Ship multi-target collaborative avoidance trajectory planning method and system for complex navigation channel

Abstract

The invention provides a ship multi-target collaborative avoidance trajectory planning method and system for a complex channel, and relates to the technical field of ship avoidance planning, and the method comprises the steps: obtaining the position, motion state and channel environment constraint information of a ship, constructing a multi-ship motion model, extracting the relative motion relation of the ship, and calculating a collision risk region; and establishing a collaborative avoidance topological graph to determine an avoidance sequence, constructing a multi-objective optimization function to solve a collaborative avoidance trajectory, and issuing and executing the collaborative avoidance trajectory. According to the invention, multi-ship coordinated collision avoidance can be realized, the navigation efficiency of a channel is improved, the energy consumption cost is reduced, the track smoothness is ensured, and the navigation safety is effectively enhanced.

Description

Methods and systems for multi-objective cooperative collision avoidance trajectory planning for ships in complex waterways Technical Field

[0001] This invention relates to the field of ship collision avoidance planning technology, and in particular to a method and system for ship multi-objective cooperative collision avoidance trajectory planning for complex waterways. Background Technology

[0002] With the rapid development of the maritime transport industry, waterway traffic is becoming increasingly busy, and the density of ship traffic is constantly increasing. Especially in complex waterway environments, the problem of ship collision avoidance has become more prominent. Ship collision avoidance refers to taking reasonable operational measures to avoid collision accidents when multiple ships are at risk of collision during navigation. Traditional ship collision avoidance mainly relies on the crew's judgment and decision-making based on experience and international maritime collision avoidance regulations. This often makes it difficult to make optimal decisions in complex waterway environments and when multiple ships are passing each other.

[0003] With the development of computer technology and artificial intelligence, automated ship collision avoidance technology has become an important research direction in the field of intelligent ships. Currently, various ship collision avoidance trajectory planning methods have been proposed, including methods based on geometric models, methods based on artificial potential fields, and methods based on optimal control. These methods can achieve collision avoidance decisions for single ships or in simple navigation environments to a certain extent, but they still have some obvious defects and shortcomings. Summary of the Invention

[0004] The embodiments of the present invention provide a method and system for multi-objective cooperative collision avoidance trajectory planning for ships in complex waterways, which can solve the problems in the prior art.

[0005] A first aspect of this invention provides a method for planning multi-objective cooperative avoidance trajectories for ships in complex waterways, comprising: acquiring the current position information, motion state information, and waterway environmental constraint information of target ships, and constructing a multi-ship motion state space model including ship dynamics constraints and waterway boundary constraints; based on the multi-ship motion state space model, extracting the relative motion relationships between each target ship and calculating collision risk areas; according to the collision risk areas and in conjunction with the avoidance priority constraints of maritime collision avoidance rules, establishing a directed acyclic cooperative avoidance topology graph with each target ship as a node and avoidance relationships as directed edges, and determining the avoidance execution order of each target ship; according to the avoidance execution order, constructing a multi-objective optimization function including navigation time cost, energy consumption cost, and avoidance action smoothness, and introducing trajectory coupling constraint terms with adjacent nodes in the directed acyclic cooperative avoidance topology graph into the multi-objective optimization function, solving for the cooperative avoidance trajectory of each target ship; and distributing the cooperative avoidance trajectory to the corresponding target ship for execution.

[0006] The process involves acquiring the current position information, motion state information, and channel environmental constraint information of target vessels, and constructing a multi-ship motion state space model that includes ship dynamics constraints and channel boundary constraints. This includes: extracting the spatial coordinates and heading angle information of each target vessel based on its current position information, and combining this with the velocity vector and angular velocity from the motion state information to establish the motion state vector of each target vessel; constructing a set of dynamic equations describing the time evolution of the motion state vector based on the vessel's steering response characteristics and propulsion system output characteristics, and introducing constraints characterizing the boundary of the vessel's maneuverability into the dynamic equations to obtain a ship dynamics constraint model; performing geometric modeling on the channel environmental constraint information, extracting the boundary contour lines of the navigable waterway and the spatial occupancy range of the restricted area, and transforming the boundary contour lines and the spatial occupancy range into a set of inequality constraints restricting the range of values ​​for the motion state vector to obtain a channel boundary constraint model; and coupling and fusing the ship dynamics constraint model and the channel boundary constraint model to construct a multi-ship motion state space model that includes the motion state vector, the set of dynamic equations, and the set of inequality constraints.

[0007] Based on the multi-ship motion state space model, the relative motion relationships between the target ships are extracted and the collision risk area is calculated. This includes: obtaining the motion state vectors of each target ship from the multi-ship motion state space model; constructing a ship pair for any two target ships; calculating the velocity vector difference and position vector difference of the ship pair to obtain the relative velocity vector and relative position vector; projecting and decomposing the relative velocity vector along the direction of the relative position vector to obtain the radial relative velocity component and the tangential relative velocity component; determining that the ship pair is in a near motion state when the radial relative velocity component is negative; extracting the corresponding hull outline geometric parameters; and calculating the maximum hull outline... For small-interval ships, the ratio of the minimum interval to the radial relative velocity component is determined as the nearest encounter time. Using the nearest encounter time as a node, the motion state vectors of the ship pair are substituted into the multi-ship motion state space model for forward evolution to obtain the predicted position and calculate the spatial distance between the ship pairs. When the spatial distance is less than the safe distance threshold, a spatial envelope with a radius equal to the sum of the ship's outer contour parameters and the safe distance threshold is constructed with the predicted position as the center. The time window of the nearest encounter time and the spatial envelope are combined to form a spatiotemporal collision risk region. All ship pairs are traversed, and their respective spatiotemporal collision risk regions are merged in terms of spatiotemporal dimensions to obtain a collision risk region composed of multiple discrete spatiotemporal blocks.

[0008] Based on the collision risk area and the avoidance priority constraints of maritime collision avoidance rules, a directed acyclic collaborative avoidance topology is established with each target vessel as a node and avoidance relationships as directed edges. The avoidance execution order for each target vessel is determined, including: extracting vessel pairs with spatiotemporal collision risks from the collision risk area; for each vessel pair, obtaining the corresponding heading angle and relative bearing angle; calculating the cosine of the heading angle difference and the sine of the relative bearing angle; and using the cosine and sine values ​​as a two-dimensional vector; mapping the quadrant region where the two-dimensional vector is located to an encounter situation, crossing situation, or overtaking situation; and determining the yielding order for each vessel pair based on the avoidance priority constraints of maritime collision avoidance rules. Ships and ships traveling in the straight direction are considered. A topology graph is constructed with each target ship as a node. Directed edges are established from the giving-way ship node to the traveling-way ship node. The nearest encounter time and the radius of the spatial envelope of the collision risk area for the corresponding ship pair are marked on the directed edges to form a cooperative avoidance topology graph. Strongly connected component identification is performed on the cooperative avoidance topology graph, and the avoidance timeliness parameter of each directed edge is calculated. The directed edge with the smallest avoidance timeliness parameter is disconnected to obtain a directed acyclic cooperative avoidance topology graph. Based on the directed acyclic cooperative avoidance topology graph, the node with the largest out-degree is added to the execution queue and the out-degree of each node is updated in real time. The avoidance execution order of each target ship is determined according to the order in which the nodes enter the execution queue.

