Marine unmanned ship formation obstacle avoidance and cooperation method based on improved artificial potential field method

Abstract

The invention discloses a marine unmanned ship formation obstacle avoidance and cooperation method based on an improved artificial potential field method, and the method comprises the steps: obtaining a control resultant force according to the attraction force, repulsive force, cooperation force and a speed correction term of a ship body; updating the velocity vector of the boat body by using the control resultant force so as to optimize the path; the space position of the boat body is divided into two areas, the minimum value of the minimum distance of the two areas serves as the minimum distance, and the distance between the boat bodies is monitored and adjusted; and dynamically adjusting the path by using the expected path direction of the hull, the path updating step factor and the direction disturbance suppression correction term. According to the embodiment of the invention, multiple intelligent mechanisms such as nonlinear potential field adjustment, inter-boat collaborative modeling and division and conquering real-time calculation are fused, and the safety, stability and adaptability of unmanned boat formation are effectively improved in a template-free formation scene. The method has high adaptive capacity in multi-task, multi-obstacle and autonomous coordination tasks, and path conflict and collision risks can be remarkably reduced.

Description

TECHNICAL FIELD

[0001] The embodiment of the present disclosure relates to the technical field of marine equipment control, and particularly relates to a marine unmanned surface vehicle formation obstacle avoidance and cooperation method based on an improved artificial potential field method. BACKGROUND

[0002] In terms of marine resource development and marine safety guarantee, intelligent marine unmanned cluster technology is becoming a key supporting technology in marine development and security tasks due to its advantages in multi-task cooperation, environmental adaptability and robustness. Through the cooperative operation of multiple autonomous unmanned platforms, the technology can perform diversified tasks such as resource exploration, environmental monitoring, patrol and search and rescue, and significantly improves the operation efficiency and safety.

[0003] In an unmanned cluster system, intelligent decision and planning algorithms play a decisive role in the overall execution effect, especially in dynamic formation transformation, obstacle avoidance control and path optimization without preset templates. In a complex marine environment, the change of formation cannot rely on fixed templates, but needs to be self-organized to form a coordinated and orderly "natural" formation. This template-free formation mode is particularly suitable for search, patrol and avoidance tasks, and can form a diverse and dynamic formation structure through real-time sensing and cooperation between boats.

[0004] In view of the complex and changeable marine environment, the existing unmanned surface vehicle cluster faces multiple challenges in the process of dynamic formation transformation. First, since no fixed formation template is preset, each boat needs to rely on autonomous decision to adjust its route, which is prone to path intersection and collision during adjustment. Second, the traditional artificial potential field method is prone to local minimum in dense obstacle areas, resulting in failure to avoid obstacles and lack of adaptability to complex obstacle patterns. In addition, when the number of unmanned surface vehicles is large, the real-time monitoring and calculation efficiency of the minimum distance between the boats is low, the cooperation mechanism is unstable, and the system scale expansion is limited. Finally, the existing template-free formation algorithm generally lacks a stable coordination mechanism, making it difficult to realize continuous and orderly formation evolution, which restricts the real-time performance and cooperation of the system.

[0005] Therefore, it is necessary to improve one or more problems in the related technical solutions described above.

[0006] It should be noted that this section aims to provide background or context for the technical solutions of the present disclosure stated in the claims. The description herein is not admitted to be prior art merely because it is included in this section. SUMMARY

[0007] The purpose of the embodiment of the present disclosure is to provide a marine unmanned surface vehicle formation obstacle avoidance and cooperation method based on an improved artificial potential field method, thereby at least partially overcoming one or more problems caused by the limitations and defects of the related art.

[0008] This disclosure provides a method for obstacle avoidance and cooperation in marine unmanned surface vessels (USVs) formation based on an improved artificial potential field method, including: A nonlinear repulsive force function is established based on the inverse square growth relationship of the distance variable between the hull and the force field intensity. Inertial compensation is applied to the actual velocity direction of the hull in the previous step to obtain the velocity correction term; A cooperative potential field function is established based on the attractive force applied when the distance between two adjacent vessels is greater than the safe distance threshold and the repulsive force applied when the distance between two adjacent vessels is less than the safe distance threshold. Based on the attractive force, repulsive force, cooperative force, and velocity correction term acting on the hull, the resultant force for hull control is obtained; The velocity vector of the hull is updated using the control resultant force to optimize the unmanned surface vessel formation path; The space of the hull is divided into two regions. The minimum of the closest distances between the two regions is taken as the global current estimated minimum distance. The distance between the hulls in the region with a preset width at the boundary between the two regions is monitored and adjusted. The preset width is 1.5 to 2.5 times the minimum distance. The desired path direction of the hull is obtained based on the target guidance component and the inter-hull structure coupling component. By utilizing the expected path direction of the hull, the path update step size factor, and the direction disturbance suppression correction term, the path of the unmanned surface vessel formation is dynamically adjusted to achieve smooth transformation of the formation structure and coordinated movement.

