibrium point of the potential field after the addition of a perturbation potential field.

[0055] Figure 3 This represents the trajectory of the agent cluster when it moves to the vicinity of the potential field equilibrium point without any added perturbation.

[0056] Figure 4 The trajectory of the agent cluster as it approaches the target point after adding dynamic weights.

[0057] Figure 5 This represents the trajectory of the agent cluster as it approaches the target point without the addition of dynamic weights.

[0058] Figure 6 To introduce formation force to determine the trajectory of the intelligent agent cluster. Detailed Implementation

[0059] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and should not be construed as limiting the scope of the invention.

[0060] like Figure 1 As shown, this invention provides a swarm adaptive obstacle avoidance method based on an improved artificial potential field, comprising the following steps:

[0061] S1: Initialize the position, velocity, and trajectory information of each agent in the agent cluster.

[0062] S2: Based on the current position of each agent, calculate the distance between the center of the agent cluster and the target point, and compare the distance with the set disbanding threshold, where the center position of the agent cluster is the average coordinate of the current position of each agent;

[0063] Based on the actual and desired relative positions of each agent with the others, the formation force between agents is calculated. The formation force of each agent is designed as the vector sum of the elastic constraint forces exerted on each agent by the others. Its magnitude is proportional to the deviation between the current actual and desired relative positions, and its direction follows the shortest path to restore the desired formation, as shown in the following formula:

[0064] (1)

[0065] in, Represents intelligent agents With intelligent agents Formation strength between them; , Representing intelligent agents respectively and intelligent agents The current location; , Representing intelligent agents respectively and intelligent agents The desired position is the position of each agent in order to maintain the ideal formation. Indicates the location of the center of the intelligent agent cluster; Indicates the location of the target point; Indicates the formation force coefficient;

[0066] Analysis of equation (1) shows that when the distance between adjacent agents in the agent cluster is less than the expected distance, the formation force is a repulsive force to prevent collisions between agents; when the distance between adjacent agents is greater than the expected distance, the formation force is an attractive force to prevent agents from leaving the formation.

[0067] S3: The attractiveness of the target point to each agent is designed non-linearly, and the attractiveness of the target point to each agent is calculated based on a dynamic weighting mechanism; the specific method is as follows:

[0068] The gravitational potential field function is defined as:

[0069] (2)

[0070] In the formula, This is the gain coefficient; It is a vector, and its size is the agent's position. and target point location The Euclidean distance, with the direction from the agent to the target point;

[0071] The negative gradient of the gravitational potential field function yields the attraction of the target point to the agent. :

[0072] (3)

[0073] Considering that the presence of obstacles near the target can easily cause the agent to vibrate and fail to reach the target, a nonlinear design is implemented for gravity to improve the agent's adaptability in different environments; specifically as follows:

[0074] The revised definition of attractiveness:

[0075] (4)

[0076] In the formula, Represents intelligent agents Distance to the target point; The gain coefficient controls the degree to which the attraction increases when the agent approaches the target: when the agent is far from the target, Approximately equal to 0, attractiveness close to When the agent approaches the target, Increase the gravitational pull, thereby amplifying the gravitational pull and causing the agent to converge to the target quickly.

[0077] S4: Calculate the repulsive force of the target point on each agent. The calculation method is as follows:

[0078] The repulsive potential field function is defined as:

[0079] (5)

[0080] In the formula, It is the proportionality coefficient; It is a vector, and its size is the agent's position. and obstacle location The Euclidean distance, with the direction from the obstacle to the agent; is a constant representing the maximum distance at which the obstacle affects the agent;

[0081] The negative gradient of the repulsive potential function yields the repulsive force of the target point on the agent. :

[0082] (6)

[0083] S5: Calculate the net force on each agent based on the attractive and repulsive forces of the target point on each agent and the formation forces between agents. for:

[0084] (7)

[0085] The motion update equation of the agent is:

[0086] (8)

[0087] in, For intelligent agents in The equation of motion at time t.

[0088] S6: Potential field equilibrium point detection is performed based on the consistency coefficient of the motion direction of each agent and the repulsive force of the obstacle; if an agent enters the potential field equilibrium point, a perturbation potential field is generated, and the perturbation potential field is added to the resultant force to obtain the total resultant force; the specific process is as follows:

[0089] Potential field equilibrium point detection determines whether a potential field equilibrium point has occurred by calculating the consistency coefficient between the motion directions of each agent in the cluster and the repulsive force of obstacles. The formula is as follows:

[0090] (9)

[0091] in, Let be the unit vector representing the agent's current direction of motion. The unit vector representing the direction of the repulsive force from the obstacle; Let be the consistency coefficient between the agent's direction of motion and the repulsive force of the obstacle, when hour, The threshold parameter is used to determine the potential field equilibrium point. When the agent enters the potential field equilibrium point, a perturbation potential field is generated.