[0009] The process involves identifying strongly connected components in the cooperative avoidance topology graph and calculating the avoidance timeliness parameter for each directed edge. The directed edge with the smallest avoidance timeliness parameter is then disconnected to obtain a directed acyclic cooperative avoidance topology graph. This includes: constructing a reachability matrix for each node in the cooperative avoidance topology graph; identifying strongly connected components with bidirectional reachable paths through matrix exponentiation; and extracting the subgraph structure formed by the directed edges within each strongly connected component. For each directed edge, the time window width and spatial envelope volume of the corresponding ship pair's collision risk region are extracted. The reciprocal of the time window width is used as the time sensitivity, and the spatial envelope... The ratio of the volume of the waterway to the total volume of the navigable waterway is used as the spatial conflict intensity. All closed loops containing each directed edge are extracted from the subgraph structure. The total number of edges in each closed loop is counted, and the reciprocal of the minimum total number of edges is used as the topological coupling coefficient. A nonlinear weighted sum is then performed, combining the time sensitivity and the spatial conflict intensity, to obtain the avoidance timeliness parameter for each directed edge. In the subgraph structure of each strongly connected component, the directed edge with the smallest avoidance timeliness parameter is selected sequentially for disconnection. After each disconnection, the reachability matrix is ​​recalculated. The disconnection operation is terminated when there is no bidirectional reachable path in the matrix, resulting in a directed acyclic topology graph.

[0010] Based on the avoidance execution order, a multi-objective optimization function is constructed, incorporating navigation time cost, energy consumption cost, and avoidance action smoothness. A trajectory coupling constraint term with adjacent nodes in the directed acyclic cooperative avoidance topology is introduced into this multi-objective optimization function. The cooperative avoidance trajectory of each target vessel is then solved, including: extracting the set of incoming nodes corresponding to each target vessel from the directed acyclic cooperative avoidance topology according to the avoidance execution order; substituting the initial trajectory of the target vessel corresponding to the incoming node into the multi-ship motion state space model for forward evolution to obtain the predicted motion state and unfold it in the spatiotemporal domain to form a trajectory occupancy spatiotemporal band; constructing a trajectory point set for each target vessel and calculating navigation... The time summation, propulsion power time integral, and heading change angular acceleration summation are used as navigation time cost, energy consumption cost, and avoidance maneuver smoothness, respectively, and weighted summation is performed to construct a multi-objective optimization function. The set of trajectory points of each target vessel and the spatiotemporal band occupied by the trajectory are subjected to spatiotemporal domain intersection detection. The trajectory points are required not to enter the spatial projection area of ​​the spatiotemporal band, and the time of passing through the collision risk area is later than the corresponding vessel of the incoming node plus a preset time margin, which is used as the trajectory coupling constraint term. The trajectory coupling constraint term is used as the constraint condition, and the multi-objective optimization function is iteratively solved with the spatial coordinates and timestamps of the trajectory points as optimization variables to obtain the cooperative avoidance trajectory of each target vessel.

[0011] Using the trajectory coupling constraint term as a constraint condition, and taking the spatial coordinates and timestamps of the trajectory points as optimization variables, the multi-objective optimization function is iteratively solved to obtain the cooperative avoidance trajectories of each target vessel. This includes: constructing a local optimization variable vector from the spatial coordinates and timestamps of the trajectory points of each target vessel; decomposing the multi-objective optimization function into local optimization sub-functions based on the node connection relationships in the directed acyclic cooperative avoidance topology graph; decomposing the trajectory coupling constraint term into coupling constraint sub-terms; and introducing Lagrange multipliers and auxiliary variables to construct an augmented Lagrange function for the coupling constraint sub-terms. In each global iteration, each target vessel fixes the local optimization variables of other vessels. The variable vector is transformed, and the spatial coordinates and timestamps of the ship's trajectory points are used as optimization variables. The augmented Lagrangian function is solved locally, and the spatial coordinates and timestamps of the ship's trajectory points are updated according to the gradient. After all target ships have completed local optimization, the auxiliary variables are recalculated based on the updated trajectory point spatial coordinates and timestamps. The degree of violation of coupling constraint sub-items is detected and the Lagrange multipliers are updated. The iteration terminates when the norm of the change of spatial coordinates and timestamps of all target ship trajectory points is less than the original residual threshold, and the sum of the degree of violation of coupling constraint sub-items is less than the dual residual threshold. The local optimization variable vector of each target ship is output as the cooperative avoidance trajectory of each target ship.

[0012] A second aspect of this invention provides a multi-objective cooperative avoidance trajectory planning system for ships in complex waterways, comprising: a first unit for acquiring the current position information, motion state information, and waterway environmental constraint information of target ships, and constructing a multi-ship motion state space model including ship dynamics constraints and waterway boundary constraints; a second unit for extracting the relative motion relationships between target ships and calculating collision risk areas based on the multi-ship motion state space model; a third unit for establishing a directed acyclic cooperative avoidance topology graph with each target ship as a node and avoidance relationships as directed edges, based on the collision risk areas and the avoidance priority constraints of maritime collision avoidance rules, and determining the avoidance execution order of each target ship; a fourth unit for constructing a multi-objective optimization function including navigation time cost, energy consumption cost, and avoidance action smoothness based on the avoidance execution order, and introducing trajectory coupling constraint terms with adjacent nodes in the directed acyclic cooperative avoidance topology graph into the multi-objective optimization function, and solving for the cooperative avoidance trajectory of each target ship; and a fifth unit for distributing the cooperative avoidance trajectory to the corresponding target ship for execution.

[0013] A third aspect of the present invention provides an electronic device, comprising: a processor; and a memory for storing processor-executable instructions; wherein the processor is configured to invoke the instructions stored in the memory to execute the aforementioned method.

[0014] A fourth aspect of the present invention provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the aforementioned method.

[0015] The beneficial effects of this application are as follows: by constructing a multi-ship motion state space model that includes ship dynamics constraints and waterway environment constraints, the planned avoidance trajectory is made more in line with the actual ship handling characteristics and waterway safety requirements, thereby improving the feasibility and practicality of trajectory planning.

[0016] By extracting the relative motion relationships between ships and calculating the collision risk area, and combining international maritime collision avoidance rules, a collaborative avoidance topology map was established, realizing the systematic processing of complex multi-ship avoidance scenarios and effectively solving the multi-ship interactive avoidance problem that is difficult to handle in traditional methods.

[0017] The avoidance execution sequence calculated based on the collaborative avoidance topology graph ensures that avoidance behavior complies with international maritime collision avoidance rules, improving the compliance and reliability of avoidance decisions. By constructing a multi-objective optimization function that includes navigation time cost, energy consumption cost, and the smoothness of avoidance actions, and introducing a trajectory coupling constraint term for adjacent nodes, comprehensive optimization of navigation efficiency, energy consumption, and operational comfort is achieved, avoiding the limitations of optimizing a single indicator. Attached Figure Description

[0018] Figure 1 is a flowchart illustrating the multi-target cooperative avoidance trajectory planning method for ships in complex waterways according to an embodiment of the present invention; Figure 2 is a flowchart illustrating the method for solving the cooperative avoidance trajectory of each target ship according to an embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] The technical solution of the present invention will be described in detail below with reference to specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments.

[0021] Figure 1 is a flowchart illustrating the multi-objective cooperative avoidance trajectory planning method for ships in complex waterways according to an embodiment of the present invention. As shown in Figure 1, the method includes: acquiring the current position information, motion state information, and waterway environmental constraint information of the target ships, and constructing a multi-ship motion state space model that includes ship dynamics constraints and waterway boundary constraints; based on the multi-ship motion state space model, extracting the relative motion relationships between each target ship and calculating the collision risk area; according to the collision risk area and combined with the avoidance priority constraints of maritime collision avoidance rules, establishing a directed acyclic cooperative avoidance topology graph with each target ship as a node and avoidance relationships as directed edges, and determining the avoidance execution order of each target ship; according to the avoidance execution order, constructing a multi-objective optimization function that includes navigation time cost, energy consumption cost, and avoidance action smoothness, and introducing trajectory coupling constraint terms with adjacent nodes in the directed acyclic cooperative avoidance topology graph into the multi-objective optimization function, solving for the cooperative avoidance trajectory of each target ship; and distributing the cooperative avoidance trajectory to the corresponding target ship for execution.