[0009] In one embodiment of this disclosure, the attractive force acting on the hull is calculated based on the relative relationship between the hull and the target. The model is as follows:

[0010] in, As the attractiveness coefficient, , These are the positions of the hull and the target, respectively. This represents the direction vector between the hull and the target.

[0011] In one embodiment of this disclosure, the nonlinear repulsive force function The expression is as follows:

[0012] in, It is the repulsive force coefficient; , which is the current Euclidean distance between the hull and the obstacle; d 0 indicates the threshold radius of the repulsive force; The value should be a very small positive number to prevent the denominator from approaching zero. This indicates the location of the obstacle.

[0013] In one embodiment of this disclosure, the velocity correction term The expression is as follows:

[0014] in, To adjust the weighting coefficients, This represents the velocity vector at the previous moment.

[0015] In one embodiment of this disclosure, the cooperative potential field function The expression is as follows:

[0016] in, k cool For coordination force adjustment coefficient, This is the actual distance between the two boats. ds The preset safe distance threshold, The first j , No. i The position vector of the vessel.

[0017] In one embodiment of this disclosure, the control resultant force is... The expression is as follows: .

[0018] In one embodiment of this disclosure, the globally currently estimated minimum distance for:

[0019] in, d L , d R These are the shortest distances between the two regions obtained by dividing the spatial position of the hull.

[0020] In one embodiment of this disclosure, when the real-time minimum distance between the two boats is less than a preset safe distance threshold, a collision avoidance mechanism is activated. This mechanism adds a reinforcing repulsive force component to the cooperative potential field of the boats, or introduces a lateral adjustment vector into the control resultant force, forcing a slight deviation in the boat trajectory, thereby gradually increasing the distance between the boats.

[0021] In one embodiment of this disclosure, the desired path direction of the hull is... The expression is as follows:

[0022] in, Indicates the desired path direction of the i-th ship. , These represent the positions of the i-th and j-th ships, respectively. Guide the target component. This refers to the inter-vessel structural coupling component. This is the relative position weighting factor.

[0023] In one embodiment of this disclosure, the path update step size factor The expression is as follows:

[0024] in, Based on step size, Let be the local density estimate for the i-th vessel. Density threshold; Directional perturbation suppression correction term The expression is as follows:

[0025] in, The path direction at the previous moment; , is the smoothing coefficient.

[0026] The technical solutions provided by the embodiments of this disclosure may include the following beneficial effects: This disclosure presents an improved artificial potential field method for obstacle avoidance and coordination in marine unmanned surface vessel (USV) formations. This method integrates multiple intelligent mechanisms, including nonlinear potential field adjustment, inter-vessel cooperative modeling, and divide-and-conquer real-time computation, effectively improving the safety, stability, and adaptability of USV formations in template-less formation scenarios. It exhibits high adaptability in multi-task, multi-obstacle, and autonomous coordination tasks, significantly reducing path conflicts and collision risks, lowering the overall collision rate by over 65%, improving path planning efficiency by 40%, and significantly enhancing formation stability and obstacle avoidance success rate. This method provides a future-oriented, flexible, and reliable natural formation control approach for intelligent USV formation systems. Attached Figure Description

[0027] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0028] Figure 1 A flowchart illustrating a method for obstacle avoidance and cooperation in marine unmanned surface vessels based on an improved artificial potential field method in an exemplary embodiment of this disclosure is shown. Figure 2This diagram illustrates the formation transformation results without specifying the template position in an exemplary embodiment of this disclosure. Figure 3 A graph showing the time-velocity analysis results in an exemplary embodiment of this disclosure is provided. Detailed Implementation

[0029] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0030] Furthermore, the accompanying drawings are merely illustrative diagrams of embodiments of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities.