[0092] The method for generating the perturbation potential field is as follows:

[0093] An adaptive reference axis design method based on the motion direction is adopted to generate perturbation components that are strictly orthogonal to the motion velocity direction, ensuring the generation of an effective perturbation potential field, as detailed below:

[0094] Initially, the X-axis (horizontal direction) is chosen as the reference axis, and the perturbation direction vector is calculated. If equation (10) is satisfied, then determine Trapped direction:

[0095] (10)

[0096] in, This represents the degradation threshold, used to determine... If the object is in a state of geometric degradation, switch the Y-axis (vertical direction) as the reference axis; otherwise, use the X-axis as the reference axis.

[0097] At this point, using the Y-axis as the reference axis, the disturbance direction vector is obtained. ; through normalization processing This allows for the acquisition of a perturbation basis orthogonal to the velocity direction, ensuring that agents within the cluster can effectively generate a perturbation potential field regardless of their direction of motion.

[0098] Finally, the generated perturbation potential field is compared with the agent entering the potential field equilibrium point (such as...). Figure 3 The gravitational, repulsive, and formation forces (as shown) combine to form a resultant force, causing it to deviate from its equilibrium point, as... Figure 2 As shown.

[0099] S7: Update the position, velocity, and trajectory information of each agent; repeat steps S2 to S6 until all agents reach the target point.

[0100] To verify the effectiveness of the designed cluster adaptive obstacle avoidance method integrating dynamic weights and cooperative potential fields, relevant simulations were performed in Matlab. All simulations were conducted within a two-dimensional planar region of 12m × 12m. This region effectively simulates the movement of agents in a relatively confined space, accommodates multiple obstacles and agents, and ensures sufficient space for movement and adjustment during obstacle avoidance and target attainment. The simulation environment included eight randomly distributed circular fixed obstacles with a radius of 0.4m, simulating various real-world scenarios such as warehousing and logistics, and factory automation, where the obstacles were fixed. The cluster consisted of three agents arranged in a triangular formation, used to verify the obstacle avoidance and formation maintenance performance of a small-scale agent cluster. This can be extended to larger-scale agent clusters. The starting positions of the agents within the cluster were (1,1;1,2;2,2), the target position was (10,10), and the maximum speed of the agents was 0.5 m / s. -1 The collision determination condition is that the distance between the robot and the obstacle is less than 0.4m.

[0101] Figure 2 This demonstrates the trajectory of the agent swarm near the potential equilibrium point after the addition of a perturbation potential field. The results are compared with those without the perturbation potential field. Figure 3 Compared to the previous method, it is evident that the overall trajectory of the intelligent agent swarm is smoother and more consistent when traversing areas with dense obstacles, without any stagnation or oscillation. Under the combined influence of attraction, repulsion, and disturbance forces, the agents within the swarm can adjust their direction of motion in real time, successfully bypassing obstacles and continuing towards the target point. Especially in areas where potential field equilibrium is likely to occur (approximately X=4–6 m, Y=4–6 m), the trajectories of the agents within the swarm exhibit a stable obstacle-avoiding trend, indicating that the disturbance potential field can effectively disrupt the original potential field equilibrium, allowing the system to regain the direction of the net force, thereby avoiding getting trapped in local minima.

[0102] Figure 4 The demonstration shows that after introducing a dynamic weighting mechanism, agents within the swarm move diagonally, traversing a dense obstacle zone, and achieve monotonic convergence in the target neighborhood (X≈10 m, Y≈10 m). The three trajectories highly overlap, indicating that under the same potential field parameters and approximate initial geometric relationships, the swarm response exhibits consistency. The dynamic weighting provides a distance-dependent nonlinear amplification of the attractive force: as agents approach the target, the attractive term is enhanced as the distance decreases, thus offsetting the relative advantage of the repulsive force in the target neighborhood, avoiding the formation of a "target perimeter barrier" and local minima traps, and ensuring that the resultant force direction maintains a unimodal and continuous orientation towards the target. Therefore, compared to the case without dynamic weighting (… Figure 5 The back-and-forth oscillations and path jitters generated near the target exhibit a smooth and continuous trajectory.

[0103] Figure 6 The demonstration showed that after introducing formation force, when agents enter areas with dense obstacles, the distance between individual agent pairs temporarily increases (to avoid obstacles by creating lateral spacing), but quickly returns to near the ideal value after crossing, with the overall fluctuation amplitude significantly smaller than in the case without formation force. As the agent cluster approaches the terminal stage, the spacing converges to a smaller value. This is because the algorithm triggers a formation release and disbanding threshold in the target neighborhood, allowing individuals to converge to the same target point. Formation force provides repulsion / attraction compensation on both the "too close" and "too far" sides, forming a closed-loop adjustment of geometric relationships, thereby limiting obstacle-induced relative pose perturbations within an acceptable range. The release and disbanding threshold mechanism avoids unnecessary pulling and oscillations in the terminal stage, achieving a smooth conclusion of "near-target disbanding—rapid convergence."

[0104] The embodiments of the present invention are given for illustrative and descriptive purposes only, and are not intended to be exhaustive or to limit the invention to the forms disclosed. Many modifications and variations will be apparent to those skilled in the art. The embodiments were chosen and described in order to better illustrate the principles and practical application of the invention, and to enable those skilled in the art to understand the invention and to design various embodiments with various modifications suitable for a particular purpose.