[0022] In one optional implementation, the current position information, motion state information, and channel environmental constraint information of the target vessels are acquired, and a multi-ship motion state space model including ship dynamics constraints and channel boundary constraints is constructed. This includes: extracting the spatial coordinates and heading angle information of each target vessel based on its current position information, and combining the velocity vector and angular velocity from the motion state information to establish the motion state vector of each target vessel; constructing a set of dynamic equations describing the time evolution of the motion state vector based on the vessel's steering response characteristics and propulsion system output characteristics, and introducing constraints characterizing the boundary of the vessel's maneuverability into the dynamic equations to obtain a ship dynamics constraint model; performing geometric modeling on the channel environmental constraint information, extracting the boundary contour line of the navigable waterway and the spatial occupancy range of the restricted area, and transforming the boundary contour line and the spatial occupancy range into a set of inequality constraints restricting the range of values ​​of the motion state vector to obtain a channel boundary constraint model; and coupling and fusing the ship dynamics constraint model and the channel boundary constraint model to construct a multi-ship motion state space model including the motion state vector, the set of dynamic equations, and the set of inequality constraints.

[0023] In this specific embodiment, the current position information, motion state information, and waterway environmental constraint information of the target vessel are acquired. For the position information, the latitude and longitude coordinates of the vessel are collected through the Automatic Identification System (AIS), radar, or shore-based monitoring system, and the geographic coordinates are converted into planar coordinates (x, y) in the Cartesian coordinate system. At the same time, the heading angle ψ information is extracted from the vessel navigation equipment. This angle represents the angle between the vessel's bow and due north, with clockwise being positive. Combined with the speed information, the longitudinal speed u, lateral speed v, and turning angular velocity r of the vessel are obtained, forming a complete motion state vector [x, y, ψ, u, v, r].

[0024] For each target ship, a three-degree-of-freedom equation of motion is established based on its physical characteristics. Taking a certain type of container ship as an example, its dynamic equation can be expressed as: Ship position change equation: Through coordinate transformation, the velocity components in the ship's coordinate system are converted to the global coordinate system, realizing dynamic position updates. The projections of the longitudinal velocity u and the lateral velocity v in the global coordinate system determine the ship's trajectory on the plane.

[0025] The equation for changes in ship attitude is: the rate of change of the heading angle is equal to the angular velocity of the turning angle r, which represents the change of the heading angle over time.

[0026] Ship speed variation equation: Considering factors such as ship mass, moment of inertia, hydrodynamic coefficient and external disturbances, an acceleration equation is established. The longitudinal acceleration is affected by the thrust and drag torque provided by the main propulsion system, while the lateral acceleration and steering acceleration are mainly affected by the rudder torque and the interaction force between the hull and the water.

[0027] Introducing maneuverability boundary constraints into the dynamic equations, for the steering system, the range of the rudder angle δ is set to [-δ]. max , δ max The typical value is ±35 degrees; the rate of change of rudder angle is limited to [-δ']. max , δ' max The range is typically ±5 degrees / second. For the main unit system, the range of variation for the thruster rotation speed n is set to [n]. min n max The rate of change of rotational speed does not exceed ±n' max This is to prevent main engine overload and, at the same time, limit the range of ship speed changes to ensure that the longitudinal acceleration |du / dt|≤a max Lateral acceleration |dv / dt|≤a max Angular acceleration |dr / dt|≤r max These parameters are determined based on the ship's size and structural characteristics.

[0028] The channel environmental constraint information processing adopts a polygon fitting method, extracting the channel boundary point set from the electronic chart system. For irregular channel boundaries, piecewise linear interpolation technology is applied to construct continuous boundary curves. For straight channels, the line connecting the two endpoints is taken as the boundary; for curved channels, multi-segment polylines are used for approximation. The density of inflection points of the polylines is dynamically adjusted according to the curvature change. More inflection points are set in areas with large curvature to improve fitting accuracy.

[0029] The no-navigation zone is also represented by polygons. Based on the shape characteristics of the area, the irregular area is decomposed into a combination of several simple polygons. Each polygon consists of a vertex sequence {(x i y i Let $\mathbf{i}$ be defined as $\mathbf{i}$, where $n$ is the number of vertices. For a circular no-fly zone, it is represented by the center and radius of the circle and converted into an approximate regular polygon. The number of sides is determined according to the accuracy requirements.

[0030] The channel boundaries and restricted navigation areas are transformed into a set of inequality constraints. For line segment boundaries, let the two endpoints of the boundary line segment be (x1, y1) and (x2, y2). Then, the inequality constraint that the center point (x, y) of the ship must satisfy is that the distance from the point to the line is not less than the safe distance Dsafe. For polygonal restricted navigation areas, the ship must satisfy the constraint that the minimum distance from the point to the polygon boundary is greater than the safe distance. The safe distance Dsafe is dynamically calculated based on the ship size, maneuverability, and channel traffic rules, and is usually 1.2 to 2 times the ship length.

[0031] When constructing a multi-ship motion state space model, the dynamic constraints of each ship are coupled with the channel boundary constraints, and a state vector X is established for each ship i. i=[x i y i , ψ i u i v i r i and control input vector U i =[δ i n i The state vectors of all ships are merged into an extended state vector X = [X1, X2, ..., X...]. n ], where n is the number of ships. Similarly, by merging all control inputs, we obtain the extended control vector U = [U1, U2, ..., U...]. n ].

[0032] Based on the extended state vector, a comprehensive set of dynamic equations, dX / dt=f(X, U, t), is constructed. This set of equations includes the motion equations of all ships. Simultaneously, all constraints are combined into a set of inequalities g(X, U)≤0, including constraints on ship maneuverability, channel boundary constraints, and collision avoidance safety constraints between ships. For collision avoidance constraints, a minimum safe distance Dij between any two ships i and j is set, ensuring that sqrt((x, U, t) is satisfied at any given time. i -x j ) 2 +(y i -y j ) 2 )≥D ij .

[0033] The resulting multi-ship motion state space model contains a complete set of state vectors, dynamic equations, and constraints, which can be used for subsequent trajectory planning and collision avoidance decision calculations. This model has strong practicality and can accurately describe the motion characteristics and safety constraints of ships in complex waterway environments.

[0034] In one optional implementation, based on the multi-ship motion state space model, the relative motion relationships between the target ships are extracted and the collision risk area is calculated. This includes: obtaining the motion state vectors of each target ship from the multi-ship motion state space model; constructing a ship pair for any two target ships; calculating the velocity vector difference and position vector difference of the ship pair to obtain the relative velocity vector and relative position vector; projecting and decomposing the relative velocity vector along the direction of the relative position vector to obtain the radial relative velocity component and the tangential relative velocity component; determining that the ship pair is in a near motion state when the radial relative velocity component is negative; extracting the corresponding hull outline geometric parameters; and calculating the collision risk area. The minimum spacing of the ship's outer contour is used to determine the nearest encounter time by the ratio of the minimum spacing to the radial relative velocity component. Using the nearest encounter time as a node, the motion state vectors of the ship pair are substituted into the multi-ship motion state space model for forward evolution to obtain the predicted position and calculate the spatial distance between the ship pairs. When the spatial distance is less than the safety distance threshold, a spatial envelope with a radius equal to the sum of the ship's outer contour parameters and the safety distance threshold is constructed with the predicted position as the center. The time window of the nearest encounter time and the spatial envelope are combined to form a spatiotemporal collision risk region. All ship pairs are traversed, and their respective spatiotemporal collision risk regions are merged in terms of spatiotemporal dimensions to obtain a collision risk region composed of multiple discrete spatiotemporal blocks.

[0035] In this specific embodiment, the motion state vectors of each target ship are obtained from a multi-ship motion state space model. These state vectors include key parameters such as the ship's current position, heading, and speed. Assuming there are N target ships within the monitoring area at a certain moment, the motion state vector of each ship can be represented as (x... i y i , θ i v i ), where x i and y i θ represents the position coordinates of the ship in a Cartesian coordinate system. i The angle of the ship's heading, v i Indicates the speed of a ship.