[0031] This example implementation provides a method for obstacle avoidance and coordination in marine unmanned surface vessels (USVs) formation based on an improved artificial potential field method. Please refer to [link / reference]. Figure 1 The method may include: S101-S108, as follows: S101, a nonlinear repulsive force function is established based on the inverse square growth relationship of the distance variable between the hull and the force field intensity. S102, perform inertial compensation on the actual velocity direction of the hull in the previous step to obtain the velocity correction term; S103, Establish a cooperative potential field function based on the attractive force applied when the distance between two adjacent boats is greater than the safe distance threshold and the repulsive force applied when the distance between two adjacent boats is less than the safe distance threshold; S104, based on the attractive force, repulsive force, cooperative force and velocity correction term acting on the hull, the resultant force for hull control is obtained; S105, The velocity vector of the hull is updated using the control resultant force to optimize the unmanned surface vessel formation path; S106, the spatial position of the hull is divided into two regions, and the minimum of the closest distances between the two regions is taken as the minimum distance currently estimated globally. The distance between the hulls in the region with a preset width at the boundary between the two regions is monitored and adjusted, wherein the preset width is 1.5 to 2.5 times the minimum distance. S107, the desired path direction of the hull is obtained based on the target guidance component and the inter-hull structure coupling component; S108 utilizes the hull's desired path direction, path update step size factor, and direction disturbance suppression correction term to dynamically adjust the path of the unmanned surface vessel formation, achieving smooth transformation of the formation structure and coordinated movement.

[0032] This embodiment integrates multiple intelligent mechanisms, including nonlinear potential field adjustment, inter-vessel cooperative modeling, and divide-and-conquer real-time computation, effectively improving the safety, stability, and adaptability of unmanned surface vessel (USV) formations in template-free formation scenarios. It exhibits high adaptability in multi-task, multi-obstacle, and autonomous coordination tasks, significantly reducing path conflicts and collision risks, lowering the overall system collision rate by over 65%, improving path planning efficiency by 40%, and significantly enhancing formation stability and obstacle avoidance success rate. This method provides a future-oriented, flexible, and reliable natural formation control approach for intelligent USV formation systems.

[0033] The following describes the specific implementation process of the obstacle avoidance and cooperation method for marine unmanned surface vessels based on the improved artificial potential field method.

[0034] I. Establishing a three-degree-of-freedom motion model and hull coordinate system for the unmanned surface vessel In the marine environment, unmanned surface vessels (USVs) often navigate at low speeds, and their main motions are forward movement, lateral movement, and turning around the vertical axis, which are three degrees of freedom in planar motion. Therefore, a three-degree-of-freedom planar motion model is usually established to describe their navigation state and assist in path planning and controller design.

[0035] 1. Coordinate system definition and transformation To more accurately describe the motion of unmanned surface vessels (USVs), two coordinate systems are needed: the inertial frame and the body frame. The inertial frame, usually represented by the geographic coordinate system NE, is a reference coordinate system fixed on Earth, with the x-axis pointing due north and the y-axis pointing due east, used to represent the absolute position of the USV on the sea surface. The body frame is a coordinate system fixed to the hull, with its origin at the USV's center of gravity, and it changes with the hull's motion. Xb, along the bow, represents the longitudinal direction of the USV's motion. Yb, along the starboard side, represents the lateral direction of the USV's motion.

[0036] When the unmanned surface vessel is at a heading angle When the angle between the bow and true north is known, the velocity in the ship's coordinate system can be converted to the rate of change of position in the inertial coordinate system using a rotation matrix. The coordinate transformation matrix (rotation matrix) is shown below:

[0037] This matrix represents the conversion of velocity vectors (such as propulsion speed, lateral speed, and turning angular velocity) in the hull coordinate system into velocities in the geographic inertial coordinate system, that is, the projection of the velocity onto the geographic direction after considering the current orientation of the hull.

[0038] 2. Kinematic Model When modeling an unmanned surface vessel (USV), the six-DOF (degrees of freedom) model needs to be simplified to facilitate better analysis of its motion control state. Before simplification, the following assumptions need to be made: Assumption 1: For unmanned surface vessels, it is assumed that they are typically operating at low speeds, meaning that the lateral and longitudinal velocities of the unmanned vessel satisfy... The higher-order nonlinear damping terms can be ignored. Considering only the linear damping term Then the formula is satisfied: .

[0039] Assumption 2: Assume that the mass distribution of the unmanned surface vessel is uniform and that it is symmetrical about both sides and about both front and back in the ship's coordinate system.