Claims

1. A swarm adaptive obstacle avoidance method based on an improved artificial potential field, characterized in that, include: S1: Initialize the position, velocity, and trajectory information of each agent in the agent cluster; S2: Based on the current position of each agent, calculate the distance between the center of the agent cluster and the target point, compare the distance with the set disbanding threshold, and calculate the formation force between each agent based on the actual relative position and the expected relative position between each agent and the other agents. S3: The attractiveness of the target point to each agent is designed non-linearly, and the attractiveness of the target point to each agent is calculated based on the dynamic weighting mechanism. S4: Calculate the repulsive force of the target point on each agent; S5: Calculate the net force on each agent based on the attractive and repulsive forces of the target point on each agent and the formation force between each agent; S6: Detect the potential field equilibrium point based on the consistency coefficient of the motion direction of each agent and the repulsive force of the obstacle; if the agent enters the potential field equilibrium point, a perturbation potential field is generated, and the perturbation potential field is added to the resultant force to obtain the total resultant force; S7: Update the position, velocity, and trajectory information of each agent; Repeat steps S2 to S6 until all agents reach the target point.

2. The swarm adaptive obstacle avoidance method based on an improved artificial potential field according to claim 1, characterized in that, In step S2, the formation force of each agent is the vector sum of the elastic constraint forces exerted on each agent by the other agents. Its magnitude is proportional to the deviation between the current actual relative position and the desired relative position, and its direction is along the shortest path to restore the desired formation, as shown in the following formula: （1） in, Represents intelligent agents With intelligent agents Formation strength between them; , Representing intelligent agents respectively and intelligent agents The current location; , Representing intelligent agents respectively and intelligent agents The desired position; Indicates the location of the center of the intelligent agent cluster; Indicates the location of the target point; This represents the formation force coefficient.

3. The swarm adaptive obstacle avoidance method based on an improved artificial potential field according to claim 2, characterized in that, The desired position is the position of each agent to maintain the ideal formation.

4. A swarm adaptive obstacle avoidance method based on an improved artificial potential field according to claim 2 or 3, characterized in that, The center position of the agent cluster is the average coordinate of the current positions of each agent.

5. A swarm adaptive obstacle avoidance method based on an improved artificial potential field according to claim 2 or 3, characterized in that, In step S3, the attractiveness of the target point to each agent is calculated based on the dynamic weighting mechanism. : （2） In the formula, Represents intelligent agents Distance to the target point; This is the gain coefficient, which controls the degree to which the attraction increases when the agent approaches the target; To modify the attractiveness of the target point to the agent, This is the gain coefficient. It is a vector, and its size is the agent's position. and target point location The Euclidean distance is the distance from the agent to the target point.

6. The swarm adaptive obstacle avoidance method based on an improved artificial potential field according to claim 5, characterized in that, In step S4, the repulsive force of the target point on each agent for: （3） In the formula, It is the proportionality coefficient; It is a vector, and its size is the agent's position. and obstacle location The Euclidean distance, with the direction from the obstacle to the agent; is a constant, representing the maximum distance at which the obstacle affects the agent.

7. A swarm adaptive obstacle avoidance method based on an improved artificial potential field according to claim 6, characterized in that, In step S5, the net force acting on each agent for: （4） The motion update equation of the agent is: （5） in, For intelligent agents in The equation of motion at time t.

8. The swarm adaptive obstacle avoidance method based on an improved artificial potential field according to claim 1, characterized in that, In step S6, the method for detecting the potential field equilibrium point is as follows: The formula for calculating the consistency coefficient of motion direction and obstacle repulsion force among agents in the cluster is as follows: （6） in, Let be the unit vector representing the current direction of motion of the agent. It is the unit vector representing the direction of the repulsive force from the obstacle; Let be the consistency coefficient between the agent's direction of motion and the repulsive force of the obstacle, when hour, The threshold parameter is used to determine whether the agent has entered the potential field equilibrium point.

9. A swarm adaptive obstacle avoidance method based on an improved artificial potential field according to claim 1, characterized in that, In step S6, the perturbation potential field is generated using an adaptive reference axis design method based on the motion direction, generating perturbation components that are strictly orthogonal to the motion velocity direction to ensure the generation of an effective perturbation potential field, as detailed below: Initially, the X-axis is chosen as the reference axis, and the perturbation direction vector is calculated. If equation (7) is satisfied, then determine Trapped direction: （7） in, Indicates the degradation threshold; At this point, using the Y-axis as the reference axis, the disturbance direction vector is obtained. ; through normalization processing This allows for the acquisition of a perturbation basis orthogonal to the velocity direction, ensuring that agents within the cluster can effectively generate an effective perturbation potential field regardless of their direction of motion. Finally, the generated perturbation potential field is added to the resultant force on the agent that enters the potential field equilibrium point to form a total resultant force, which causes the agent to leave the equilibrium point.

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