[0036] For any two target ships, construct a ship pair and calculate their relative motion relationship. Taking ship A and ship B as an example, calculate their relative position vector ΔP = (x B - x A y B - y A This refers to the position difference vector from ship A to ship B. Simultaneously, the relative velocity vector ΔV = (v_A - v_B) between the two ships is calculated. B ·cosθ B - v A ·cosθ Av B ·sinθ B -v A ·sinθ A ), which represents the speed of ship B relative to ship A.

[0037] By projecting the relative velocity vector onto the direction of the relative position vector, we obtain the radial relative velocity component v. r and tangential relative velocity component v t The radial relative velocity component represents the approach or departure velocities of the two ships along the line connecting them, and is calculated as v. r = (ΔP·ΔV) / |ΔP|, where · represents the vector dot product operation, |ΔP| represents the magnitude of the relative position vector, and the tangential relative velocity component represents the relative velocity of the two ships in the direction perpendicular to the line connecting them, which can be obtained by the difference between ΔV and its radial component.

[0038] When the radial relative velocity component v r When the value is negative, it indicates that the two ships are approaching each other. At this time, it is necessary to further assess the collision risk. After determining that the ships are in a state of approaching motion, the corresponding geometric parameters of the ship's outer contour are extracted. The outer contour of the ship can usually be simplified into an elliptical or rectangular model. For ships A and B, their length and width parameters are represented by (LA, WA) and (LB, WB), respectively.

[0039] Based on the ship's geometric parameters, calculate the minimum distance D between the outer contours of the two ship bodies. min Considering factors such as ship heading and shape, the minimum spacing is not only related to the distance between the center points of the two ships, but also to the ship's heading angle and hull size. The minimum spacing can be obtained through geometric calculations. For example, for a ship model simplified to a rectangle, the overlap of the projections of the two rectangles in various directions can be calculated to determine the minimum spacing.

[0040] Minimum spacing D min The ratio of the radial relative velocity component vr to the nearest encounter time t is determined. CPA = -D min / v r The closest meeting point represents the point in time when the two ships will reach their closest distance while maintaining their current course and speed.

[0041] Based on the most recent meeting time t CPA Using nodes, the motion state vectors of the ship pairs are substituted into the multi-ship motion state space model for forward evolution. During the forward evolution, the kinematic model can be used to predict the ship's position at time t. CPA The predicted position can be represented as the position coordinates at time (x) i + v i ·cosθ i ·t CPAy i + v i ·sinθ i ·t CPA ).

[0042] Based on the predicted position, the ship's position at t is calculated. CPA The spatial distance DCPA at any given time is used to determine if there is a potential collision risk if DCPA is less than the preset safe distance threshold Dsafe. The safe distance threshold can be dynamically adjusted according to factors such as the characteristics of the navigation waters, the type of vessel, and weather conditions. It can generally be set to several times the length of the vessel.

[0043] When a collision risk is confirmed, a spatial envelope is constructed centered on the predicted location. The radius of the spatial envelope is the sum of the hull's outer contour parameters and the safe distance threshold, i.e., RA = (LA / 2 + WA / 2) / 2 + Dsafe and RB = (LB / 2 + WB / 2) / 2 + Dsafe. The time window [t] of the nearest encounter time is then used. CPA - Δt, tCPA + Δt] combine with the spatial envelope to form a spatiotemporal collision risk region, where Δt can be determined based on the ship's maneuverability and response time.

[0044] The system iterates through all ship pairs, calculates their respective spatiotemporal collision risk areas, and merges these areas in terms of spatiotemporal dimensions. During the spatiotemporal dimension merging process, risk areas with overlapping time dimensions and similar spatial locations are aggregated to form larger continuous risk areas; while completely separate risk areas are kept independent. After merging, a set of collision risk areas composed of multiple discrete spatiotemporal blocks is obtained, which provides an important basis for subsequent route planning and collision avoidance decisions.

[0045] The above method enables accurate assessment of multi-vehicle collision risks, effectively identifies potential dangerous encounter scenarios, and provides reliable risk perception capabilities for automatic collision avoidance systems. In practical applications, the method can be adjusted according to the characteristics of different waters and vessel types to improve the adaptability and accuracy of collision risk assessment.

[0046] In one optional implementation, based on the collision risk area and the avoidance priority constraints of maritime collision avoidance rules, a directed acyclic collaborative avoidance topology is established with each target vessel as a node and avoidance relationships as directed edges. The avoidance execution order for each target vessel is determined, including: extracting each vessel pair with spatiotemporal collision risk from the collision risk area; for each vessel pair, obtaining the corresponding heading angle and relative bearing angle; calculating the cosine of the heading angle difference and the sine of the relative bearing angle; and using the cosine and sine values ​​as a two-dimensional vector; mapping the quadrant region where the two-dimensional vector is located to an encounter situation, crossing situation, or overtaking situation; and, based on the avoidance priority constraints of maritime collision avoidance rules, determining the avoidance execution order for each target vessel. The system identifies the give-way vessel and the direct-route vessel for each vessel pair. A topology graph is constructed using each target vessel as a node. Directed edges are established from the give-way vessel node to the direct-route vessel node. The nearest encounter time and the radius of the spatial envelope of the collision risk area for each vessel pair are marked on these directed edges, forming a cooperative avoidance topology graph. Strongly connected component identification is performed on the cooperative avoidance topology graph, and the avoidance timeliness parameter of each directed edge is calculated. The directed edge with the smallest avoidance timeliness parameter is disconnected, resulting in a directed acyclic cooperative avoidance topology graph. Based on this graph, the node with the largest out-degree is added to the execution queue, and the out-degree of each node is updated in real time. The avoidance execution order for each target vessel is determined according to the order in which nodes enter the execution queue.

[0047] In this specific embodiment, ship pairs with spatiotemporal collision risks are extracted from the collision risk area. For all target ships in the sea area, their future navigation trajectories are predicted based on their current position, heading, and speed. Potential collision risks are identified by calculating the closest distance point between the ships and the time of arrival at that point (i.e., the closest encounter time). If the closest distance point between two ships is less than the safe distance threshold and the time of arrival at that point is within a predetermined time window, then the pair of ships is considered to have a collision risk.

[0048] For each pair of vessels at risk of collision, obtain the corresponding heading angle and relative bearing angle. Assume that the heading angle of vessel A is θ. A The heading angle of ship B is θ B Then the difference in heading angle Δθ = θ A -θ B Simultaneously, calculate the relative azimuth angle φ of ship B with respect to ship A. Based on these two angles, calculate the two-dimensional vector v = (cos(Δθ), sin(φ)).

[0049] Based on the quadrant region where the two-dimensional vector v lies, the vessels can be mapped to the corresponding encounter situation. The specific mapping rules are as follows: when v falls in the first quadrant (cos(Δθ)>0, sin(φ)>0), it corresponds to a cross encounter situation; when v falls in the second quadrant (cos(Δθ)<0, sin(φ)>0), it corresponds to a face-to-face encounter situation; when v falls in the third or fourth quadrant (sin(φ)<0), it corresponds to an overtaking situation. After determining the situation, the give-way vessel and the vessel proceeding in the straight course are determined according to the International Regulations for Preventing Collisions at Sea (COLREGs). For example, in a cross encounter situation, the vessel seeing another vessel on its starboard side is the give-way vessel; in a face-to-face encounter situation, both vessels should yield to starboard; in an overtaking situation, the overtaking vessel is the give-way vessel.

[0050] A topology graph is constructed with each target vessel as a node. For each pair of vessels, a directed edge is established from the give-way vessel node to the direct-traffic vessel node. The nearest encounter time and the radius of the spatial envelope of the collision risk area of ​​the corresponding vessel pair are marked on the directed edge. For example, if vessel A is the give-way vessel and vessel B is the direct-traffic vessel, a directed edge is established from A to B, and their TCPA value is marked as 10 minutes and the spatial envelope radius is 300 meters. Directed edges between all vessel pairs are established in this way to form the initial cooperative avoidance topology graph.