[0040] Assumption 3: The origin of the ship's coordinate system is the center of gravity of the unmanned ship, and the axes of the ship's coordinate system coincide with the principal axis of inertia of the unmanned ship.

[0041] Assumption 4: Ignore hydrodynamic coefficients of order 2 and above.

[0042] Based on the above assumptions, for most surface vessel motion control problems, the ship's three degrees of freedom of roll, pitch, and heave are typically ignored, and their corresponding velocity and angular velocity terms are set to 0, thus satisfying the following conditions: Considering only the ship's three degrees of freedom—pitch, sway, and bow—the unmanned surface vessel's position change rate in the inertial coordinate system originates from its velocity in the ship's coordinate system. Transformed using the rotation matrix above, the following kinematic model is obtained:

[0043] in, This indicates the position and heading angle of the unmanned surface vessel in the inertial coordinate system. This represents the velocity vector in the ship's coordinate system. u Indicates the speed of the ship in the longitudinal direction of its forward movement. v Indicates the lateral drift speed of the ship. r This represents the angular velocity of the ship's rotation about its vertical axis (bow roll rate).

[0044] 3. Dynamic model (force-motion relationship) Unmanned surface vessels (USVs) not only exhibit changes in position, but their velocity also varies with time under the influence of external thrust, drag, and interference forces. A dynamic model is required, based on Newton's second law, to establish the following form:

[0045] Where M is the mass and additional mass matrix; Here, represents the Coriolis force and centrifugal force matrix; D is the damping matrix, describing the resistance of the hydrodynamic forces. , which is the control input vector, representing the main thrust, lateral thrust, and bow torque; d ext Indicates external disturbance. d int This represents uncertainties and modeling errors within the system.

[0046] II. Obstacle Avoidance and Cooperative Path Guidance Based on Improved Artificial Potential Field Method To achieve coordinated obstacle avoidance and path guidance for multiple vessels in complex and dynamic marine environments, a path planning and control method with both local responsiveness and global consistency needs to be designed. Currently, the commonly used artificial potential field method guides the vessel towards the target point by constructing an attractive field, while simultaneously driving the vessel away from obstacles by constructing a repulsive force field, thus achieving path planning and obstacle avoidance control. However, in practical applications, the traditional artificial potential field method has significant limitations. For example, it is prone to getting stuck in local minima in areas with dense obstacles or narrow spaces, causing the vessel to stagnate, or producing discontinuous obstacle avoidance trajectories in complex structures, making it difficult to meet the requirements for continuous, safe, and efficient propulsion of multi-vehicle formations.

[0047] To address the aforementioned issues, this invention proposes an improved artificial potential field method for obstacle avoidance and collaborative path guidance. This method integrates three key mechanisms based on the traditional potential field model: (1) designing a nonlinear repulsive force function to enhance sensitivity to changes in obstacle distance and improve navigability in complex terrain; (2) introducing a velocity history correction term to escape local equilibrium zones and improve global motion coherence; and (3) constructing a collaborative potential field function between vessels to achieve elastic guidance and maintain safe distances between vessels, ensuring the stable evolution of the formation structure. Through these mechanisms, each unmanned surface vessel can autonomously achieve dynamic obstacle avoidance, formation maintenance, and target tracking based on local perception and computation, without relying on a preset formation template, thus meeting the collaborative navigation requirements of multi-vessel systems in complex environments.

[0048] 1. Attraction Model During target navigation, the unmanned surface vessel (USV) needs to continuously monitor its actual position in the inertial coordinate system. With the mission objective The relative relationship between them generates a guiding force, propelling the hull towards the target point step by step. Therefore, an attraction model is constructed as follows:

[0049] in, As the attractiveness coefficient, , The approximation speed is controlled based on the hull position and the target position. This represents the direction vector between the submarine and the target. The model generates the force direction by calculating the real-time position difference, guiding the submarine to approach the target quickly and stably, and providing continuous guidance during the path advancement, thus providing a directional basis for the overall target convergence of the formation.

[0050] 2. Construction of Nonlinear Repulsive Force Function In obstacle avoidance, traditional repulsive force models often employ linear or exponential functions, which can lead to abrupt force field changes in densely packed obstacle areas, causing drastic fluctuations in the hull's motion or navigation path instability. To avoid these problems, this invention constructs a nonlinear repulsive force function and introduces a finite effective distance. By adjusting the inverse square growth relationship of the distance variable, the force field strength is flexibly adjusted. The expression for the repulsive force is:

[0051] in, It is the repulsive force coefficient; , which is the current Euclidean distance between the hull and the obstacle; d 0 indicates the threshold radius of the repulsive force; The value should be a very small positive number to prevent the denominator from approaching zero. This indicates the location of the obstacle.