[0051] In real-world multi-ship collision avoidance scenarios at sea, circular dependencies can occur, meaning directed cycles exist in the topology graph. For example, ship A needs to avoid ship B, B needs to avoid ship C, and C needs to avoid ship A, forming a circular dependency. To resolve this, we perform strong connected component identification on the cooperative avoidance topology graph to find all subgraphs with circular dependencies. For each strongly connected component with a circular dependency, we calculate the avoidance timeliness parameter of each directed edge, find the directed edge with the smallest timeliness parameter, and disconnect it, thus breaking the circular dependency. This process is repeated until no directed cycles exist in the topology graph, resulting in a directed acyclic cooperative avoidance topology graph.

[0052] Based on the directed acyclic collaborative avoidance topology, the avoidance execution order of each ship is determined. The out-degree of each node (ship) is calculated, which is the number of directed edges originating from that node. The out-degree represents the number of other ships that the ship needs to avoid. The node with the largest out-degree is added to the execution queue, indicating that the ship needs to perform the avoidance operation first. Whenever a node is added to the execution queue, the node and its related directed edges are removed from the graph, and the out-degree of the remaining nodes is updated. This process is continued, adding the node with the largest out-degree to the execution queue in turn, until all nodes have been added to the queue. The order in which the nodes enter the execution queue is the avoidance execution order of each target ship.

[0053] The collision avoidance sequence obtained by the above method fully considers the collision avoidance relationship and timeliness between vessels, ensuring that in multi-vessel coordinated collision avoidance, each vessel can perform collision avoidance operations in a reasonable order, thereby improving maritime traffic safety.

[0054] In one optional implementation, strongly connected component identification is performed on the cooperative avoidance topology graph, and the avoidance timeliness parameter of each directed edge is calculated. The directed edge with the smallest avoidance timeliness parameter is disconnected to obtain a directed acyclic cooperative avoidance topology graph. This includes: constructing a reachability matrix for each node in the cooperative avoidance topology graph; identifying strongly connected components with bidirectional reachable paths through matrix exponentiation; and extracting the subgraph structure formed by the directed edges within each strongly connected component. For each directed edge, the time window width and spatial envelope volume of the collision risk region of the corresponding ship pair are extracted, and the reciprocal of the time window width is used as the time sensitivity. The ratio of the volume of the spatial envelope to the total volume of the navigable waterway is used as the spatial conflict intensity. All closed loops containing each directed edge are extracted from the subgraph structure. The total number of edges in each closed loop is counted, and the reciprocal of the minimum total number of edges is used as the topological coupling coefficient. A nonlinear weighted sum is then performed, combining the time sensitivity and the spatial conflict intensity, to obtain the avoidance timeliness parameter for each directed edge. In the subgraph structure of each strongly connected component, the directed edge with the smallest avoidance timeliness parameter is sequentially selected for disconnection. After each disconnection, the reachability matrix is ​​recalculated. The disconnection operation is terminated when there is no bidirectional reachable path in the matrix, resulting in a directed acyclic topology graph.

[0055] In this specific embodiment, a cooperative avoidance topology graph needs to be obtained, where nodes represent sailing ships and directed edges represent avoidance relationships. If ship A needs to avoid ship B, a directed edge from A to B is established between the two nodes. In complex navigation environments, this avoidance relationship will form a circular dependency, leading to avoidance decision conflicts.

[0056] When performing strongly connected component identification on a cooperative avoidance topology graph, a reachability matrix R is constructed for each node in the graph. The matrix R has dimensions n×n, where n is the number of ships. If a path exists from ship i to ship j, then R[i, j] = 1; otherwise, it is 0. The reachability matrix R is then calculated using the power operation. 2 R 3 ...R n When R[i,j]=1 and R[j,i]=1, it means that there is a bidirectional reachable path between nodes i and j, and they belong to the same strongly connected component. Based on this principle, all strongly connected components in the graph can be identified, and the directed edges inside each strongly connected component can be extracted to form a subgraph structure.

[0057] For each directed edge, its avoidance timeliness parameter needs to be calculated. This step requires extracting the collision risk area between the corresponding ship pairs. Assuming that ships A and B have a collision risk within the time interval [t1, t2], the width of this time interval is Δt = t2 - t1. The reciprocal of the time window width is defined as the time sensitivity St = 1 / Δt, representing the urgency of the decision-making time. At the same time, the water space envelope volume V occupied by the two ships within this time window is calculated. s The total volume V of the navigable waterway t The ratio of the two values ​​yields the spatial conflict intensity S. s =V s / V t This reflects the limited space available for obstacle avoidance maneuvers.

[0058] From the subgraph structure of strongly connected components, extract all closed loops containing each directed edge. For example, if a directed edge e connects ships A and B, we need to find all closed loops containing e. Suppose we find k closed loops with path lengths L1, L2...L... k Then take the minimum value L. min =min(L1, L2...L k ), calculate the topological coupling coefficient S c =1 / L min The shorter the loop, the higher the coupling degree of the avoidance relationship, and the greater the possibility of decision-making conflict.

[0059] Based on the above parameters, calculate the avoidance timeliness parameter P for each directed edge: P = α·S t + β·S s + γ·S c In this formula, α, β, and γ are weighting coefficients that can be adjusted according to the actual navigation environment. This nonlinear weighted summation takes into account the combined effects of time urgency, space constraints, and topology.

[0060] In the process of breaking directed edges to form an acyclic topology, the subgraph within each strongly connected component is determined. For each subgraph, the avoidance timeliness parameter of each directed edge is calculated, and the directed edge with the smallest parameter value is selected for breaking. After breaking, the reachability matrix is ​​recalculated, and it is checked whether a bidirectional reachable path still exists. If it does, the next directed edge with the smallest parameter is selected for breaking; if it does not, the subgraph has been transformed into a directed acyclic graph, and the breaking operation is terminated. After performing this operation on all strongly connected components, the entire cooperative avoidance topology is transformed into a directed acyclic graph, thereby eliminating cyclic avoidance relationships.

[0061] In a practical application scenario, suppose there are four ships A, B, C, and D in a certain waterway intersection area. The initial avoidance relationship forms two cycles: A→B→C→A and C→D→C. Through reachability matrix analysis, two strongly connected components, {A, B, C} and {C, D}, are identified. After calculating the avoidance timeliness parameters of each directed edge, assuming that the parameter of the A→B edge is the smallest, disconnecting this edge eliminates the cycle within the {A, B, C} component. Similarly, disconnecting the C→D edge also eliminates the cycle within the {C, D} component. The final directed acyclic topology graph is B→C→A and D→C. Based on this, a clear avoidance decision sequence can be generated to ensure navigation safety.

[0062] This method solves the circular dependency problem in multi-ship avoidance decision-making through mathematical modeling and graph theory analysis, providing an effective tool for maritime traffic safety management. The core advantage of the method lies in its comprehensive consideration of time sensitivity, spatial conflict intensity and topological coupling, which minimizes the impact of broken edges on the overall avoidance effect and ensures the reliability and efficiency of avoidance decision-making.

[0063] Figure 2 is a flowchart illustrating the method for solving the cooperative avoidance trajectory of each target vessel according to an embodiment of the present invention. In an optional implementation, a multi-objective optimization function is constructed based on the avoidance execution order, including navigation time cost, energy consumption cost, and avoidance action smoothness. Trajectory coupling constraints with adjacent nodes in the directed acyclic cooperative avoidance topology are introduced into the multi-objective optimization function to solve for the cooperative avoidance trajectory of each target vessel. This includes: extracting the set of incoming nodes corresponding to each target vessel from the directed acyclic cooperative avoidance topology based on the avoidance execution order; substituting the initial trajectory of the target vessel corresponding to the incoming node into the multi-ship motion state space model for forward evolution to obtain the predicted motion state and unfolding it in the spatiotemporal domain to form a trajectory occupancy spatiotemporal band; and constructing a trajectory point set for each target vessel. The cumulative sum of navigation time, propulsion power time integral, and heading change angular acceleration is calculated and used as the navigation time cost, energy consumption cost, and avoidance maneuver smoothness, respectively. A weighted summation is then performed to construct a multi-objective optimization function. The set of trajectory points of each target vessel is subjected to spatiotemporal domain intersection detection with the spatiotemporal control zone occupied by the trajectory. The trajectory points are required not to enter the spatial projection area of ​​the spatiotemporal control zone, and the time of passing through the collision risk area must be later than the vessel corresponding to the incoming node plus a preset time margin, which is used as the trajectory coupling constraint term. The trajectory coupling constraint term is used as the constraint condition, and the multi-objective optimization function is iteratively solved with the spatial coordinates and timestamps of the trajectory points as optimization variables to obtain the cooperative avoidance trajectory of each target vessel.

[0064] In this specific embodiment, the ingress node information of each target vessel is extracted from the directed acyclic cooperative avoidance topology graph according to the determined avoidance execution order. For each node in the topology graph, all its ingress nodes are identified and formed into a set. For example, for node i, its ingress node set is denoted as Pre(i), representing all vessels that take precedence over vessel i in the avoidance execution. The motion trajectories of these priority vessels will constrain the avoidance decision of vessel i.

[0065] The initial trajectories of the target ships corresponding to these incoming edge nodes are substituted into the multi-ship motion state space model for forward evolution. The motion state of the ships can be described by parameters such as position coordinates (x, y), heading angle θ, and velocity v. Based on these parameters, the motion state of each priority ship in the future time window is predicted, and a series of state values ​​at discrete time points are obtained. The predicted trajectory of the ship is formed by connecting these predicted state points.

[0066] To ensure safe avoidance, these predicted trajectories need to be deployed in the spatiotemporal domain to form a trajectory occupancy spatiotemporal band. Specifically, at each discrete time point, with the ship's current position as the center, considering the ship's actual size and safety margin, a spatial region occupied by the ship is constructed. Connecting these spatial regions in chronological order forms the trajectory occupancy spatiotemporal band. This band represents the spatial region occupied by priority ships within a specific time period, and other ships should avoid entering these regions to prevent collision risks.

[0067] For each target vessel, a set of trajectory points is constructed. This set consists of a series of trajectory points, each containing position coordinates and a corresponding timestamp. Based on these trajectory points, three indicators are calculated: navigation time cost, energy consumption cost, and smoothness of avoidance maneuvers.

[0068] The navigation time cost is calculated by summing the time differences between adjacent time points in the trajectory point set, representing the total time required for the ship to complete the navigation. For the trajectory point set {p} of ship i... i1 p i2 , ..., p in}, where each point contains a timestamp t ij The time cost of travel is the sum of the differences between adjacent timestamps.

[0069] Energy consumption cost is calculated by integrating the product of ship propulsion power and time. Ship propulsion power is related to its speed and sailing resistance and can be estimated by empirical formulas or physical models. The total energy consumption cost is obtained by integrating the propulsion power over the entire sailing time.

[0070] The smoothness of the avoidance maneuver is calculated by accumulating the angular acceleration of the heading change. For the heading angle change between adjacent trajectory points, the second derivative, i.e., the angular acceleration, is calculated and accumulated to obtain the smoothness index of the avoidance maneuver. The larger the angular acceleration, the more drastic the heading change and the less smooth the avoidance maneuver.

[0071] We construct a multi-objective optimization function by weighting and summing the three indicators mentioned above. Let the travel time cost be T_cost, the energy cost be E_cost, and the smoothness of the avoidance maneuver be S_cost. Then the multi-objective optimization function is: J = w_T·T_cost + w_E·E_cost + w_S·S_cost, where w_T, w_E, and w_S are the weight coefficients of each indicator, which can be adjusted according to the specific application scenario.

[0072] To ensure the coordination of trajectories, coupling constraints need to be applied to the trajectories of each vessel. The intersection of the trajectory point set of each target vessel with the spatiotemporal control zone occupied by the trajectory of the priority vessel needs to be detected. The trajectory points are required not to enter the spatial projection area of ​​the spatiotemporal control zone to ensure that spatial conflicts are avoided. In addition, when a vessel needs to pass through a potential collision risk area, its passage time is required to be later than the time when the vessel corresponding to the incoming node passes through the area plus a preset time margin to ensure a safe time interval.

[0073] Using trajectory coupling constraints as constraints, and spatial coordinates and timestamps of trajectory points as optimization variables, the multi-objective optimization function is iteratively solved. Specifically, optimization algorithms such as gradient descent and genetic algorithms can be used. During the iteration process, the position and time of the trajectory points are continuously adjusted until all constraints are met and the optimization function value is minimized. The final set of trajectory points is connected to form the cooperative avoidance trajectories of each target ship. These trajectories not only meet the avoidance safety requirements, but also achieve comprehensive optimization in terms of time, energy consumption and operational smoothness.

[0074] In practical applications, the weighting coefficients of various parameters can be adjusted according to the characteristics of different waterways and vessel types to adapt to different navigation environments and needs. For example, safety margins and time margins can be increased in busy waterways, while the weight of energy consumption costs can be increased in energy-saving navigation scenarios. Through this multi-objective optimization method, intelligent decision-making for cooperative collision avoidance by vessels is achieved.

[0075] In one optional implementation, the trajectory coupling constraint term is used as a constraint condition, and the multi-objective optimization function is iteratively solved using the spatial coordinates and timestamps of the trajectory points as optimization variables to obtain the cooperative avoidance trajectories of each target vessel. This includes: constructing a local optimization variable vector from the spatial coordinates and timestamps of the trajectory points of each target vessel; decomposing the multi-objective optimization function into local optimization sub-functions based on the node connection relationships in the directed acyclic cooperative avoidance topology graph; decomposing the trajectory coupling constraint term into coupling constraint sub-terms; and introducing Lagrange multipliers and auxiliary variables to construct an augmented Lagrange function for the coupling constraint sub-terms. In each global iteration, each target vessel fixes other... The local optimization variable vector of the ship uses the spatial coordinates and timestamps of its own trajectory points as optimization variables. The augmented Lagrangian function is solved locally, and the spatial coordinates and timestamps of the ship's trajectory points are updated according to the gradient. After all target ships have completed local optimization, the auxiliary variables are recalculated based on the updated spatial coordinates and timestamps of the trajectory points. The degree of violation of the coupling constraint sub-items is detected and the Lagrange multipliers are updated. The iteration terminates when the norm of the change of the spatial coordinates and timestamps of all target ship trajectory points is less than the original residual threshold and the sum of the degree of violation of the coupling constraint sub-items is less than the dual residual threshold. The local optimization variable vector of each target ship is output as the cooperative avoidance trajectory of each target ship.

[0076] In this specific embodiment, the spatial coordinates and timestamps of the trajectory points of each target vessel constitute a local optimization variable vector. For each target vessel participating in cooperative avoidance, its planned trajectory is discretized into a series of trajectory points. Each trajectory point contains spatial coordinates and corresponding timestamp information. The spatial coordinates are represented using a two-dimensional coordinate system, including horizontal and vertical components. The timestamp records the expected time for the vessel to arrive at the trajectory point. The spatial coordinates and timestamps of all trajectory points of a single vessel are arranged in chronological order to form the local optimization variable vector of that vessel. The dimension of this vector depends on the accuracy of trajectory discretization; the more discretized points, the higher the dimension of the variable vector, and the more accurate the trajectory description.

[0077] Based on a pre-constructed directed acyclic cooperative obstacle avoidance topology, the constraints between ships are determined. Nodes in the topology represent ships participating in obstacle avoidance, and directed edges represent the obstacle avoidance priority relationships between ships. Using this topology, the original multi-objective optimization function is decomposed according to the node connectivity. Each local optimization sub-function contains only optimization objectives directly related to that ship, such as minimizing travel time, minimizing energy consumption, and minimizing deviation from the original route. Simultaneously, the trajectory coupling constraint terms describing collision avoidance, speed limits, and channel boundaries are correspondingly decomposed into multiple coupling constraint sub-terms. Each coupling constraint sub-term only involves ships directly connected in the topology.