[0052] This nonlinear repulsive force function can generate gentle offset guidance at long distances, and gradually increases the force when approaching obstacles, guiding the hull to adjust its course in advance. This effectively avoids the high-frequency adjustments and path jitter caused by sudden changes in the force field in traditional models, and improves obstacle avoidance stability and passage consistency in complex areas.

[0053] 3. Speed ​​history correction mechanism To further enhance the navigation system's path continuity and ability to evade local traps, a velocity history correction term is introduced into the resultant force model. This correction term compensates for inertia based on the actual velocity direction of the hull in the previous step, maintaining propulsion within a minimum region where attractive and repulsive forces cancel each other out, causing the resultant force to approach zero. The specific expression of the velocity correction term is as follows:

[0054] in, This represents the velocity vector of the motion at the previous moment. To adjust the weighting coefficients, this mechanism incorporates historical motion trends into the current control input, maintaining the continuity of the path, enhancing the system's escape capability in low potential energy regions, and preventing path stagnation or control oscillations.

[0055] 4. Inter-ship cooperative potential field model In multi-submarine formation operations, maintaining the distance between submarine hulls is crucial for preserving formation alignment and preventing collisions. To address this, this invention designs a cooperative potential field function to simulate the elastic attraction and repulsion relationships between submarine hulls. When the distance between two adjacent submarine hulls exceeds a set safe distance threshold, the system applies an attractive force to promote convergence; when the distance is too close, a repulsive force is applied to maintain spacing, forming an elastic coupling mechanism. The cooperative force is defined as follows:

[0056] in, k cool For coordination force adjustment coefficient, This is the actual distance between the two boats. ds The preset safe distance threshold, The first j , No. i The position vector of the vessel. ds This represents the target spacing that the formation control aims to maintain. The distance between the vessels is greater than... ds Attracted, the distance between the boats is less than ds Time rejection.

[0057] The cooperative potential field enables each vessel to automatically adjust its own state according to the position of neighboring vessels, achieving natural formation control without relying on a global template, and maintaining the overall stable and orderly operation of the system.

[0058] 5. Formation obstacle avoidance cooperative model and updates During integrated path control, the resultant force acting on each vessel consists of attractive force, repulsive force, cooperative force, and velocity correction term. The final resultant control force is expressed as follows:

[0059] Based on the result of the combined force calculation, the velocity vector of the hull is updated using a discrete iterative method:

[0060] in: This is the speed adjustment coefficient. The time step is defined as follows. Within each decision cycle, this control strategy calculates the navigation resultant force in real time based on current environmental perception and local interaction information, and dynamically updates the velocity and direction to achieve obstacle avoidance, self-adjustment, and formation maintenance of the formation.

[0061] Based on the aforementioned modeling and control mechanisms, the improved artificial potential field method proposed in this invention not only enhances the traditional linear repulsion model in terms of force field structure, but also achieves stability in the path control process and coordination in formation organization by introducing historical velocity inertial compensation and inter-ship cooperation mechanisms. This method does not rely on external path templates or centralized scheduling; it can complete dynamic obstacle avoidance and path optimization solely based on local perception and distributed potential field effects. It possesses good environmental adaptability and system scalability, and is particularly suitable for autonomous navigation and cooperative control tasks in marine unmanned surface vessel formations under highly dynamic, dense obstacle, and multi-objective mission conditions.

[0062] III. Minimum Distance Perception and Dynamic Collision Avoidance Strategy Based on Divide and Conquer To ensure that multi-boat formation systems can effectively avoid path crossings and collisions during navigation, it is necessary to construct an efficient, real-time distance monitoring and dynamic avoidance mechanism. Traditional methods often calculate the Euclidean distance between each pair of boats by traversing all possible combinations. However, this method has high computational complexity and slow response speed when there are many boats, making it difficult to meet the real-time requirements of high-frequency control cycles. To address this issue, this invention designs a real-time calculation and collision avoidance mechanism for minimum inter-boat distance based on a divide-and-conquer approach. This mechanism reduces the computational burden while ensuring the timeliness and accuracy of safe distance monitoring between boats, providing dynamic safety assurance for the overall formation control system.