[0078] To handle the decomposed coupled constraint sub-terms, an augmented Lagrange function is constructed by introducing Lagrange multipliers and auxiliary variables. The Lagrange multipliers are used to relax equality constraints, while the auxiliary variables are used to handle inequality constraints and complex nonlinear constraints. For the safety distance constraint between ships, relaxation variables are introduced to convert the inequality constraint into an equality constraint form. The value of the auxiliary variable reflects the degree of constraint violation. When the constraint is satisfied, the auxiliary variable tends to zero. The augmented Lagrange function adds a penalty term for constraint violation to the original objective function, and the strictness of constraint satisfaction is controlled by adjusting the penalty parameter.

[0079] In each global iteration, each target ship performs local optimization sequentially according to a predetermined order. The ship currently performing optimization has its local optimization variable vectors fixed compared to all other ships, using only the spatial coordinates and timestamp of its own trajectory point as optimization variables. In this case, the terms involving other ships in the augmented Lagrangian function can be considered constant terms, significantly reducing the size of the local optimization problem. Numerical optimization algorithms such as gradient descent or quasi-Newton methods are used to locally solve the augmented Lagrangian function, calculating the partial derivatives of the objective function with respect to the coordinates and timestamp of the ship's trajectory point. The optimization variables are updated along the negative gradient direction. To avoid oscillations caused by excessive trajectory update amplitude, an adaptive step-size strategy is adopted, dynamically adjusting the update step size according to the function value descent.

[0080] After all target vessels complete one round of local optimization, the values ​​of auxiliary variables are recalculated based on the updated spatial coordinates and timestamps of the trajectory points. For safety distance constraints, the minimum distance between vessels is calculated; if it is less than the safety threshold, the corresponding auxiliary variable is set to a positive value; otherwise, it is set to zero. For channel boundary constraints, it is checked whether the trajectory points exceed the channel range, and the excess distance is calculated as the auxiliary variable value. Based on the updated auxiliary variables, the degree of violation of each coupled constraint sub-item is evaluated. The degree of violation can be measured by the sum of squares or the sum of absolute values ​​of the constraint function values. According to the constraint violation situation, the Lagrange multipliers are adjusted using the multiplier update rule. For severely violated constraints, the corresponding Lagrange multipliers are increased, increasing the weight of that constraint in the next iteration.

[0081] The iteration termination criteria include two measures: the original residual and the dual residual. The original residual is measured by calculating the change in the spatial coordinates and timestamps of all target ship trajectory points relative to the previous iteration, using vector norm to measure the magnitude of the change. When the norm of the change is less than a preset threshold for the original residual, it indicates that the trajectory has stabilized. The dual residual is evaluated by calculating the sum of the degree of violation of the coupling constraint sub-items. When this sum is less than the dual residual threshold, it indicates that the degree of constraint violation has decreased to an acceptable range. The iteration terminates when both conditions are met simultaneously, and the local optimization variable vectors of each target ship are output as the final cooperative avoidance trajectory.

[0082] In practical applications, this method can handle the problem of coordinated collision avoidance among multiple ships in complex waterway environments. When multiple cargo ships meet in narrow waterways, it can also efficiently solve the coordinated collision avoidance trajectory that satisfies various constraints, providing effective technical support for intelligent ships to autonomously avoid collisions.

[0083] This invention provides a multi-objective cooperative collision avoidance trajectory planning system for ships in complex waterways, comprising: a first unit for acquiring the current position information, motion state information, and waterway environmental constraint information of target ships, and constructing a multi-ship motion state space model including ship dynamics constraints and waterway boundary constraints; a second unit for extracting the relative motion relationships between target ships and calculating collision risk areas based on the multi-ship motion state space model; a third unit for establishing a directed acyclic cooperative collision avoidance topology graph with each target ship as a node and the avoidance relationship as a directed edge, based on the collision risk area and the avoidance priority constraints of maritime collision avoidance rules, and determining the avoidance execution order of each target ship; a fourth unit for constructing a multi-objective optimization function including navigation time cost, energy consumption cost, and avoidance action smoothness based on the avoidance execution order, and introducing trajectory coupling constraint terms with adjacent nodes in the directed acyclic cooperative collision avoidance topology graph into the multi-objective optimization function, and solving for the cooperative avoidance trajectory of each target ship; and a fifth unit for distributing the cooperative avoidance trajectory to the corresponding target ship for execution.

[0084] A third aspect of the present invention provides an electronic device, comprising: a processor; and a memory for storing processor-executable instructions; wherein the processor is configured to invoke the instructions stored in the memory to execute the aforementioned method.

[0085] A fourth aspect of the present invention provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the aforementioned method.

[0086] This invention can be a method, apparatus, system, and / or computer program product. The computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for performing various aspects of the invention.

[0087] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for multi-objective cooperative collision avoidance trajectory planning for ships in complex waterways, characterized in that, include: The system acquires the current position, motion state, and channel environmental constraints of the target vessels, and constructs a multi-ship motion state space model that includes ship dynamics constraints and channel boundary constraints. Based on this model, it extracts the relative motion relationships between the target vessels and calculates the collision risk area. According to the collision risk area and the avoidance priority constraints of maritime collision avoidance rules, it establishes a directed acyclic cooperative avoidance topology with each target vessel as a node and avoidance relationships as directed edges, determining the avoidance execution order for each target vessel. Based on this order, it constructs a multi-objective optimization function that includes navigation time cost, energy consumption cost, and avoidance action smoothness, and introduces trajectory coupling constraint terms with adjacent nodes in the directed acyclic cooperative avoidance topology into the multi-objective optimization function to solve for the cooperative avoidance trajectory of each target vessel. Finally, it distributes the cooperative avoidance trajectory to the corresponding target vessel for execution.

2. The method according to claim 1, characterized in that, The process involves acquiring the current position information, motion state information, and channel environmental constraint information of target vessels, and constructing a multi-ship motion state space model that includes ship dynamics constraints and channel boundary constraints. This includes: extracting the spatial coordinates and heading angle information of each target vessel based on its current position information, and combining this with the velocity vector and angular velocity from the motion state information to establish the motion state vector of each target vessel; constructing a set of dynamic equations describing the time evolution of the motion state vector based on the vessel's steering response characteristics and propulsion system output characteristics, and introducing constraints characterizing the boundary of the vessel's maneuverability into the dynamic equations to obtain a ship dynamics constraint model; performing geometric modeling on the channel environmental constraint information, extracting the boundary contour lines of the navigable waterway and the spatial occupancy range of the restricted area, and transforming the boundary contour lines and the spatial occupancy range into a set of inequality constraints restricting the range of values ​​for the motion state vector to obtain a channel boundary constraint model; and coupling and fusing the ship dynamics constraint model and the channel boundary constraint model to construct a multi-ship motion state space model that includes the motion state vector, the set of dynamic equations, and the set of inequality constraints.

3. The method according to claim 1, characterized in that, Based on the multi-ship motion state space model, the relative motion relationships between the target ships are extracted and the collision risk area is calculated. This includes: obtaining the motion state vectors of each target ship from the multi-ship motion state space model; constructing a ship pair for any two target ships; calculating the velocity vector difference and position vector difference of the ship pair to obtain the relative velocity vector and relative position vector; projecting and decomposing the relative velocity vector along the direction of the relative position vector to obtain the radial relative velocity component and the tangential relative velocity component; determining that the ship pair is in a near motion state when the radial relative velocity component is negative; extracting the corresponding hull outline geometric parameters; and calculating the maximum hull outline... For small-interval ships, the ratio of the minimum interval to the radial relative velocity component is determined as the nearest encounter time. Using the nearest encounter time as a node, the motion state vectors of the ship pair are substituted into the multi-ship motion state space model for forward evolution to obtain the predicted position and calculate the spatial distance between the ship pairs. When the spatial distance is less than the safe distance threshold, a spatial envelope with a radius equal to the sum of the ship's outer contour parameters and the safe distance threshold is constructed with the predicted position as the center. The time window of the nearest encounter time and the spatial envelope are combined to form a spatiotemporal collision risk region. All ship pairs are traversed, and their respective spatiotemporal collision risk regions are merged in terms of spatiotemporal dimensions to obtain a collision risk region composed of multiple discrete spatiotemporal blocks.