[0063] 1. Ship position representation and distance definition Suppose that the unmanned surface vessel (USV) formation in the current frame contains n USVs, and the positions of each USV in the inertial coordinate system are a set of two-dimensional vectors:

[0064] Then any two boats i , j The expression for calculating the Euclidean distance between them is:

[0065] This distance value serves as the core variable for assessing the risk of collision between hulls, and is used for minimum distance extraction and safe zone determination.

[0066] 2. Divide and Conquer Structure and Minimum Distance Search Algorithm To reduce the time complexity of calculating the distance between boats, a spatial partitioning approach is adopted to construct a nearest point pair calculation process based on the divide-and-conquer method. First, the boat position set Q is sorted in ascending order by its x-coordinate, dividing it into two subsets Q'', left and right. L Q R By recursively solving for the minimum distance, the shortest distance d between the left and right subsets can be obtained. L d R Then, take the minimum value as the minimum distance of the current global estimate:

[0067] Establish a width of 2 near the partition boundaries of the left and right subsets. d min (Preset width) of the middle band area Q M The algorithm performs lateral filtering and neighborhood pairing only on the hull within the central band to determine if a shortest distance combination spanning both left and right subsets exists. Within the central band, each point only needs to be compared with a maximum of 6 points, thus significantly reducing redundant computations.

[0068] Through the above divide-and-conquer strategy, the time complexity of calculating the minimum distance between boats is reduced from the traditional... Downgraded to This greatly improves the execution efficiency of the algorithm, enabling the large formation system to stably achieve high-frequency distance monitoring during operation.

[0069] 3. Safety assessment and collision avoidance response mechanism Once the minimum distance of the hull in the current frame is obtained... The system will be based on the warning threshold. Real-time assessment of the safety status between the hulls:

[0070] When the real-time distance between two boats is less than In such cases, the system immediately triggers the collision avoidance mechanism, adding a reinforced repulsive force component to the cooperative potential field of the two hulls, or introducing a lateral adjustment vector into the overall control resultant force, forcing a slight deviation in the hull trajectory, thereby gradually increasing the distance between the hulls and ensuring the structural safety and mission continuity of the formation operation.

[0071] also, ds > > The maximum diameter of the hull, and the distance between the boats in normal formations is... ds Nearby, if the distance between the boats is less than Then it enters the collision avoidance priority mode.

[0072] IV. Path Dynamic Orchestration Mechanism and Structure Scheduling Method To enhance the structural orderliness and path coordination of unmanned surface vessels (USVs) during dynamic formation operations, this application constructs a dynamic path arrangement mechanism based on improvements to the artificial potential field method and real-time distance calculation mechanism. This mechanism can autonomously generate dynamic path adjustment strategies based on real-time environmental changes, target orientation, and inter-vessel status without template guidance, achieving smooth transformation of formation structure and coordinated movement. This mechanism is particularly suitable for formation missions facing complex sea conditions, dynamic obstacles, and changing tasks, exhibiting high flexibility and system robustness.

[0073] 1. Path direction guidance and structural offset control During formation operations without a specified template, each vessel generates a path guidance vector based on its directional relationship with the mission objective, while dynamically adjusting its structural orientation in conjunction with the distribution of surrounding vessels. The path orientation update is expressed as follows:

[0074] in, Indicates the first i The expected path and direction of the vessel. , They represent the first i , j The position of the boat Guide the target component. This refers to the inter-vessel structural coupling component. This is the relative position weighting factor. This expression ensures that the hull not only maintains propulsion in the target direction, but also achieves relative coordination with surrounding hulls in the local structure, avoiding directional dispersion and formation fragmentation.

[0075] 2. Structural density adjustment and inter-submarine synchronization strategy To avoid collision risks caused by excessive spacing or localized overcrowding during formation flying, this invention introduces a density-aware synchronization adjustment strategy. The path update step size adjustment factor is calculated using the neighboring density information of the hull within a local area.

[0076] in, Based on step size, Let be the local density estimate for the i-th vessel. The density threshold is used. This mechanism can effectively regulate the propulsion speed of each vessel, causing vessels in dense areas to decelerate and those in sparse areas to accelerate appropriately, thereby improving the structural consistency and dynamic balance of the overall formation.

[0077] 3. Orientation perturbation suppression and path smoothing mechanism In dynamic environments, to prevent drastic changes in orientation during path adjustment, this invention introduces a path smoothing function to suppress orientation disturbances. The orientation disturbance suppression correction term is defined as follows:

[0078] in, This represents the path direction at the previous moment. , which is a smoothing coefficient, adjusts the weighted fusion ratio between the current direction and the historical direction. This mechanism can significantly reduce the risk of path abrupt changes and ensure the stability and controllability of the submarine's propulsion process.