4. The method according to claim 1, characterized in that, Based on the collision risk area and the avoidance priority constraints of maritime collision avoidance rules, a directed acyclic collaborative avoidance topology is established with each target vessel as a node and avoidance relationships as directed edges. The avoidance execution order for each target vessel is determined, including: extracting vessel pairs with spatiotemporal collision risks from the collision risk area; for each vessel pair, obtaining the corresponding heading angle and relative bearing angle; calculating the cosine of the heading angle difference and the sine of the relative bearing angle; and using the cosine and sine values ​​as a two-dimensional vector; mapping the quadrant region where the two-dimensional vector is located to an encounter situation, crossing situation, or overtaking situation; and determining the yielding order for each vessel pair based on the avoidance priority constraints of maritime collision avoidance rules. Ships and ships traveling in the straight direction are considered. A topology graph is constructed with each target ship as a node. Directed edges are established from the giving-way ship node to the traveling-way ship node. The nearest encounter time and the radius of the spatial envelope of the collision risk area for the corresponding ship pair are marked on the directed edges to form a cooperative avoidance topology graph. Strongly connected component identification is performed on the cooperative avoidance topology graph, and the avoidance timeliness parameter of each directed edge is calculated. The directed edge with the smallest avoidance timeliness parameter is disconnected to obtain a directed acyclic cooperative avoidance topology graph. Based on the directed acyclic cooperative avoidance topology graph, the node with the largest out-degree is added to the execution queue and the out-degree of each node is updated in real time. The avoidance execution order of each target ship is determined according to the order in which the nodes enter the execution queue.

5. The method according to claim 4, characterized in that, The process involves identifying strongly connected components in the cooperative avoidance topology graph and calculating the avoidance timeliness parameter for each directed edge. The directed edge with the smallest avoidance timeliness parameter is then disconnected to obtain a directed acyclic cooperative avoidance topology graph. This includes: constructing a reachability matrix for each node in the cooperative avoidance topology graph; identifying strongly connected components with bidirectional reachable paths through matrix exponentiation; and extracting the subgraph structure formed by the directed edges within each strongly connected component. For each directed edge, the time window width and spatial envelope volume of the corresponding ship pair's collision risk region are extracted. The reciprocal of the time window width is used as the time sensitivity, and the spatial envelope... The ratio of the volume of the waterway to the total volume of the navigable waterway is used as the spatial conflict intensity. All closed loops containing each directed edge are extracted from the subgraph structure. The total number of edges in each closed loop is counted, and the reciprocal of the minimum total number of edges is used as the topological coupling coefficient. A nonlinear weighted sum is then performed, combining the time sensitivity and the spatial conflict intensity, to obtain the avoidance timeliness parameter for each directed edge. In the subgraph structure of each strongly connected component, the directed edge with the smallest avoidance timeliness parameter is selected sequentially for disconnection. After each disconnection, the reachability matrix is ​​recalculated. The disconnection operation is terminated when there is no bidirectional reachable path in the matrix, resulting in a directed acyclic topology graph.

6. The method according to claim 1, characterized in that, Based on the avoidance execution order, a multi-objective optimization function is constructed, incorporating navigation time cost, energy consumption cost, and avoidance action smoothness. A trajectory coupling constraint term with adjacent nodes in the directed acyclic cooperative avoidance topology is introduced into this multi-objective optimization function. The cooperative avoidance trajectory of each target vessel is then solved, including: extracting the set of incoming nodes corresponding to each target vessel from the directed acyclic cooperative avoidance topology according to the avoidance execution order; substituting the initial trajectory of the target vessel corresponding to the incoming node into the multi-ship motion state space model for forward evolution to obtain the predicted motion state and unfold it in the spatiotemporal domain to form a trajectory occupancy spatiotemporal band; constructing a trajectory point set for each target vessel and calculating navigation... The time summation, propulsion power time integral, and heading change angular acceleration summation are used as navigation time cost, energy consumption cost, and avoidance maneuver smoothness, respectively, and weighted summation is performed to construct a multi-objective optimization function. The set of trajectory points of each target vessel and the spatiotemporal band occupied by the trajectory are subjected to spatiotemporal domain intersection detection. The trajectory points are required not to enter the spatial projection area of ​​the spatiotemporal band, and the time of passing through the collision risk area is later than the corresponding vessel of the incoming node plus a preset time margin, which is used as the trajectory coupling constraint term. The trajectory coupling constraint term is used as the constraint condition, and the multi-objective optimization function is iteratively solved with the spatial coordinates and timestamps of the trajectory points as optimization variables to obtain the cooperative avoidance trajectory of each target vessel.

7. The method according to claim 6, characterized in that, Using the trajectory coupling constraint term as a constraint condition, and taking the spatial coordinates and timestamps of the trajectory points as optimization variables, the multi-objective optimization function is iteratively solved to obtain the cooperative avoidance trajectories of each target vessel. This includes: constructing a local optimization variable vector from the spatial coordinates and timestamps of the trajectory points of each target vessel; decomposing the multi-objective optimization function into local optimization sub-functions based on the node connection relationships in the directed acyclic cooperative avoidance topology graph; decomposing the trajectory coupling constraint term into coupling constraint sub-terms; and introducing Lagrange multipliers and auxiliary variables to construct an augmented Lagrange function for the coupling constraint sub-terms. In each global iteration, each target vessel fixes the local optimization variables of other vessels. The variable vector is transformed, and the spatial coordinates and timestamps of the ship's trajectory points are used as optimization variables. The augmented Lagrangian function is solved locally, and the spatial coordinates and timestamps of the ship's trajectory points are updated according to the gradient. After all target ships have completed local optimization, the auxiliary variables are recalculated based on the updated trajectory point spatial coordinates and timestamps. The degree of violation of coupling constraint sub-items is detected and the Lagrange multipliers are updated. The iteration terminates when the norm of the change of spatial coordinates and timestamps of all target ship trajectory points is less than the original residual threshold, and the sum of the degree of violation of coupling constraint sub-items is less than the dual residual threshold. The local optimization variable vector of each target ship is output as the cooperative avoidance trajectory of each target ship.

8. A ship multi-objective cooperative collision avoidance trajectory planning system for complex waterways, used to implement the method as described in any one of claims 1-7, characterized in that, include: The first unit is used to acquire the target ship's current position information, motion state information, and waterway environmental constraint information, and to construct a multi-ship motion state space model that includes ship dynamics constraints and waterway boundary constraints. The second unit is used to extract the relative motion relationships between the target ships and calculate the collision risk area based on the multi-ship motion state space model. The third unit is used to establish a directed acyclic cooperative avoidance topology graph with each target vessel as a node and avoidance relationships as directed edges, based on the collision risk area and the avoidance priority constraints of the maritime collision avoidance rules, and to determine the avoidance execution order of each target vessel; the fourth unit is used to construct a multi-objective optimization function containing navigation time cost, energy consumption cost and avoidance action smoothness based on the avoidance execution order, and to introduce trajectory coupling constraint terms with adjacent nodes in the directed acyclic cooperative avoidance topology graph into the multi-objective optimization function, and solve for the cooperative avoidance trajectory of each target vessel; the fifth unit is used to distribute the cooperative avoidance trajectory to the corresponding target vessel for execution.

9. An electronic device, characterized in that, include: processor; A memory for storing processor-executable instructions; wherein the processor is configured to invoke the instructions stored in the memory to perform the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having computer program instructions stored thereon, characterized in that, When the computer program instructions are executed by the processor, they implement the method described in any one of claims 1 to 7.

Images