[0079] In summary, this invention proposes a method for obstacle avoidance and coordination in marine unmanned surface vessels (USVs) formation based on an improved artificial potential field method. First, this method introduces a nonlinear repulsive force model and a historical velocity adjustment mechanism to avoid the traditional potential field from getting stuck in local minima, thus improving the response capability to complex obstacle areas. Second, it maintains stable vessel spacing through an inter-vessel cooperative force model, constructing an elastic coupling mechanism between vessels to enhance formation stability. Third, it employs a divide-and-conquer algorithm to calculate the minimum distance between vessels in real time, ensuring that paths do not intersect and maintaining swarm safety. Finally, it introduces a dynamic velocity vector adjustment mechanism, enabling the formation structure to spontaneously form and adaptively evolve with the environment.

[0080] V. Experiment and Results Analysis This experiment was conducted using the Win-Qt simulation platform, with data processing and visualization performed using MATLAB. The experiment ran on a Windows high-performance computing platform with 8 cores and 16GB of memory. During the simulation, the system loaded a formation control task without specifying template positions. Given randomly distributed initial positions, the system guided unmanned surface vessels to form a formation using an improved artificial potential field algorithm and a dynamic path scheduling strategy.

[0081] The unmanned surface vessel (USV) starts at a random position without a pre-defined target template. Dynamic obstacles and disturbances are introduced into the external environment to simulate obstacle avoidance and cooperative transformation processes under complex sea conditions. The USV's position and velocity changes are recorded during the simulation to analyze formation evolution and velocity trends.

[0082] 2. Analysis of Experimental Results This experiment does not pre-set template positions for the unmanned surface vessel (USV) formation; each USV autonomously forms a formation during navigation. The formation control algorithm guides the USVs to maintain reasonable relative distances and directions, without requiring the formation to approximate a specific template. The position information of the USVs at each time step during this process is recorded, and the dynamic changes in the formation are observed. The formation transformation results without specifying a template position are as follows: Figure 2 As shown.

[0083] from Figure 2 As can be seen, in simulation tests without specifying a template position, the unmanned surface vessel system exhibits good self-organizing capabilities. In the initial formation stage, the hulls gradually approach each other under the guidance and cooperative forces, forming a relatively symmetrical and evenly distributed formation. Even without a specific formation template, the hulls maintain reasonable spacing and directional consistency, gradually forming near-linear, grid-like, or closed-loop structures, fully verifying the adaptive characteristics of the system's path guidance mechanism.

[0084] By recording the velocity information of each unmanned surface vessel (USV) at various time steps during formation changes, a time-velocity analysis plot is generated. The experiment will analyze the velocity trends during the initial, intermediate, and final stages of formation changes, and compare the velocity differences between positions with and without specified templates. The time-velocity plot helps determine the stability of the formation and the smoothness of the transformation. The time-velocity analysis results are as follows: Figure 3 As shown.

[0085] from Figure 3 The speed-time analysis chart shows that the submarine accelerated and concentrated on adjusting its path in the early stages of formation, then stabilized and gradually decelerated in the middle and later stages, eventually maintaining a low-speed navigation state in the structurally stable region. Throughout the process, the submarine's speed changes were smooth without significant jumps, indicating that the path scheduling process possessed good stability and continuity.

[0086] Experimental results show that the proposed improved artificial potential field control method and path dynamic arrangement mechanism, under conditions without a preset template, possess good self-organization and environmental adaptability. The formation evolution diagram shows that the unmanned surface vessels can gradually form a structurally stable and orderly formation from an initial dispersed state, verifying the synergy and consistency of formation control. The time-velocity analysis diagram shows that the velocity changes of each vessel are continuous throughout the transformation process, the process of approaching the final state is smooth, and the motion path does not show abrupt changes or disturbances, demonstrating the system's good dynamic response and stable control characteristics.

[0087] In a multi-task, multi-obstacle, autonomous coordination task environment, further simulation verification shows that the control system can significantly reduce path conflict and collision risk, with an overall collision rate reduction of more than 65%, a path planning efficiency improvement of about 40%, and a significant improvement in formation stability and obstacle avoidance success rate, indicating that the proposed method has excellent system robustness and engineering practical value.

[0088] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for obstacle avoidance and cooperation in marine unmanned surface vessel (USV) formations based on an improved artificial potential field method, characterized in that: include: A nonlinear repulsive force function is established based on the inverse square growth relationship of the distance variable between the hull and the force field intensity. Inertial compensation is applied to the actual velocity direction of the hull in the previous step to obtain the velocity correction term; A cooperative potential field function is established based on the attractive force applied when the distance between two adjacent vessels is greater than the safe distance threshold and the repulsive force applied when the distance between two adjacent vessels is less than the safe distance threshold. The resultant force for hull control is obtained based on the attractive force, repulsive force, cooperative force, and velocity correction term acting on the hull. The velocity vector of the hull is updated using the control resultant force to optimize the unmanned surface vessel formation path; The space of the hull is divided into two regions. The minimum of the closest distances between the two regions is taken as the global current estimated minimum distance. The distance between the hulls in the region with a preset width at the boundary between the two regions is monitored and adjusted. The preset width is 1.5 to 2.5 times the minimum distance. The desired path direction of the hull is obtained based on the target guidance component and the inter-hull structure coupling component. By utilizing the expected path direction of the hull, the path update step size factor, and the direction disturbance suppression correction term, the path of the unmanned surface vessel formation is dynamically adjusted to achieve smooth transformation of the formation structure and coordinated movement.

2. The method for obstacle avoidance and cooperation in marine unmanned surface vessels based on the improved artificial potential field method according to claim 1, characterized in that, The attractive force acting on the hull is calculated based on the relative relationship between the hull and the target. The model is as follows: in, As the attractiveness coefficient, , These are the positions of the hull and the target, respectively. This represents the direction vector between the hull and the target.

3. The method for obstacle avoidance and cooperation in marine unmanned surface vessels based on the improved artificial potential field method according to claim 2, characterized in that, The nonlinear repulsive force function The expression is as follows: in, It is the repulsive force coefficient; , which is the current Euclidean distance between the hull and the obstacle; d 0 indicates the threshold radius of the repulsive force; The value should be a very small positive number to prevent the denominator from approaching zero. This indicates the location of the obstacle.

4. The method for obstacle avoidance and coordination in marine unmanned surface vessels based on the improved artificial potential field method according to claim 3, characterized in that, Speed ​​correction The expression is as follows: in, To adjust the weighting coefficients, This represents the velocity vector at the previous moment.

5. The method for obstacle avoidance and cooperation in marine unmanned surface vessels based on the improved artificial potential field method according to claim 4, characterized in that, Cooperative potential function The expression is as follows: in, k cool For coordination force adjustment coefficient, This is the actual distance between the two boats. ds The preset safe distance threshold, The first j , No. i The position vector of the vessel.

6. The method for obstacle avoidance and cooperation in marine unmanned surface vessels based on the improved artificial potential field method according to claim 5, characterized in that, Controlling the resultant force The expression is as follows: 。 7. The method for obstacle avoidance and cooperation in marine unmanned surface vessels based on the improved artificial potential field method according to claim 6, characterized in that, The minimum distance currently estimated globally for: in, d L , d R These are the shortest distances between the two regions obtained by dividing the spatial position of the hull.

8. The method for obstacle avoidance and cooperation in marine unmanned surface vessels based on the improved artificial potential field method according to claim 7, characterized in that, When the real-time minimum distance between the two boats is less than the preset safe distance threshold, the collision avoidance mechanism is activated. This adds a reinforcing repulsive force component to the cooperative potential field of the boats, or introduces a lateral adjustment vector into the control resultant force, forcing the boat trajectories to deviate slightly, thereby gradually increasing the distance between the boats.

9. The method for obstacle avoidance and cooperation in marine unmanned surface vessels based on the improved artificial potential field method according to claim 8, characterized in that, Desired Path Direction of the Submarine The expression is as follows: in, Indicates the first i The expected path and direction of the vessel. , They represent the first i , j The position of the boat Guide the target component. This refers to the inter-vessel structural coupling component. This is the relative position weighting factor.

10. The method for obstacle avoidance and cooperation in marine unmanned surface vessels based on the improved artificial potential field method according to claim 9, characterized in that, Path update step size factor The expression is as follows: in, Based on step size, Let be the local density estimate for the i-th vessel. Density threshold; Directional disturbance suppression correction term The expression is as follows: in, The path direction at the previous moment; , is the smoothing coefficient.

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